Actuarial Tables

Based on the

U. S. Life Tables: 1989-91

Actuarial Study No. 113

Social Security Administration

Office of the Chief Actuary

March 1998

SSA Pub. No. 11-11543
Additional copies may be obtained from:

Social Security Administration

Office of the Chief Actuary

Room 700, Altmeyer Bldg.

Baltimore, MD 21235

Voice: (410)-965-3015

Fax: (410)-965-6693

Web site: http://www.ssa.gov/OACT/pubs.html
Actuarial Tables

Based on the

U. S. Life Tables: 1989-91

Actuarial Study No. 113

by Felicitie C. Bell

 Alice H. Wade, A.S.A.

Social Security Administration

Office of the Chief Actuary

March 1998

SSA Pub. No. 11-11543
i

List of Actuarial Tables Based on U. S. Mortality During 1989-91

Table Race and Sex Interest Rate Page

 (percent)

1.A. Total Population...............................................................................1 4

1.B. Total Population...............................................................................2 5

1.C. Total Population...............................................................................3 6

1.D. Total Population...............................................................................4 7

1.E. Total Population...............................................................................5 8

1.F. Total Population...............................................................................6 9

1.G. Total Population...............................................................................7 10

1.H. Total Population...............................................................................8 11

1.I. Total Population...............................................................................9 12

1.J. Total Population.............................................................................10 13

1.K. Total Population.............................................................................11 14

1.L. Total Population.............................................................................12 15

2.A. Total Males.......................................................................................1 16

2.B. Total Males.......................................................................................2 17

2.C. Total Males.......................................................................................3 18

2.D. Total Males.......................................................................................4 19

2.E. Total Males.......................................................................................5 20

2.F. Total Males.......................................................................................6 21

2.G. Total Males.......................................................................................7 22

2.H. Total Males.......................................................................................8 23

2.I. Total Males.......................................................................................9 24

2.J. Total Males.....................................................................................10 25

2.K. Total Males.....................................................................................11 26

2.L. Total Males.....................................................................................12 27

3.A. Total Females...................................................................................1 28

3.B. Total Females...................................................................................2 29

3.C. Total Females...................................................................................3 30

3.D. Total Females...................................................................................4 31

3.E. Total Females...................................................................................5 32

3.F. Total Females...................................................................................6 33

3.G. Total Females...................................................................................7 34

3.H. Total Females...................................................................................8 35

3.I. Total Females...................................................................................9 36

3.J. Total Females.................................................................................10 37

3.K. Total Females.................................................................................11 38

3.L. Total Females.................................................................................12 39

4.A. Total White Population ....................................................................1 40

4.B. Total White Population ....................................................................2 41

4.C. Total White Population ....................................................................3 42
ii

Table Race and Sex Interest Rate Page

 (percent)

4.D. Total White Population ....................................................................4 43

4.E. Total White Population ....................................................................5 44

4.F. Total White Population ....................................................................6 45

4.G. Total White Population ....................................................................7 46

4.H. Total White Population ....................................................................8 47

4.I. Total White Population ....................................................................9 48

4.J. Total White Population ..................................................................10 49

4.K. Total White Population ..................................................................11 50

4.L. Total White Population ..................................................................12 51

5.A. White Males.....................................................................................1 52

5.B. White Males.....................................................................................2 53

5.C. White Males.....................................................................................3 54

5.D. White Males.....................................................................................4 55

5.E. White Males.....................................................................................5 56

5.F. White Males.....................................................................................6 57

5.G. White Males.....................................................................................7 58

5.H. White Males.....................................................................................8 59

5.I. White Males.....................................................................................9 60

5.J. White Males...................................................................................10 61

5.K. White Males...................................................................................11 62

5.L. White Males...................................................................................12 63

6.A. White Females .................................................................................1 64

6.B. White Females .................................................................................2 65

6.C. White Females .................................................................................3 66

6.D. White Females .................................................................................4 67

6.E. White Females .................................................................................5 68

6.F. White Females .................................................................................6 69

6.G. White Females .................................................................................7 70

6.H. White Females .................................................................................8 71

6.I. White Females .................................................................................9 72

6.J. White Females ...............................................................................10 73

6.K. White Females ...............................................................................11 74

6.L. White Females ...............................................................................12 75

7.A. Total Other than White Population ..................................................1 76

7.B. Total Other than White Population ..................................................2 77

7.C. Total Other than White Population ..................................................3 78

7.D. Total Other than White Population ..................................................4 79

7.E. Total Other than White Population ..................................................5 80

7.F. Total Other than White Population ..................................................6 81

7.G. Total Other than White Population ..................................................7 82

7.H. Total Other than White Population ..................................................8 83

7.I. Total Other than White Population ..................................................9 84
iii

Table Race and Sex Interest Rate Page

 (percent)

7.J. Total Other than White Population ................................................10 85

7.K. Total Other than White Population ................................................11 86

7.L. Total Other than White Population ................................................12 87

8.A. Males Other than White...................................................................1 88

8.B. Males Other than White...................................................................2 89

8.C. Males Other than White...................................................................3 90

8.D. Males Other than White...................................................................4 91

8.E. Males Other than White...................................................................5 92

8.F. Males Other than White...................................................................6 93

8.G. Males Other than White...................................................................7 94

8.H. Males Other than White...................................................................8 95

8.I. Males Other than White...................................................................9 96

8.J. Males Other than White.................................................................10 97

8.K. Males Other than White.................................................................11 98

8.L. Males Other than White.................................................................12 99

9.A. Females Other than White ...............................................................1 100

9.B. Females Other than White ...............................................................2 101

9.C. Females Other than White ...............................................................3 102

9.D. Females Other than White ...............................................................4 103

9.E. Females Other than White ...............................................................5 104

9.F. Females Other than White ...............................................................6 105

9.G. Females Other than White ...............................................................7 106

9.H. Females Other than White ...............................................................8 107

9.I. Females Other than White ...............................................................9 108

9.J. Females Other than White .............................................................10 109

9.K. Females Other than White .............................................................11 110

9.L. Females Other than White .............................................................12 111

10.A. Total Black Population.....................................................................1 112

10.B. Total Black Population.....................................................................2 113

10.C. Total Black Population.....................................................................3 114

10.D. Total Black Population.....................................................................4 115

10.E. Total Black Population.....................................................................5 116

10.F. Total Black Population.....................................................................6 117

10.G. Total Black Population.....................................................................7 118

10.H. Total Black Population.....................................................................8 119

10.I. Total Black Population.....................................................................9 120

10.J. Total Black Population...................................................................10 121

10.K. Total Black Population...................................................................11 122

10.L. Total Black Population...................................................................12 123

11.A. Black Males .....................................................................................1 124

11.B. Black Males .....................................................................................2 125
iv

Table Race and Sex Interest Rate Page

 (percent)

11.C. Black Males .....................................................................................3 126

11.D. Black Males .....................................................................................4 127

11.E. Black Males .....................................................................................5 128

11.F. Black Males .....................................................................................6 129

11.G. Black Males .....................................................................................7 130

11.H. Black Males .....................................................................................8 131

11.I. Black Males .....................................................................................9 132

11.J. Black Males ...................................................................................10 133

11.K. Black Males ...................................................................................11 134

11.L. Black Males ...................................................................................12 135

12.A. Black Females..................................................................................1 136

12.B. Black Females..................................................................................2 137

12.C. Black Females..................................................................................3 138

12.D. Black Females..................................................................................4 139

12.E. Black Females..................................................................................5 140

12.F. Black Females..................................................................................6 141

12.G. Black Females..................................................................................7 142

12.H. Black Females..................................................................................8 143

12.I. Black Females..................................................................................9 144

12.J. Black Females................................................................................10 145

12.K. Black Females................................................................................11 146

12.L. Black Females................................................................................12 147
1

Actuarial Tables Based on the U. S. Life Tables: 1989-91

I. Introduction

The National Center for Health Statistics (NCHS) prepares, at 10 year intervals, life tables 

for the death registration states based on a census of population and deaths in a three year 

period containing the census year. The series of tables began with tables for the period 

1900-1902. The most recent set of tables is for the period 1989-1991. The actuarial 

functions published in this study are based on the most recent set of tables as published in 

"U. S. Decennial Life Tables for 1989-91", Vol. 1, No. 1, DHHS Publication No. 

PHS-98-1150-1 by the National Center for Health Statistics. Copies of this publication 

may be downloaded from the NCHS web site at http://www.cdc.gov/nchswww/data/ with 

the file name dec89_91.pdf. A printed copy may be obtained from the Government 

Printing Office (phone number: 202-512-1800) for a price of $3.50. The publication 

number which must be given to the Government Printing Office when requesting the 

publication is 017-022-01395-9.

The actuarial functions in this study can be used to calculate present values of expected 

future payments contingent upon the death or survival of a designated individual. A series 

of periodic payments to continue during the life of an individual is called a life annuity. 

A payment to be made on the death of an individual is called a life insurance.

As with the 1989-91 decennial life tables, the actuarial functions included in here were 

calculated by sex and for both sexes combined for the total population, the white 

population, the population other than white and the black population. For each race sex 

combinations described, actuarial functions were tabulated using interest rates of 1%, 2%, 

3%, 4%, 5%, 6%, 7%, 8%, 9%, 10%, 11%, and 12%. The values were calculated to more 

decimal places than are shown and were rounded individually by the computer.

Therefore, there may be small discrepancies from the mathematical relationships that 

should hold among the various columns.

Actuarial textbooks1 should be consulted for more detailed information about actuarial 

functions than is presented in this study.

II. Life Annuities

Let i denote the annual assumed rate of interest expressed in decimal form (e.g.,i = .07 if 

the rate is 7 percent). Then $1 deposited now will accumulate at compound interest to 

(1+i)

n at the end of n years. Conversely, the present value today of a payment of $1 due 

at the end of n years is (1+i)

-n = vn where v is used to denote the reciprocal of (1+i).

Thus, the present value of a series of payments of $1 due at the end of each of the next 

10 years is given by the equation

v + v2 + v3 + ... + v10 .

1 Bowers, N.L. Jr., et.al., Actuarial Mathematics (2nd ed.), Itasca,IL Society of Actuaries, 1997
2

Now suppose that the series of payments is paid at the end of the year only if an

individual now exact age x is alive at the time the payment is to be made. In the life

table lx is the number of survivors to age x out of l0 births. Therefore, using the mortality 

experience of a specific life table, the probability of an individual exact age x surviving to 

age x + t is

lx+t ÷ lx .

The formula for the present value of the series of payments of $1 due at the end of each

of the next 10 years to an individual exact age x provided that individual is alive at the 

time each payment is to be made becomes

(vlx+1 ÷ lx) + (v2lx+2 ÷ lx) + ... + (v10lx+10 ÷ lx) . 

If the period of payments is extended from 10 years to the lifetime of the individual the 

present value or life annuity, denoted ax, is as follows

ax = (vlx+1 ÷ lx) + (v2

lx+2 ÷ lx) + (v3lx+3 ÷ lx) + ... 

where the addition continues to the end of the life table1.

The preceding formula provides a means of calculating ax, the present value at age x of a 

life annuity of $1 per year. However, it would be laborious to make this calculation for 

many different ages and interest rates. Thus a shortcut method of tabulating certain 

auxiliary values called commutation functions is used. If each term of the right hand side 

of the equation were multiplied by vx ÷ vx the equation becomes

ax = ((vx+1lx+1) ÷ (vxlx)) + ((vx+2lx+2) ÷ (vxlx)) + ...

If we define the following commutation functions

Dx = vxlx

and

Nx = Dx + Dx+1 + Dx+2 + ... ,

the formula can be written as

ax = Nx+1 ÷ Dx .

The preceding formula is a special case of the general life annuity formula. The value at 

age k of a life annuity of R per annum under which the first payment is made at age y and 

the last payment at age j-1 (all payments being contingent upon the survival of the 

annuitant) is

R(Ny - Nj

) ÷ Dk .

1 In this study, the end of the life table differed with each race-sex combination of the population. The ending age was chosen to be 

consistent with the values published in "U.S. Decennial Life Tables for 1989-91". Actuarial functions, however, are not shown beyond 

age 109.
3

III. Life Insurance

A life insurance is a contract to pay a designated amount of money on the death of a 

certain individual, called the insured. In the life table, the probability of an individual 

exact age x dying between ages x + t and x + t + 1 can be expressed as

(lx+t - lx+t+1) ÷ lx

or

dx+t ÷ lx

where dx+t = lx+t - lx+t+1 denotes the number of deaths between ages x + t and x + t + 1 in 

the life table. Then the present value, denoted Ax, of the payment of $1 on the next 

birthday of the insured following his date of death is as follows

Ax = (vdx ÷ lx) + (v2dx+1 ÷ lx) + (v3dx+2 ÷ lx) + ... 

Multiplying each term of the right hand side of the equation by vx ÷ vx yields

Ax = ((vx+1dx) ÷ (vxlx)) + ((vx+2dx+1) ÷ (vx

lx)) + ...

Introduction of two new commutation functions,

Cx = vx+1dx

and

Mx = Cx + Cx+1 + Cx+2 + ...

gives

Ax = Mx ÷ Dx .

In fact, there is a general life insurance formula,

R(My - Mj) ÷ Dk .

which gives the present value determined at age k for life insurance coverage commencing 

at age y and terminating at age j with R as the amount of insurance.
Table 1.A. -- Actuarial Functions at 1.0 Percent Interest for 1989-91 United States 

Total Population

x D N M a x D N M a

0 ......... 100,000.000 5,272,092.88 47,801.061 51.7209 55 ......... 51,869.670 1,142,892.81 40,553.900 21.0339

1 ......... 98,083.168 5,172,092.88 46,874.328 51.7317 56 ......... 50,959.159 1,091,023.14 40,156.950 20.4098

2 ......... 97,041.467 5,074,009.71 46,803.747 51.2870 57 ......... 50,028.699 1,040,063.98 39,731.036 19.7893

3 ......... 96,034.072 4,976,968.24 46,757.158 50.8250 58 ......... 49,074.609 990,035.28 39,272.279 19.1741

4 ......... 95,047.683 4,880,934.17 46,721.602 50.3525 59 ......... 48,093.366 940,960.68 38,776.924 18.5653

5 ......... 94,078.073 4,785,886.49 46,693.058 49.8714 60 ......... 47,083.809 892,867.31 38,243.538 17.9634

6 ......... 93,121.172 4,691,808.42 46,667.623 49.3839 61 ......... 46,047.018 845,783.50 37,672.924 17.3678

7 ......... 92,176.794 4,598,687.24 46,645.238 48.8899 62 ......... 44,985.672 799,736.48 37,067.489 16.7776

8 ......... 91,242.913 4,506,510.45 46,623.997 48.3903 63 ......... 43,899.690 754,750.81 36,426.910 16.1926

9 ......... 90,321.231 4,415,267.54 46,605.711 47.8840 64 ......... 42,786.898 710,851.12 35,748.769 15.6138

10 ......... 89,411.571 4,324,946.31 46,590.321 47.3712 65 ......... 41,646.798 668,064.22 35,032.301 15.0412

11 ......... 88,511.967 4,235,534.73 46,575.980 46.8527 66 ......... 40,481.002 626,417.43 34,278.850 14.4744

12 ......... 87,621.412 4,147,022.77 46,561.780 46.3289 67 ......... 39,292.109 585,936.42 33,490.759 13.9123

13 ......... 86,735.421 4,059,401.36 46,543.329 45.8021 68 ......... 38,077.549 546,644.31 32,665.229 13.3561

14 ......... 85,848.816 3,972,665.93 46,515.490 45.2751 69 ......... 36,834.368 508,566.76 31,799.053 12.8069

15 ......... 84,959.205 3,886,817.12 46,475.868 44.7492 70 ......... 35,558.253 471,732.40 30,887.635 12.2665

16 ......... 84,065.150 3,801,857.91 46,422.993 44.2251 71 ......... 34,246.072 436,174.14 29,927.516 11.7365

17 ......... 83,168.649 3,717,792.76 46,358.820 43.7019 72 ......... 32,897.280 401,928.07 28,917.795 11.2177

18 ......... 82,271.628 3,634,624.11 46,285.251 43.1783 73 ......... 31,512.350 369,030.79 27,858.580 10.7107

19 ......... 81,378.422 3,552,352.49 46,206.615 42.6523 74 ......... 30,097.986 337,518.44 26,756.220 10.2140

20 ......... 80,491.560 3,470,974.06 46,125.480 42.1222 75 ......... 28,660.653 307,420.45 25,616.887 9.7262

21 ......... 79,611.848 3,390,482.50 46,042.714 41.5877 76 ......... 27,206.113 278,759.80 24,446.115 9.2462

22 ......... 78,737.649 3,310,870.66 45,956.751 41.0494 77 ......... 25,736.665 251,553.69 23,246.035 8.7741

23 ......... 77,870.569 3,232,133.01 45,869.252 40.5065 78 ......... 24,253.612 225,817.02 22,017.800 8.3107

24 ......... 77,011.366 3,154,262.44 45,781.045 39.9584 79 ......... 22,755.485 201,563.41 20,759.808 7.8578

25 ......... 76,160.764 3,077,251.07 45,692.931 39.4047 80 ......... 21,240.437 178,807.93 19,470.062 7.4183

26 ......... 75,317.911 3,001,090.31 45,604.146 38.8456 81 ......... 19,710.281 157,567.49 18,150.207 6.9942

27 ......... 74,484.283 2,925,772.40 45,516.239 38.2804 82 ......... 18,171.637 137,857.21 16,806.714 6.5864

28 ......... 73,656.751 2,851,288.11 45,426.176 37.7105 83 ......... 16,635.697 119,685.57 15,450.691 6.1945

29 ......... 72,835.307 2,777,631.36 45,334.007 37.1358 84 ......... 15,119.286 103,049.87 14,098.990 5.8158

30 ......... 72,018.458 2,704,796.06 45,238.299 36.5570 85 ......... 13,636.422 87,930.59 12,765.822 5.4482

31 ......... 71,205.501 2,632,777.60 45,138.396 35.9744 86 ......... 12,191.215 74,294.17 11,455.629 5.0941

32 ......... 70,396.492 2,561,572.10 45,034.392 35.3878 87 ......... 10,787.595 62,102.95 10,172.714 4.7569

33 ......... 69,592.201 2,491,175.61 44,927.096 34.7968 88 ......... 9,439.319 51,315.36 8,931.247 4.4363

34 ......... 68,791.233 2,421,583.40 44,815.160 34.2019 89 ......... 8,159.995 41,876.04 7,745.381 4.1319

35 ......... 67,995.067 2,352,792.17 44,700.095 33.6024 90 ......... 6,961.436 33,716.04 6,627.614 3.8433

36 ......... 67,201.634 2,284,797.10 44,579.880 32.9991 91 ......... 5,849.294 26,754.61 5,584.397 3.5740

37 ......... 66,411.018 2,217,595.47 44,454.628 32.3920 92 ......... 4,830.554 20,905.31 4,623.571 3.3277

38 ......... 65,623.989 2,151,184.45 44,325.134 31.7805 93 ......... 3,917.824 16,074.76 3,758.668 3.1030

39 ......... 64,839.251 2,085,560.46 44,190.138 31.1651 94 ......... 3,120.417 12,156.93 3,000.051 2.8959

40 ......... 64,057.575 2,020,721.21 44,050.434 30.5454 95 ......... 2,440.998 9,036.52 2,351.528 2.7020

41 ......... 63,279.036 1,956,663.64 43,906.128 29.9212 96 ......... 1,872.995 6,595.52 1,807.693 2.5214

42 ......... 62,502.391 1,893,384.60 43,756.009 29.2930 97 ......... 1,407.046 4,722.52 1,360.288 2.3563

43 ......... 61,726.448 1,830,882.21 43,598.901 28.6612 95 ......... 1,035.237 3,315.48 1,002.411 2.2026

44 ......... 60,950.061 1,769,155.76 43,433.667 28.0263 99 ......... 746.447 2,280.24 723.870 2.0548

45 ......... 60,169.577 1,708,205.70 43,256.649 27.3899 100 ......... 526.570 1,533.79 511.384 1.9128

46 ......... 59,384.653 1,648,036.12 43,067.463 26.7519 101 ......... 362.770 1,007.22 352.798 1.7765

47 ......... 58,591.832 1,588,651.47 42,862.610 26.1139 102 ......... 243.588 644.45 237.207 1.6457

48 ......... 57,791.523 1,530,059.64 42,642.417 25.4755 103 ......... 159.058 400.87 155.089 1.5202

49 ......... 56,982.279 1,472,268.12 42,405.367 24.8373 104 ......... 100.751 241.81 98.357 1.4000

50 ......... 56,164.546 1,415,285.84 42,151.815 24.1989 105 ......... 61.735 141.06 60.338 1.2849

51 ......... 55,336.349 1,359,121.29 41,879.703 23.5611 106 ......... 36.476 79.32 35.691 1.1746

52 ......... 54,494.012 1,303,784.94 41,585.250 22.9253 107 ......... 20.707 42.85 20.283 1.0691

53 ......... 53,636.373 1,249,290.93 41,267.156 22.2919 108 ......... 11.248 22.14 11.029 0.9682

54 ......... 52,761.743 1,195,654.56 40,923.579 21.6614 109 ......... 5.818 10.89 5.711 0.8717

x x x x x x x x

4
Table 1.B. -- Actuarial Functions at 2.0 Percent Interest for 1989-91 United States 

Total Population

x D N M a x D N M a

0 ......... 100,000.000 3,877,708.17 23,966.506 37.7771 55 ......... 30,170.298 584,643.71 18,706.696 18.3781

1 ......... 97,121.569 3,777,708.17 23,048.859 37.8967 56 ......... 29,350.099 554,473.41 18,478.071 17.8917

2 ......... 95,148.020 3,680,586.60 22,979.655 37.6827 57 ......... 28,531.705 525,123.31 18,235.169 17.4049

3 ......... 93,237.141 3,585,438.58 22,934.424 37.4550 58 ......... 27,713.193 496,591.61 17,976.102 16.9190

4 ......... 91,374.780 3,492,201.44 22,900.241 37.2184 59 ......... 26,892.805 468,878.41 17,699.110 16.4351

5 ......... 89,555.945 3,400,826.66 22,873.070 36.9743 60 ......... 26,070.161 441,985.61 17,403.776 15.9537

6 ......... 87,775.971 3,311,270.72 22,849.094 36.7241 61 ......... 25,246.131 415,915.45 17,090.926 15.4744

7 ......... 86,033.980 3,223,494.75 22,828.201 36.4677 62 ......... 24,422.422 390,669.32 16,762.239 14.9963

8 ......... 84,327.409 3,137,460.77 22,808.571 36.2057 63 ......... 23,599.195 366,246.89 16,417.883 14.5195

9 ......... 82,657.195 3,053,133.36 22,791.835 35.9373 64 ......... 22,775.490 342,647.70 16,056.908 14.0446

10 ......... 81,022.520 2,970,476.16 22,777.890 35.6624 65 ......... 21,951.275 319,872.21 15,679.271 13.5719

11 ......... 79,420.975 2,889,453.64 22,765.021 35.3815 66 ......... 21,127.621 297,920.93 15,286.034 13.1010

12 ......... 77,851.085 2,810,032.67 22,752.405 35.0950 67 ......... 20,306.070 276,793.31 14,878.750 12.6311

13 ......... 76,308.360 2,732,181.58 22,736.172 34.8045 68 ......... 19,485.463 256,487.24 14,456.301 12.1630

14 ......... 74,787.865 2,655,873.22 22,711.920 34.5121 69 ......... 18,664.491 237,001.78 14,017.398 11.6980

15 ......... 73,287.258 2,581,085.36 22,677.741 34.2187 70 ......... 17,841.220 218,337.29 13,560.097 11.2378

16 ......... 71,805.089 2,507,798.10 22,632.577 33.9251 71 ......... 17,014.379 200,496.07 13,083.084 10.7839

17 ......... 70,342.870 2,435,993.01 22,578.301 33.6303 72 ......... 16,184.025 183,481.69 12,586.345 10.3372

18 ......... 68,901.984 2,365,650.14 22,516.687 33.3336 73 ......... 15,350.713 167,297.67 12,070.366 9.8984

19 ......... 67,485.754 2,296,748.16 22,451.476 33.0331 74 ......... 14,517.987 151,946.95 11,538.635 9.4661

20 ......... 66,095.879 2,229,262.40 22,384.852 32.7277 75 ......... 13,689.142 137,428.97 10,994.457 9.0393

21 ......... 64,732.585 2,163,166.52 22,317.555 32.4170 76 ......... 12,867.016 123,739.82 10,440.745 8.6168

22 ......... 63,394.107 2,098,433.94 22,248.343 32.1014 77 ......... 12,052.713 110,872.81 9,878.737 8.1990

23 ......... 62,081.328 2,035,039.83 22,178.586 31.7802 78 ......... 11,246.831 98,820.09 9,309.182 7.7865

24 ......... 60,794.414 1,972,958.50 22,108.953 31.4530 79 ......... 10,448.671 87,573.26 8,731.548 7.3813

25 ......... 59,533.490 1,912,164.09 22,040.076 31.1191 80 ......... 9,657.386 77,124.59 8,145.140 6.9861

26 ......... 58,297.445 1,852,630.60 21,971.355 30.7789 81 ......... 8,873.811 67,467.21 7,550.925 6.6030

27 ......... 57,086.983 1,794,333.15 21,903.980 30.4316 82 ......... 8,100.888 58,593.39 6,951.998 6.2330

28 ......... 55,899.280 1,737,246.17 21,835.630 30.0781 83 ......... 7,343.460 50,492.51 6,353.411 5.8758

29 ......... 54,733.953 1,681,346.89 21,766.367 29.7185 84 ......... 6,608.642 43,149.05 5,762.583 5.5292

30 ......... 53,589.521 1,626,612.94 21,695.150 29.3532 85 ......... 5,902.046 36,540.40 5,185.568 5.1911

31 ......... 52,465.137 1,573,023.42 21,621.540 28.9823 86 ......... 5,224.808 30,638.36 4,624.056 4.8640

32 ......... 51,360.528 1,520,558.28 21,545.660 28.6056 87 ......... 4,577.931 25,413.55 4,079.626 4.5513

33 ......... 50,275.945 1,469,197.75 21,468.146 28.2227 88 ......... 3,966.491 20,835.62 3,557.949 4.2529

34 ......... 49,210.068 1,418,921.81 21,388.071 27.8340 89 ......... 3,395.290 16,869.13 3,064.523 3.9684

35 ......... 48,163.660 1,369,711.74 21,306.567 27.4387 90 ......... 2,868.184 13,473.84 2,603.991 3.6977

36 ......... 47,134.956 1,321,548.08 21,222.248 27.0375 91 ......... 2,386.343 10,605.65 2,178.389 3.4443

37 ......... 46,123.751 1,274,413.12 21,135.258 26.6303 92 ......... 1,951.405 8,219.31 1,790.243 3.2120

38 ......... 45,130.309 1,228,289.37 21,046.204 26.2165 93 ......... 1,567.172 6,267.91 1,444.272 2.9995

39 ......... 44,153.473 1,183,159.06 20,954.276 25.7965 94 ......... 1,235.963 4,700.73 1,143.792 2.8033

40 ......... 43,193.518 1,139,005.59 20,860.075 25.3698 95 ......... 957.374 3,464.77 889.437 2.6190

41 ......... 42,250.236 1,095,812.07 20,763.724 24.9362 96 ......... 727.398 2,507.40 678.233 2.4471

42 ......... 41,322.550 1,053,561.84 20,664.475 24.4961 97 ......... 541.084 1,780.00 506.182 2.2897

43 ......... 40,409.453 1,012,239.29 20,561.624 24.0496 95 ......... 394.201 1,238.91 369.909 2.1428

44 ......... 39,510.000 971,829.83 20,454.513 23.5971 99 ......... 281.448 844.71 264.885 2.0013

45 ......... 38,621.670 932,319.83 20,340.889 23.1398 100 ......... 196.597 563.26 185.552 1.8651

46 ......... 37,744.138 893,698.16 20,220.645 22.6778 101 ......... 134.114 366.67 126.924 1.7340

47 ......... 36,875.131 855,954.03 20,091.719 22.2122 102 ......... 89.170 232.55 84.610 1.6080

48 ......... 36,014.869 819,078.90 19,954.498 21.7428 103 ......... 57.655 143.38 54.844 1.4869

49 ......... 35,162.417 783,064.03 19,808.220 21.2699 104 ......... 36.162 85.73 34.481 1.3707

50 ......... 34,318.030 747,901.61 19,653.293 20.7933 105 ......... 21.941 49.57 20.969 1.2591

51 ......... 33,480.490 713,583.58 19,488.655 20.3134 106 ......... 12.837 27.63 12.295 1.1521

52 ......... 32,647.602 680,103.09 19,312.247 19.8316 107 ......... 7.216 14.79 6.926 1.0495

53 ......... 31,818.750 647,455.49 19,123.544 19.3482 108 ......... 3.881 7.57 3.733 0.9512

54 ......... 30,993.031 615,636.74 18,921.722 18.8637 109 ......... 1.988 3.69 1.916 0.8571

x x x x x x x x

5
Table 1.C. -- Actuarial Functions at 3.0 Percent Interest for 1989-91 United States 

Total Population

x D N M a x D N M a

0 ......... 100,000.000 2,995,255.19 12,759.558 28.9526 55 ......... 17,641.751 303,680.34 8,796.692 16.2137

1 ......... 96,178.641 2,895,255.19 11,850.820 29.1029 56 ......... 16,995.526 286,038.59 8,664.304 15.8302

2 ......... 93,309.454 2,799,076.55 11,782.953 28.9978 57 ......... 16,361.221 269,043.07 8,525.015 15.4439

3 ......... 90,547.776 2,705,767.10 11,739.026 28.8822 58 ......... 15,737.563 252,681.85 8,377.898 15.0560

4 ......... 87,877.588 2,615,219.32 11,706.152 28.7598 59 ......... 15,123.419 236,944.28 8,222.129 14.6674

5 ......... 85,292.169 2,527,341.73 11,680.274 28.6316 60 ......... 14,518.459 221,820.86 8,057.657 14.2785

6 ......... 82,785.319 2,442,049.56 11,657.662 28.4986 61 ......... 13,923.057 207,302.40 7,885.123 13.8891

7 ......... 80,354.582 2,359,264.24 11,638.147 28.3607 62 ......... 13,338.023 193,379.35 7,705.614 13.4984

8 ......... 77,996.001 2,278,909.66 11,619.991 28.2183 63 ......... 12,763.296 180,041.32 7,519.374 13.1062

9 ......... 75,708.944 2,200,913.66 11,604.663 28.0707 64 ......... 12,198.217 167,278.03 7,326.041 12.7133

10 ......... 73,491.180 2,125,204.72 11,592.013 27.9178 65 ......... 11,642.636 155,079.81 7,125.748 12.3200

11 ......... 71,339.101 2,051,713.54 11,580.454 27.7600 66 ......... 11,096.987 143,437.18 6,919.206 11.9258

12 ......... 69,250.041 1,980,374.44 11,569.232 27.5974 67 ......... 10,561.931 132,340.19 6,707.363 11.5299

13 ......... 67,218.750 1,911,124.40 11,554.932 27.4314 68 ......... 10,036.704 121,778.26 6,489.765 11.1333

14 ......... 65,239.766 1,843,905.65 11,533.776 27.2635 69 ......... 9,520.495 111,741.55 6,265.886 10.7369

15 ......... 63,310.053 1,778,665.88 11,504.251 27.0945 70 ......... 9,012.201 102,221.06 6,034.888 10.3425

16 ......... 61,427.435 1,715,355.83 11,465.614 26.9249 71 ......... 8,511.093 93,208.86 5,796.272 9.9515

17 ......... 59,592.305 1,653,928.39 11,419.633 26.7541 72 ......... 8,017.126 84,697.76 5,550.201 9.5646

18 ......... 57,804.916 1,594,336.09 11,367.942 26.5813 73 ......... 7,530.498 76,680.64 5,297.081 9.1827

19 ......... 56,067.100 1,536,531.17 11,313.765 26.4052 74 ......... 7,052.847 69,150.14 5,038.765 8.8046

20 ......... 54,379.264 1,480,464.07 11,258.951 26.2248 75 ......... 6,585.629 62,097.29 4,776.970 8.4292

21 ......... 52,740.572 1,426,084.81 11,204.121 26.0396 76 ......... 6,130.019 55,511.66 4,513.175 8.0557

22 ......... 51,148.596 1,373,344.24 11,148.279 25.8501 77 ......... 5,686.326 49,381.65 4,248.026 7.6843

23 ......... 49,603.095 1,322,195.64 11,092.543 25.6555 78 ......... 5,254.605 43,695.32 3,981.926 7.3156

24 ......... 48,103.248 1,272,592.54 11,037.446 25.4554 79 ......... 4,834.303 38,440.71 3,714.671 6.9517

25 ......... 46,648.214 1,224,489.30 10,983.477 25.2494 80 ......... 4,424.818 33,606.41 3,445.990 6.5950

26 ......... 45,236.203 1,177,841.08 10,930.152 25.0376 81 ......... 4,026.326 29,181.59 3,176.376 6.2477

27 ......... 43,866.872 1,132,604.88 10,878.380 24.8191 82 ......... 3,639.941 25,155.27 2,907.263 5.9109

28 ......... 42,537.184 1,088,738.01 10,826.368 24.5950 83 ......... 3,267.574 21,515.33 2,640.913 5.5845

29 ......... 41,246.042 1,046,200.82 10,774.173 24.3649 84 ......... 2,912.056 18,247.75 2,380.568 5.2663

30 ......... 39,991.555 1,004,954.78 10,721.027 24.1292 85 ......... 2,575.450 15,335.70 2,128.779 4.9546

31 ......... 38,772.354 964,963.23 10,666.629 23.8879 86 ......... 2,257.791 12,760.25 1,886.134 4.6517

32 ......... 37,587.530 926,190.87 10,611.097 23.6409 87 ......... 1,959.050 10,502.46 1,653.154 4.3610

33 ......... 36,436.571 888,603.34 10,554.920 23.3877 88 ......... 1,680.915 8,543.41 1,432.078 4.0826

34 ......... 35,317.842 852,166.77 10,497.451 23.1285 89 ......... 1,424.883 6,862.49 1,225.004 3.8162

35 ......... 34,231.240 816,848.93 10,439.523 22.8627 90 ......... 1,191.989 5,437.61 1,033.612 3.5618

36 ......... 33,174.868 782,617.69 10,380.178 22.5907 91 ......... 982.112 4,245.62 858.453 3.3229

37 ......... 32,147.977 749,442.82 10,319.546 22.3123 92 ......... 795.314 3,263.51 700.260 3.1034

38 ......... 31,150.161 717,294.85 10,258.078 22.0270 93 ......... 632.515 2,468.19 560.626 2.9022

39 ......... 30,180.040 686,144.68 10,195.243 21.7350 94 ......... 493.995 1,835.68 440.529 2.7160

40 ......... 29,237.246 655,964.64 10,131.479 21.4359 95 ......... 378.932 1,341.68 339.854 2.5407

41 ......... 28,321.090 626,727.40 10,066.894 21.1294 96 ......... 285.112 962.75 257.070 2.3768

42 ......... 27,430.321 598,406.31 10,001.011 20.8155 97 ......... 210.025 677.64 190.288 2.2265

43 ......... 26,563.769 570,975.99 9,933.400 20.4945 95 ......... 151.526 467.61 137.906 2.0860

44 ......... 25,720.340 544,412.22 9,863.673 20.1666 99 ......... 107.135 316.09 97.928 1.9504

45 ......... 24,897.954 518,691.88 9,790.424 19.8327 100 ......... 74.109 208.95 68.023 1.8195

46 ......... 24,096.007 493,793.92 9,713.660 19.4928 101 ......... 50.065 134.84 46.137 1.6934

47 ......... 23,312.674 469,697.92 9,632.152 19.1477 102 ......... 32.964 84.78 30.495 1.5719

48 ......... 22,547.754 446,385.24 9,546.242 18.7973 103 ......... 21.107 51.82 19.598 1.4550

49 ......... 21,800.333 423,837.49 9,455.551 18.4418 104 ......... 13.110 30.71 12.216 1.3425

50 ......... 21,070.251 402,037.16 9,360.431 18.0808 105 ......... 7.877 17.60 7.364 1.2343

51 ......... 20,356.453 380,966.91 9,260.329 17.7148 106 ......... 4.564 9.72 4.281 1.1304

52 ......... 19,657.330 360,610.45 9,154.113 17.3448 107 ......... 2.541 5.16 2.390 1.0306

53 ......... 18,972.270 340,953.12 9,041.597 16.9711 108 ......... 1.353 2.62 1.277 0.9348

54 ......... 18,300.510 321,980.85 8,922.427 16.5941 109 ......... 0.686 1.26 0.650 0.8430

x x x x x x x x

6
Table 1.D. -- Actuarial Functions at 4.0 Percent Interest for 1989-91 United States 

Total Population

x D N M a x D N M a

0 ......... 100,000.000 2,409,764.88 7,316.735 23.0976 55 ......... 10,369.442 160,016.09 4,214.977 14.4315

1 ......... 95,253.846 2,309,764.88 6,416.735 23.2485 56 ......... 9,893.551 149,646.65 4,137.910 14.1257

2 ......... 91,523.669 2,214,511.04 6,350.167 23.1960 57 ......... 9,432.725 139,753.10 4,057.606 13.8158

3 ......... 87,960.856 2,122,987.37 6,307.495 23.1356 58 ......... 8,985.926 130,320.38 3,973.604 13.5027

4 ......... 84,546.118 2,035,026.51 6,275.868 23.0700 59 ......... 8,552.227 121,334.45 3,885.517 13.1875

5 ......... 81,269.687 1,950,480.39 6,251.210 23.0001 60 ......... 8,131.182 112,782.22 3,793.404 12.8703

6 ......... 78,122.591 1,869,210.71 6,229.871 22.9266 61 ......... 7,722.744 104,651.04 3,697.703 12.5510

7 ......... 75,099.638 1,791,088.12 6,211.633 22.8495 62 ......... 7,327.104 96,928.30 3,599.092 12.2287

8 ......... 72,194.384 1,715,988.48 6,194.827 22.7690 63 ......... 6,943.967 89,601.19 3,497.767 11.9035

9 ......... 69,403.626 1,643,794.09 6,180.776 22.6846 64 ......... 6,572.718 82,657.23 3,393.594 11.5758

10 ......... 66,722.771 1,574,390.47 6,169.291 22.5960 65 ......... 6,213.036 76,084.51 3,286.708 11.2459

11 ......... 64,146.117 1,507,667.70 6,158.898 22.5036 66 ......... 5,864.912 69,871.47 3,177.548 10.9135

12 ......... 61,668.965 1,443,521.58 6,148.904 22.4076 67 ......... 5,528.453 64,006.56 3,066.663 10.5777

13 ......... 59,284.470 1,381,852.62 6,136.292 22.3088 68 ......... 5,203.018 58,478.11 2,953.860 10.2393

14 ......... 56,985.819 1,322,568.15 6,117.813 22.2087 69 ......... 4,887.960 53,275.09 2,838.918 9.8992

15 ......... 54,768.514 1,265,582.33 6,092.271 22.1078 70 ......... 4,582.504 48,387.13 2,721.460 9.5591

16 ......... 52,628.931 1,210,813.81 6,059.169 22.0066 71 ......... 4,286.089 43,804.63 2,601.296 9.2202

17 ......... 50,565.725 1,158,184.88 6,020.152 21.9045 72 ......... 3,998.513 39,518.54 2,478.569 8.8833

18 ......... 48,577.450 1,107,619.16 5,976.713 21.8011 73 ......... 3,719.695 35,520.03 2,353.540 8.5492

19 ......... 46,663.995 1,059,041.71 5,931.622 21.6951 74 ......... 3,450.261 31,800.33 2,227.172 8.2168

20 ......... 44,824.044 1,012,377.71 5,886.440 21.5856 75 ......... 3,190.720 28,350.07 2,100.333 7.8852

21 ......... 43,055.281 967,553.67 5,841.679 21.4724 76 ......... 2,941.421 25,159.35 1,973.753 7.5535

22 ......... 41,354.160 924,498.39 5,796.529 21.3556 77 ......... 2,702.284 22,217.93 1,847.748 7.2219

23 ......... 39,718.985 883,144.23 5,751.899 21.2348 78 ......... 2,473.108 19,515.64 1,722.506 6.8911

24 ......... 38,147.638 843,425.24 5,708.206 21.1095 79 ......... 2,253.413 17,042.54 1,597.931 6.5630

25 ......... 36,638.033 805,277.60 5,665.818 20.9793 80 ......... 2,042.708 14,789.12 1,473.895 6.2400

26 ......... 35,187.399 768,639.57 5,624.338 20.8442 81 ......... 1,840.872 12,746.42 1,350.625 5.9241

27 ......... 33,794.153 733,452.17 5,584.454 20.7035 82 ......... 1,648.211 10,905.54 1,228.767 5.6166

28 ......... 32,454.694 699,658.02 5,544.771 20.5580 83 ......... 1,465.372 9,257.33 1,109.321 5.3174

29 ......... 31,166.997 667,203.32 5,505.331 20.4074 84 ......... 1,293.380 7,791.96 993.689 5.0245

30 ......... 29,928.493 636,036.33 5,465.557 20.2519 85 ......... 1,132.879 6,498.58 882.933 4.7363

31 ......... 28,737.079 606,107.83 5,425.239 20.0915 86 ......... 983.599 5,365.70 777.226 4.4552

32 ......... 27,591.043 577,370.76 5,384.476 19.9260 87 ......... 845.247 4,382.10 676.705 4.1844

33 ......... 26,489.009 549,779.71 5,343.635 19.7550 88 ......... 718.270 3,536.86 582.237 3.9241

34 ......... 25,428.823 523,290.70 5,302.258 19.5786 89 ......... 603.011 2,818.59 494.603 3.6742

35 ......... 24,409.485 497,861.88 5,260.951 19.3962 90 ......... 499.599 2,215.58 414.385 3.4347

36 ......... 23,428.748 473,452.40 5,219.040 19.2082 91 ......... 407.675 1,715.98 341.676 3.2092

37 ......... 22,485.234 450,023.65 5,176.632 19.0142 92 ......... 326.961 1,308.30 276.642 3.0014

38 ......... 21,577.839 427,538.41 5,134.053 18.8138 93 ......... 257.533 981.34 219.789 2.8105

39 ......... 20,704.814 405,960.58 5,090.946 18.6071 94 ......... 199.199 723.81 171.361 2.6336

40 ......... 19,865.151 385,255.76 5,047.622 18.3935 95 ......... 151.332 524.61 131.155 2.4666

41 ......... 19,057.646 365,390.61 5,004.161 18.1729 96 ......... 112.769 373.28 98.412 2.3101

42 ......... 18,280.753 346,332.96 4,960.254 17.9452 97 ......... 82.271 260.51 72.252 2.1664

43 ......... 17,533.022 328,052.21 4,915.629 17.7105 95 ......... 58.785 178.24 51.930 2.0320

44 ......... 16,813.095 310,519.19 4,870.049 17.4689 99 ......... 41.164 119.45 36.569 1.9019

45 ......... 16,119.015 293,706.09 4,822.627 17.2211 100 ......... 28.201 78.29 25.190 1.7761

46 ......... 15,449.834 277,587.08 4,773.407 16.9670 101 ......... 18.868 50.09 16.941 1.6546

47 ......... 14,803.851 262,137.25 4,721.649 16.7074 102 ......... 12.304 31.22 11.103 1.5373

48 ......... 14,180.443 247,333.39 4,667.620 16.4419 103 ......... 7.802 18.92 7.075 1.4243

49 ......... 13,578.553 233,152.95 4,611.132 16.1707 104 ......... 4.800 11.11 4.372 1.3153

50 ......... 12,997.624 219,574.40 4,552.455 15.8934 105 ......... 2.856 6.31 2.613 1.2104

51 ......... 12,436.560 206,576.77 4,491.299 15.6104 106 ......... 1.639 3.46 1.506 1.1094

52 ......... 11,893.963 194,140.21 4,427.031 15.3226 107 ......... 0.904 1.82 0.834 1.0123

53 ......... 11,369.078 182,246.25 4,359.606 15.0300 108 ......... 0.477 0.91 0.441 0.9189

54 ......... 10,861.080 170,877.17 4,288.881 14.7330 109 ......... 0.239 0.44 0.223 0.8293

x x x x x x x x

7
Table 1.E. -- Actuarial Functions at 5.0 Percent Interest for 1989-91 United States 

Total Population

x D N M a x D N M a

0 ......... 100,000.000 2,003,900.24 4,576.179 19.0390 55 ......... 6,126.009 85,454.50 2,056.747 12.9495

1 ......... 94,346.667 1,903,900.24 3,684.751 19.1798 56 ......... 5,789.198 79,328.49 2,011.651 12.7028

2 ......... 89,788.662 1,809,553.57 3,619.444 19.1535 57 ......... 5,466.980 73,539.29 1,965.109 12.4515

3 ......... 85,471.547 1,719,764.91 3,577.980 19.1209 58 ......... 5,158.426 68,072.31 1,916.887 12.1963

4 ......... 81,371.034 1,634,293.36 3,547.540 19.0845 59 ......... 4,862.701 62,913.88 1,866.802 11.9381

5 ......... 77,472.717 1,552,922.33 3,524.034 19.0448 60 ......... 4,579.268 58,051.18 1,814.926 11.6770

6 ......... 73,763.392 1,475,449.61 3,503.887 19.0025 61 ......... 4,307.825 53,471.91 1,761.543 11.4127

7 ......... 70,233.793 1,401,686.22 3,486.830 18.9574 62 ......... 4,048.208 49,164.09 1,707.061 11.1447

8 ......... 66,873.759 1,331,452.43 3,471.263 18.9099 63 ......... 3,799.987 45,115.88 1,651.612 10.8726

9 ......... 63,676.403 1,264,578.67 3,458.371 18.8595 64 ......... 3,562.571 41,315.89 1,595.148 10.5972

10 ......... 60,633.756 1,200,902.26 3,447.934 18.8058 65 ......... 3,335.542 37,753.32 1,537.765 10.3185

11 ......... 57,737.080 1,140,268.51 3,438.579 18.7493 66 ......... 3,118.661 34,417.78 1,479.719 10.0361

12 ......... 54,978.786 1,082,531.43 3,429.670 18.6900 67 ......... 2,911.752 31,299.12 1,421.318 9.7492

13 ......... 52,349.611 1,027,552.64 3,418.533 18.6287 68 ......... 2,714.251 28,387.37 1,362.472 9.4586

14 ......... 49,840.611 975,203.03 3,402.371 18.5664 69 ......... 2,525.611 25,673.12 1,303.081 9.1651

15 ......... 47,445.121 925,362.42 3,380.244 18.5038 70 ......... 2,345.231 23,147.51 1,242.969 8.8700

16 ......... 45,157.427 877,917.30 3,351.841 18.4413 71 ......... 2,172.641 20,802.27 1,182.057 8.5746

17 ......... 42,973.915 832,759.87 3,318.683 18.3783 72 ......... 2,007.564 18,629.63 1,120.439 8.2797

18 ......... 40,890.972 789,785.96 3,282.117 18.3144 73 ......... 1,849.789 16,622.07 1,058.262 7.9859

19 ......... 38,906.188 748,894.98 3,244.522 18.2487 74 ......... 1,699.460 14,772.28 996.018 7.6923

20 ......... 37,016.201 709,988.80 3,207.210 18.1805 75 ......... 1,556.653 13,072.82 934.137 7.3980

21 ......... 35,216.912 672,972.60 3,170.598 18.1094 76 ......... 1,421.360 11,516.17 872.971 7.1022

22 ......... 33,503.338 637,755.68 3,134.020 18.0356 77 ......... 1,293.368 10,094.81 812.663 6.8051

23 ......... 31,872.129 604,252.34 3,098.207 17.9586 78 ......... 1,172.407 8,801.44 753.290 6.5072

24 ......... 30,319.681 572,380.22 3,063.480 17.8782 79 ......... 1,058.084 7,629.03 694.796 6.2102

25 ......... 28,842.517 542,060.54 3,030.111 17.7938 80 ......... 950.013 6,570.95 637.110 5.9167

26 ......... 27,436.721 513,218.02 2,997.768 17.7055 81 ......... 847.990 5,620.94 580.327 5.6285

27 ......... 26,099.408 485,781.30 2,966.965 17.6127 82 ......... 752.011 4,772.95 524.728 5.3469

28 ......... 24,826.223 459,681.89 2,936.609 17.5160 83 ......... 662.221 4,020.93 470.748 5.0719

29 ......... 23,614.139 434,855.67 2,906.727 17.4151 84 ......... 578.929 3,358.71 418.991 4.8016

30 ......... 22,459.809 411,241.53 2,876.879 17.3101 85 ......... 502.258 2,779.78 369.887 4.5346

31 ......... 21,360.325 388,781.72 2,846.910 17.2011 86 ......... 431.922 2,277.53 323.468 4.2730

32 ......... 20,313.156 367,421.39 2,816.899 17.0879 87 ......... 367.634 1,845.60 279.748 4.0202

33 ......... 19,316.082 347,108.24 2,787.118 16.9699 88 ......... 309.431 1,477.97 239.051 3.7764

34 ......... 18,366.383 327,792.15 2,757.233 16.8474 89 ......... 257.303 1,168.54 201.658 3.5415

35 ......... 17,462.243 309,425.77 2,727.682 16.7197 90 ......... 211.147 911.24 167.755 3.3156

36 ......... 16,601.010 291,963.53 2,697.985 16.5871 91 ......... 170.656 700.09 137.319 3.1023

37 ......... 15,780.723 275,362.52 2,668.222 16.4493 92 ......... 135.565 529.43 110.354 2.9054

38 ......... 14,999.662 259,581.80 2,638.624 16.3058 93 ......... 105.762 393.87 87.006 2.7241

39 ......... 14,255.712 244,582.13 2,608.944 16.1568 94 ......... 81.027 288.11 67.307 2.5557

40 ......... 13,547.323 230,326.42 2,579.398 16.0016 95 ......... 60.970 207.08 51.109 2.3964

41 ......... 12,872.856 216,779.10 2,550.042 15.8400 96 ......... 45.000 146.11 38.043 2.2469

42 ......... 12,230.488 203,906.24 2,520.666 15.6720 97 ......... 32.518 101.11 27.703 2.1094

43 ......... 11,618.512 191,675.76 2,491.095 15.4974 95 ......... 23.014 68.59 19.747 1.9805

44 ......... 11,035.333 180,057.24 2,461.178 15.3164 99 ......... 15.962 45.58 13.791 1.8555

45 ......... 10,479.012 169,021.91 2,430.349 15.1296 100 ......... 10.831 29.62 9.421 1.7345

46 ......... 9,948.318 158,542.90 2,398.656 14.9367 101 ......... 7.177 18.79 6.283 1.6174

47 ......... 9,441.578 148,594.58 2,365.646 14.7383 102 ......... 4.636 11.61 4.083 1.5042

48 ......... 8,957.849 139,153.00 2,331.515 14.5342 103 ......... 2.912 6.97 2.580 1.3948

49 ......... 8,495.941 130,195.15 2,296.172 14.3244 104 ......... 1.774 4.06 1.581 1.2892

50 ......... 8,055.008 121,699.21 2,259.808 14.1085 105 ......... 1.046 2.29 0.937 1.1874

51 ......... 7,633.897 113,644.21 2,222.268 13.8868 106 ......... 0.594 1.24 0.535 1.0892

52 ......... 7,231.305 106,010.31 2,183.195 13.6599 107 ......... 0.325 0.65 0.294 0.9946

53 ......... 6,846.354 98,779.00 2,142.592 13.4280 108 ......... 0.170 0.32 0.154 0.9036

54 ......... 6,478.153 91,932.65 2,100.407 13.1912 109 ......... 0.084 0.15 0.077 0.8160

x x x x x x x x

8
Table 1.F. -- Actuarial Functions at 6.0 Percent Interest for 1989-91 United States 

Total Population

x D N M a x D N M a

0 ......... 100,000.000 1,711,205.67 3,139.301 16.1121 55 ......... 3,637.194 46,212.27 1,021.405 11.7055

1 ......... 93,456.604 1,611,205.67 2,256.283 16.2401 56 ......... 3,404.793 42,575.08 994.883 11.5045

2 ......... 88,102.528 1,517,749.07 2,192.203 16.2271 57 ......... 3,184.954 39,170.28 967.768 11.2985

3 ......... 83,075.290 1,429,646.54 2,151.901 16.2090 58 ......... 2,976.846 35,985.33 939.940 11.0884

4 ......... 78,343.608 1,346,571.25 2,122.594 16.1880 59 ......... 2,779.714 33,008.48 911.310 10.8748

5 ......... 73,886.646 1,268,227.64 2,100.176 16.1645 60 ......... 2,592.998 30,228.77 881.935 10.6578

6 ......... 69,685.349 1,194,341.00 2,081.142 16.1391 61 ......... 2,416.282 27,635.77 851.992 10.4373

7 ......... 65,724.934 1,124,655.65 2,065.181 16.1116 62 ......... 2,249.240 25,219.49 821.721 10.2125

8 ......... 61,990.225 1,058,930.71 2,050.750 16.0822 63 ......... 2,091.407 22,970.25 791.204 9.9832

9 ......... 58,469.506 996,940.49 2,038.912 16.0506 64 ......... 1,942.242 20,878.85 760.421 9.7499

10 ......... 55,150.419 938,470.98 2,029.419 16.0166 65 ......... 1,801.315 18,936.60 729.432 9.5127

11 ......... 52,020.268 883,320.57 2,020.991 15.9803 66 ......... 1,668.303 17,135.29 698.381 9.2711

12 ......... 49,067.773 831,300.30 2,013.039 15.9419 67 ......... 1,542.924 15,466.99 667.434 9.0245

13 ......... 46,280.506 782,232.52 2,003.194 15.9020 68 ......... 1,424.700 13,924.06 636.546 8.7733

14 ......... 43,646.701 735,952.02 1,989.040 15.8616 69 ......... 1,313.177 12,499.36 605.666 8.5184

15 ......... 41,156.939 692,305.32 1,969.846 15.8211 70 ......... 1,207.886 11,186.18 574.706 8.2610

16 ......... 38,802.895 651,148.38 1,945.440 15.7809 71 ......... 1,108.439 9,978.30 543.630 8.0021

17 ......... 36,578.281 612,345.48 1,917.216 15.7407 72 ......... 1,014.557 8,869.86 512.490 7.7426

18 ......... 34,476.982 575,767.20 1,886.386 15.7000 73 ......... 926.004 7,855.30 481.364 7.4830

19 ......... 32,494.056 541,290.22 1,854.987 15.6581 74 ......... 842.723 6,929.30 450.499 7.2225

20 ......... 30,623.901 508,796.16 1,824.118 15.6143 75 ......... 764.626 6,086.57 420.103 6.9602

21 ......... 28,860.469 478,172.26 1,794.115 15.5684 76 ......... 691.584 5,321.95 390.342 6.6953

22 ......... 27,197.165 449,311.79 1,764.422 15.5205 77 ......... 623.371 4,630.36 361.275 6.4279

23 ......... 25,628.905 422,114.63 1,735.624 15.4703 78 ......... 559.740 4,006.99 332.929 6.1587

24 ......... 24,150.550 396,485.72 1,707.962 15.4173 79 ......... 500.393 3,447.25 305.266 5.8891

25 ......... 22,757.209 372,335.17 1,681.633 15.3612 80 ......... 445.045 2,946.86 278.242 5.6215

26 ......... 21,443.787 349,577.96 1,656.355 15.3021 81 ......... 393.504 2,501.81 251.892 5.3578

27 ......... 20,206.141 328,134.18 1,632.508 15.2393 82 ......... 345.673 2,108.31 226.335 5.0991

28 ......... 19,039.117 307,928.04 1,609.228 15.1734 83 ......... 301.528 1,762.64 201.756 4.8457

29 ......... 17,938.730 288,888.92 1,586.528 15.1042 84 ......... 261.116 1,461.11 178.412 4.5956

30 ......... 16,900.870 270,950.19 1,564.067 15.0317 85 ......... 224.398 1,199.99 156.474 4.3476

31 ......... 15,921.879 254,049.32 1,541.729 14.9560 86 ......... 191.153 975.59 135.930 4.1037

32 ......... 14,998.481 238,127.44 1,519.570 14.8768 87 ......... 161.166 784.44 116.764 3.8673

33 ......... 14,127.729 223,128.96 1,497.788 14.7937 88 ......... 134.371 623.28 99.091 3.6385

34 ......... 13,306.394 209,001.23 1,476.136 14.7068 89 ......... 110.680 488.91 83.006 3.4173

35 ......... 12,531.995 195,694.83 1,454.929 14.6156 90 ......... 89.969 378.22 68.560 3.2039

36 ......... 11,801.525 183,162.84 1,433.817 14.5203 91 ......... 72.030 288.26 55.714 3.0019

37 ......... 11,112.556 171,361.31 1,412.859 14.4205 92 ......... 56.679 216.23 44.440 2.8149

38 ......... 10,462.897 160,248.76 1,392.213 14.3159 93 ......... 43.801 159.55 34.770 2.6425

39 ......... 9,850.150 149,785.86 1,371.705 14.2065 94 ......... 33.241 115.74 26.689 2.4820

40 ......... 9,272.372 139,935.71 1,351.482 14.0917 95 ......... 24.777 82.50 20.107 2.3299

41 ......... 8,727.617 130,663.34 1,331.579 13.9712 96 ......... 18.114 57.73 14.847 2.1868

42 ......... 8,213.873 121,935.72 1,311.851 13.8451 97 ......... 12.966 39.61 10.724 2.0551

43 ......... 7,729.264 113,721.85 1,292.178 13.7132 95 ......... 9.090 26.65 7.582 1.9315

44 ......... 7,272.044 105,992.59 1,272.464 13.5753 99 ......... 6.245 17.56 5.251 1.8113

45 ......... 6,840.295 98,720.54 1,252.340 13.4322 100 ......... 4.198 11.31 3.557 1.6948

46 ......... 6,432.616 91,880.25 1,231.847 13.2835 101 ......... 2.755 7.11 2.353 1.5818

47 ......... 6,047.362 85,447.63 1,210.704 13.1297 102 ......... 1.763 4.36 1.516 1.4724

48 ......... 5,683.404 79,400.27 1,189.049 12.9705 103 ......... 1.097 2.60 0.950 1.3665

49 ......... 5,339.489 73,716.86 1,166.837 12.8060 104 ......... 0.662 1.50 0.577 1.2641

50 ......... 5,014.616 68,377.37 1,144.199 12.6356 105 ......... 0.387 0.84 0.339 1.1652

51 ......... 4,707.620 63,362.76 1,121.049 12.4596 106 ......... 0.218 0.45 0.192 1.0697

52 ......... 4,417.283 58,655.14 1,097.181 12.2786 107 ......... 0.118 0.23 0.105 0.9776

53 ......... 4,142.680 54,237.86 1,072.612 12.0925 108 ......... 0.061 0.12 0.054 0.8888

54 ......... 3,882.904 50,095.18 1,047.328 11.9015 109 ......... 0.030 0.05 0.027 0.8032

x x x x x x x x

9
Table 1.G. -- Actuarial Functions at 7.0 Percent Interest for 1989-91 United States 

Total Population

x D N M a x D N M a

0 ......... 100,000.000 1,492,632.13 2,351.169 13.9263 55 ......... 2,170.108 25,286.22 515.869 10.6521

1 ......... 92,583.178 1,392,632.13 1,476.403 14.0420 56 ......... 2,012.462 23,116.11 500.193 10.4865

2 ......... 86,463.447 1,300,048.95 1,413.515 14.0358 57 ......... 1,864.929 21,103.65 484.316 10.3161

3 ......... 80,767.777 1,213,585.50 1,374.333 14.0256 58 ......... 1,726.782 19,238.72 468.174 10.1414

4 ......... 75,455.677 1,132,817.73 1,346.106 14.0130 59 ......... 1,597.362 17,511.94 451.721 9.9630

5 ......... 70,497.934 1,057,362.05 1,324.716 13.9985 60 ......... 1,476.139 15,914.57 434.999 9.7812

6 ......... 65,867.929 986,864.11 1,306.725 13.9825 61 ......... 1,362.683 14,438.44 418.113 9.5956

7 ......... 61,543.866 920,996.19 1,291.779 13.9649 62 ......... 1,256.623 13,075.75 401.200 9.4055

8 ......... 57,504.246 859,452.32 1,278.393 13.9459 63 ......... 1,157.524 11,819.13 384.310 9.2107

9 ......... 53,731.407 801,948.07 1,267.514 13.9251 64 ......... 1,064.920 10,661.60 367.432 9.0116

10 ......... 50,207.626 748,216.67 1,258.872 13.9025 65 ......... 978.420 9,596.69 350.600 8.8083

11 ......... 46,915.414 698,009.04 1,251.271 13.8780 66 ......... 897.703 8,618.26 333.891 8.6004

12 ......... 43,839.077 651,093.63 1,244.167 13.8519 67 ......... 822.478 7,720.56 317.394 8.3870

13 ......... 40,962.386 607,254.55 1,235.452 13.8247 68 ......... 752.360 6,898.08 301.083 8.1686

14 ......... 38,270.193 566,292.17 1,223.042 13.7972 69 ......... 686.985 6,145.72 284.928 7.9459

15 ......... 35,749.863 528,021.97 1,206.370 13.7699 70 ......... 625.997 5,458.74 268.883 7.7201

16 ......... 33,390.086 492,272.11 1,185.368 13.7431 71 ......... 569.089 4,832.74 252.928 7.4921

17 ......... 31,181.628 458,882.02 1,161.308 13.7164 72 ......... 516.020 4,263.65 237.090 7.2626

18 ......... 29,115.672 427,700.40 1,135.272 13.6897 73 ......... 466.579 3,747.63 221.407 7.0321

19 ......... 27,184.640 398,584.72 1,109.004 13.6621 74 ......... 420.649 3,281.05 206.000 6.8000

20 ......... 25,380.622 371,400.08 1,083.421 13.6332 75 ......... 378.099 2,860.41 190.970 6.5652

21 ......... 23,695.573 346,019.46 1,058.786 13.6027 76 ......... 338.785 2,482.31 176.391 6.3271

22 ......... 22,121.244 322,323.89 1,034.635 13.5708 77 ......... 302.515 2,143.52 162.285 6.0857

23 ......... 20,650.856 300,202.64 1,011.431 13.5371 78 ......... 269.097 1,841.01 148.657 5.8414

24 ......... 19,277.785 279,551.79 989.350 13.5012 79 ......... 238.318 1,571.91 135.482 5.5959

25 ......... 17,995.801 260,274.00 968.530 13.4630 80 ......... 209.977 1,333.59 122.732 5.3511

26 ......... 16,798.704 242,278.20 948.728 13.4224 81 ......... 183.924 1,123.61 110.416 5.1091

27 ......... 15,681.216 225,479.50 930.221 13.3790 82 ......... 160.058 939.69 98.583 4.8709

28 ......... 14,637.444 209,798.28 912.323 13.3330 83 ......... 138.313 779.63 87.308 4.6368

29 ......... 13,662.565 195,160.84 895.034 13.2843 84 ......... 118.656 641.32 76.700 4.4049

30 ......... 12,751.806 181,498.27 878.087 13.2331 85 ......... 101.017 522.66 66.824 4.1740

31 ......... 11,900.879 168,746.47 861.390 13.1793 86 ......... 85.247 421.65 57.663 3.9462

32 ......... 11,105.908 156,845.59 844.982 13.1227 87 ......... 71.203 336.40 49.195 3.7246

33 ......... 10,363.376 145,739.68 829.004 13.0630 88 ......... 58.810 265.20 41.460 3.5094

34 ......... 9,669.663 135,376.30 813.270 13.0001 89 ......... 47.988 206.39 34.486 3.3008

35 ......... 9,021.802 125,706.64 798.003 12.9337 90 ......... 38.644 158.40 28.281 3.0989

36 ......... 8,416.534 116,684.84 782.947 12.8638 91 ......... 30.650 119.76 22.815 2.9072

37 ......... 7,851.112 108,268.30 768.139 12.7902 92 ......... 23.892 89.11 18.063 2.7295

38 ......... 7,323.038 100,417.19 753.689 12.7125 93 ......... 18.291 65.21 14.025 2.5653

39 ......... 6,829.741 93,094.15 739.469 12.6307 94 ......... 13.751 46.92 10.682 2.4122

40 ......... 6,369.045 86,264.41 725.579 12.5443 95 ......... 10.154 33.17 7.984 2.2668

41 ......... 5,938.835 79,895.37 712.036 12.4530 96 ......... 7.354 23.02 5.849 2.1297

42 ......... 5,537.015 73,956.53 698.737 12.3568 97 ......... 5.215 15.66 4.190 2.0034

43 ......... 5,161.642 68,419.52 685.599 12.2554 95 ......... 3.622 10.45 2.938 1.8847

44 ......... 4,810.923 63,257.87 672.557 12.1488 99 ......... 2.465 6.83 2.018 1.7691

45 ......... 4,483.000 58,446.95 659.368 12.0375 100 ......... 1.641 4.36 1.356 1.6567

46 ......... 4,176.415 53,963.95 646.063 11.9211 101 ......... 1.067 2.72 0.890 1.5477

47 ......... 3,889.592 49,787.54 632.464 11.8002 102 ......... 0.677 1.65 0.568 1.4418

48 ......... 3,621.335 45,897.94 618.666 11.6743 103 ......... 0.417 0.98 0.353 1.3393

49 ......... 3,370.405 42,276.61 604.645 11.5435 104 ......... 0.249 0.56 0.213 1.2399

50 ......... 3,135.755 38,906.20 590.489 11.4073 105 ......... 0.144 0.31 0.124 1.1438

51 ......... 2,916.271 35,770.45 576.148 11.2658 106 ......... 0.080 0.16 0.070 1.0509

52 ......... 2,710.839 32,854.18 561.501 11.1196 107 ......... 0.043 0.08 0.038 0.9611

53 ......... 2,518.558 30,143.34 546.564 10.9685 108 ......... 0.022 0.04 0.019 0.8744

54 ......... 2,338.564 27,624.78 531.336 10.8127 109 ......... 0.011 0.02 0.010 0.7907

x x x x x x x x

10
Table 1.H. -- Actuarial Functions at 8.0 Percent Interest for 1989-91 United States 

Total Population

x D N M a x D N M a

0 ......... 100,000.000 1,324,391.78 1,896.905 12.2439 55 ......... 1,301.016 13,989.24 264.775 9.7526

1 ......... 91,725.926 1,224,391.78 1,030.238 12.3484 56 ......... 1,195.333 12,688.23 255.464 9.6148

2 ......... 84,869.684 1,132,665.86 968.510 12.3459 57 ......... 1,097.447 11,492.90 246.121 9.4724

3 ......... 78,544.937 1,047,796.17 930.406 12.3401 58 ......... 1,006.743 10,395.45 236.710 9.3258

4 ......... 72,699.598 969,251.24 903.210 12.3323 59 ......... 922.666 9,388.71 227.207 9.1756

5 ......... 67,294.025 896,551.64 882.792 12.3229 60 ......... 844.751 8,466.04 217.637 9.0219

6 ......... 62,292.268 829,257.61 865.778 12.3124 61 ......... 772.603 7,621.29 208.063 8.8644

7 ......... 57,664.022 766,965.35 851.774 12.3006 62 ......... 705.873 6,848.69 198.563 8.7024

8 ......... 53,380.187 709,301.32 839.348 12.2877 63 ......... 644.186 6,142.81 189.163 8.5358

9 ......... 49,416.094 655,921.14 829.343 12.2734 64 ......... 587.163 5,498.63 179.857 8.3647

10 ......... 45,747.768 606,505.04 821.468 12.2576 65 ......... 534.474 4,911.46 170.662 8.1893

11 ......... 42,352.182 560,757.28 814.606 12.2403 66 ......... 485.841 4,376.99 161.619 8.0091

12 ......... 39,208.630 518,405.09 808.253 12.2217 67 ......... 441.007 3,891.15 152.774 7.8233

13 ......... 36,296.565 479,196.46 800.531 12.2023 68 ......... 399.675 3,450.14 144.109 7.6324

14 ......... 33,597.036 442,899.90 789.636 12.1827 69 ......... 361.567 3,050.47 135.607 7.4368

15 ......... 31,093.866 409,302.86 775.135 12.1635 70 ......... 326.418 2,688.90 127.240 7.2376

16 ......... 28,772.519 378,209.00 757.038 12.1448 71 ......... 293.996 2,362.48 118.997 7.0358

17 ......... 26,620.681 349,436.48 736.497 12.1265 72 ......... 264.112 2,068.49 110.891 6.8318

18 ......... 24,626.757 322,815.80 714.475 12.1083 73 ......... 236.596 1,804.37 102.938 6.6264

19 ......... 22,780.540 298,189.04 692.463 12.0896 74 ......... 211.330 1,567.78 95.198 6.4186

20 ......... 21,071.852 275,408.50 671.222 12.0700 75 ......... 188.195 1,356.45 87.717 6.2077

21 ......... 19,490.711 254,336.65 650.960 12.0491 76 ......... 167.065 1,168.25 80.528 5.9928

22 ......... 18,027.273 234,845.94 631.278 12.0273 77 ......... 147.798 1,001.19 73.636 5.7740

23 ......... 16,673.185 216,818.66 612.543 12.0040 78 ......... 130.254 853.39 67.040 5.5517

24 ......... 15,420.472 200,145.48 594.881 11.9792 79 ......... 114.287 723.14 60.722 5.3274

25 ......... 14,261.715 184,725.01 578.381 11.9525 80 ......... 99.764 608.85 54.664 5.1029

26 ......... 13,189.743 170,463.29 562.833 11.9239 81 ......... 86.576 509.09 48.866 4.8802

27 ......... 12,198.329 157,273.55 548.436 11.8930 82 ......... 74.645 422.51 43.348 4.6603

28 ......... 11,280.955 145,075.22 534.643 11.8602 83 ......... 63.906 347.86 38.139 4.4434

29 ......... 10,432.128 133,794.26 521.441 11.8252 84 ......... 54.316 283.96 33.283 4.2278

30 ......... 9,646.558 123,362.14 508.622 11.7882 85 ......... 45.814 229.64 28.803 4.0125

31 ......... 8,919.484 113,715.58 496.107 11.7491 86 ......... 38.304 183.83 24.687 3.7992

32 ......... 8,246.598 104,796.10 483.924 11.7078 87 ......... 31.697 145.52 20.917 3.5911

33 ......... 7,623.984 96,549.50 472.169 11.6639 88 ......... 25.938 113.83 17.506 3.3885

34 ......... 7,047.776 88,925.51 460.701 11.6175 89 ......... 20.969 87.89 14.459 3.1914

35 ......... 6,514.694 81,877.74 449.677 11.5682 90 ......... 16.730 66.92 11.773 3.0001

36 ......... 6,021.353 75,363.04 438.905 11.5160 91 ......... 13.146 50.19 9.428 2.8180

37 ......... 5,564.831 69,341.69 428.410 11.4607 92 ......... 10.153 37.04 7.409 2.6488

38 ......... 5,142.474 63,776.86 418.262 11.4020 93 ......... 7.701 26.89 5.709 2.4922

39 ......... 4,751.657 58,634.39 408.369 11.3398 94 ......... 5.736 19.19 4.314 2.3460

40 ......... 4,390.108 53,882.73 398.795 11.2737 95 ......... 4.196 13.46 3.199 2.2068

41 ......... 4,055.666 49,492.62 389.546 11.2033 96 ......... 3.011 9.26 2.325 2.0753

42 ......... 3,746.249 45,436.95 380.548 11.1287 97 ......... 2.115 6.25 1.652 1.9541

43 ......... 3,459.942 41,690.70 371.742 11.0495 95 ......... 1.455 4.13 1.149 1.8399

44 ......... 3,194.989 38,230.76 363.081 10.9659 99 ......... 0.981 2.68 0.783 1.7286

45 ......... 2,949.645 35,035.77 354.403 10.8780 100 ......... 0.647 1.70 0.522 1.6203

46 ......... 2,722.480 32,086.13 345.730 10.7856 101 ......... 0.417 1.05 0.339 1.5149

47 ......... 2,512.032 29,363.65 336.947 10.6892 102 ......... 0.262 0.63 0.215 1.4125

48 ......... 2,317.127 26,851.62 328.118 10.5883 103 ......... 0.160 0.37 0.133 1.3131

49 ......... 2,136.599 24,534.49 319.230 10.4830 104 ......... 0.095 0.21 0.079 1.2166

50 ......... 1,969.442 22,397.89 310.339 10.3727 105 ......... 0.054 0.12 0.046 1.1231

51 ......... 1,814.634 20,428.45 301.416 10.2576 106 ......... 0.030 0.06 0.025 1.0326

52 ......... 1,671.187 18,613.81 292.385 10.1381 107 ......... 0.016 0.03 0.014 0.9451

53 ......... 1,538.272 16,942.63 283.263 10.0141 108 ......... 0.008 0.02 0.007 0.8604

54 ......... 1,415.111 15,404.36 274.048 9.8856 109 ......... 0.004 0.01 0.003 0.7786

x x x x x x x x

11
Table 1.I. -- Actuarial Functions at 9.0 Percent Interest for 1989-91 United States 

Total Population

x D N M a x D N M a

0 ......... 100,000.000 1,191,481.16 1,620.822 10.9148 55 ......... 783.667 7,819.78 137.997 8.9785

1 ......... 90,884.404 1,091,481.16 762.106 11.0096 56 ......... 713.404 7,036.12 132.440 8.8627

2 ......... 83,319.586 1,000,596.76 701.505 11.0091 57 ......... 648.974 6,322.71 126.915 8.7426

3 ......... 76,402.922 917,277.17 664.440 11.0058 58 ......... 589.875 5,673.74 121.401 8.6186

4 ......... 70,068.212 840,874.25 638.228 11.0008 59 ......... 535.652 5,083.87 115.883 8.4910

5 ......... 64,263.266 770,806.04 618.731 10.9945 60 ......... 485.919 4,548.21 110.379 8.3600

6 ......... 58,941.025 706,542.77 602.631 10.9873 61 ......... 440.341 4,062.29 104.922 8.2253

7 ......... 54,061.206 647,601.75 589.502 10.9790 62 ......... 398.618 3,621.95 99.557 8.0863

8 ......... 49,585.894 593,540.54 577.960 10.9699 63 ......... 360.445 3,223.34 94.298 7.9427

9 ......... 45,482.437 543,954.65 568.751 10.9597 64 ......... 325.524 2,862.89 89.138 7.7947

10 ......... 41,719.826 498,472.21 561.570 10.9481 65 ......... 293.595 2,537.37 84.088 7.6424

11 ......... 38,268.869 456,752.38 555.369 10.9354 66 ......... 264.431 2,243.77 79.166 7.4853

12 ......... 35,103.366 418,483.51 549.681 10.9215 67 ......... 237.827 1,979.34 74.396 7.3226

13 ......... 32,198.073 383,380.15 542.831 10.9069 68 ......... 213.560 1,741.51 69.766 7.1547

14 ......... 29,529.940 351,182.08 533.255 10.8924 69 ......... 191.425 1,527.95 65.264 6.9820

15 ......... 27,079.060 321,652.13 520.627 10.8783 70 ......... 171.231 1,336.53 60.875 6.8054

16 ......... 24,827.558 294,573.08 505.011 10.8648 71 ......... 152.808 1,165.30 56.591 6.6259

17 ......... 22,760.015 269,745.52 487.449 10.8517 72 ......... 136.016 1,012.49 52.416 6.4439

18 ......... 20,862.092 246,985.50 468.794 10.8390 73 ......... 120.728 876.47 48.358 6.2599

19 ......... 19,121.057 226,123.41 450.317 10.8259 74 ......... 106.846 755.74 44.445 6.0732

20 ......... 17,524.590 207,002.35 432.652 10.8121 75 ......... 94.276 648.90 40.697 5.8830

21 ......... 16,060.908 189,477.76 415.955 10.7975 76 ......... 82.923 554.62 37.129 5.6884

22 ......... 14,718.709 173,416.85 399.886 10.7821 77 ......... 72.687 471.70 33.740 5.4894

23 ......... 13,488.247 158,698.15 384.730 10.7657 78 ......... 63.471 399.01 30.525 5.2865

24 ......... 12,360.381 145,209.90 370.572 10.7480 79 ......... 55.180 335.54 27.475 5.0808

25 ......... 11,326.694 132,849.52 357.468 10.7289 80 ......... 47.726 280.36 24.577 4.8744

26 ......... 10,379.228 121,522.82 345.233 10.7083 81 ......... 41.037 232.63 21.829 4.6689

27 ......... 9,511.002 111,143.60 334.008 10.6858 82 ......... 35.057 191.60 19.237 4.4653

28 ......... 8,715.034 101,632.59 323.352 10.6618 83 ......... 29.738 156.54 16.813 4.2639

29 ......... 7,985.339 92,917.56 313.247 10.6360 84 ......... 25.044 126.80 14.574 4.0632

30 ......... 7,316.276 84,932.22 303.524 10.6087 85 ......... 20.930 101.76 12.528 3.8619

31 ......... 6,702.776 77,615.95 294.120 10.5797 86 ......... 17.338 80.83 10.664 3.6619

32 ......... 6,140.264 70,913.17 285.048 10.5489 87 ......... 14.216 63.49 8.974 3.4661

33 ......... 5,624.598 64,772.91 276.376 10.5160 88 ......... 11.526 49.27 7.458 3.2749

34 ......... 5,151.799 59,148.31 267.993 10.4811 89 ......... 9.233 37.75 6.116 3.0885

35 ......... 4,718.436 53,996.51 260.009 10.4437 90 ......... 7.299 28.52 4.944 2.9070

36 ......... 4,321.110 49,278.07 252.279 10.4040 91 ......... 5.682 21.22 3.931 2.7337

37 ......... 3,956.859 44,956.96 244.816 10.3618 92 ......... 4.348 15.53 3.066 2.5724

38 ......... 3,622.996 41,000.10 237.667 10.3166 93 ......... 3.268 11.19 2.344 2.4229

39 ......... 3,316.944 37,377.11 230.761 10.2685 94 ......... 2.412 7.92 1.758 2.2831

40 ......... 3,036.446 34,060.16 224.139 10.2171 95 ......... 1.748 5.51 1.294 2.1497

41 ......... 2,779.392 31,023.72 217.800 10.1621 96 ......... 1.243 3.76 0.933 2.0235

42 ......... 2,543.791 28,244.33 211.691 10.1032 97 ......... 0.865 2.52 0.658 1.9070

43 ......... 2,327.828 25,700.54 205.766 10.0406 95 ......... 0.590 1.65 0.454 1.7972

44 ......... 2,129.848 23,372.71 199.992 9.9739 99 ......... 0.394 1.06 0.307 1.6899

45 ......... 1,948.258 21,242.86 194.260 9.9035 100 ......... 0.258 0.67 0.203 1.5853

46 ......... 1,781.716 19,294.60 188.584 9.8292 101 ......... 0.164 0.41 0.131 1.4834

47 ......... 1,628.907 17,512.88 182.889 9.7513 102 ......... 0.102 0.24 0.082 1.3843

48 ......... 1,488.738 15,883.98 177.217 9.6694 103 ......... 0.062 0.14 0.050 1.2878

49 ......... 1,360.156 14,395.24 171.558 9.5835 104 ......... 0.036 0.08 0.030 1.1941

50 ......... 1,242.242 13,035.08 165.950 9.4932 105 ......... 0.021 0.04 0.017 1.1032

51 ......... 1,134.094 11,792.84 160.373 9.3985 106 ......... 0.011 0.02 0.009 1.0150

52 ......... 1,034.862 10,658.75 154.782 9.2997 107 ......... 0.006 0.01 0.005 0.9296

53 ......... 943.817 9,623.89 149.184 9.1968 108 ......... 0.003 0.01 0.003 0.8469

54 ......... 860.285 8,680.07 143.582 9.0898 109 ......... 0.001 0.00 0.001 0.7669

x x x x x x x x

12
Table 1.J. -- Actuarial Functions at 10.0 Percent Interest for 1989-91 United States 

Total Population

x D N M a x D N M a

0 ......... 100,000.000 1,084,120.30 1,443.609 9.8412 55 ......... 474.233 4,413.84 72.974 8.3073

1 ......... 90,058.182 984,120.30 592.700 9.9276 56 ......... 427.788 3,939.61 69.642 8.2093

2 ......... 81,811.570 894,062.12 533.196 9.9283 57 ......... 385.615 3,511.82 66.359 8.1071

3 ......... 74,338.092 812,250.55 497.133 9.9264 58 ......... 347.313 3,126.21 63.112 8.0011

4 ......... 67,554.812 737,912.46 471.861 9.9232 59 ......... 312.520 2,778.90 59.893 7.8919

5 ......... 61,394.838 670,357.64 453.234 9.9188 60 ......... 280.927 2,466.38 56.711 7.7794

6 ......... 55,798.248 608,962.81 437.993 9.9137 61 ......... 252.262 2,185.45 53.585 7.6634

7 ......... 50,713.364 553,164.56 425.677 9.9077 62 ......... 226.284 1,933.19 50.539 7.5432

8 ......... 46,092.329 502,451.19 414.947 9.9010 63 ......... 202.754 1,706.90 47.581 7.4186

9 ......... 41,893.635 456,358.86 406.466 9.8933 64 ......... 181.446 1,504.15 44.705 7.2898

10 ......... 38,078.569 414,465.23 399.911 9.8845 65 ......... 162.161 1,322.70 41.915 7.1567

11 ......... 34,611.273 376,386.66 394.303 9.8747 66 ......... 144.725 1,160.54 39.221 7.0189

12 ......... 31,459.695 341,775.39 389.205 9.8639 67 ......... 128.982 1,015.82 36.634 6.8757

13 ......... 28,593.640 310,315.69 383.122 9.8526 68 ......... 114.768 886.84 34.146 6.7272

14 ......... 25,985.792 281,722.05 374.696 9.8414 69 ......... 101.937 772.07 31.749 6.5740

15 ......... 23,612.435 255,736.26 363.684 9.8306 70 ......... 90.354 670.13 29.433 6.4167

16 ......... 21,452.357 232,123.83 350.191 9.8204 71 ......... 79.900 579.78 27.193 6.2563

17 ......... 19,487.106 210,671.47 335.155 9.8108 72 ......... 70.473 499.88 25.030 6.0931

18 ......... 17,699.724 191,184.36 319.327 9.8015 73 ......... 61.983 429.40 22.947 5.9277

19 ......... 16,075.125 173,484.64 303.794 9.7921 74 ......... 54.358 367.42 20.956 5.7593

20 ......... 14,599.034 157,409.52 289.078 9.7822 75 ......... 47.527 313.06 19.066 5.5871

21 ......... 13,258.066 142,810.48 275.295 9.7716 76 ......... 41.424 265.54 17.284 5.4103

22 ......... 12,039.642 129,552.42 262.150 9.7605 77 ......... 35.980 224.11 15.606 5.2288

23 ......... 10,932.845 117,512.77 249.866 9.7486 78 ......... 31.133 188.13 14.030 5.0430

24 ......... 9,927.579 106,579.93 238.495 9.7357 79 ......... 26.820 157.00 12.547 4.8539

25 ......... 9,014.642 96,652.35 228.065 9.7217 80 ......... 22.986 130.18 11.151 4.6635

26 ......... 8,185.480 87,637.71 218.416 9.7065 81 ......... 19.585 107.19 9.840 4.4734

27 ......... 7,432.574 79,452.23 209.644 9.6897 82 ......... 16.579 87.61 8.614 4.2845

28 ......... 6,748.633 72,019.65 201.392 9.6717 83 ......... 13.935 71.03 7.478 4.0972

29 ......... 6,127.367 65,271.02 193.638 9.6524 84 ......... 11.629 57.10 6.438 3.9098

30 ......... 5,562.941 59,143.65 186.246 9.6317 85 ......... 9.630 45.47 5.497 3.7213

31 ......... 5,050.134 53,580.71 179.160 9.6098 86 ......... 7.905 35.84 4.647 3.5333

32 ......... 4,584.258 48,530.58 172.387 9.5864 87 ......... 6.423 27.93 3.884 3.3489

33 ......... 4,161.092 43,946.32 165.972 9.5612 88 ......... 5.160 21.51 3.205 3.1682

34 ......... 3,776.665 39,785.23 159.827 9.5345 89 ......... 4.096 16.35 2.610 2.9915

35 ......... 3,427.532 36,008.56 154.026 9.5057 90 ......... 3.208 12.25 2.094 2.8190

36 ......... 3,110.374 32,581.03 148.462 9.4750 91 ......... 2.475 9.04 1.653 2.6540

37 ......... 2,822.290 29,470.66 143.139 9.4421 92 ......... 1.877 6.57 1.280 2.5001

38 ......... 2,560.665 26,648.37 138.086 9.4068 93 ......... 1.398 4.69 0.971 2.3572

39 ......... 2,323.041 24,087.70 133.250 9.3690 94 ......... 1.022 3.29 0.723 2.2233

40 ......... 2,107.260 21,764.66 128.654 9.3284 95 ......... 0.734 2.27 0.528 2.0954

41 ......... 1,911.332 19,657.40 124.295 9.2847 96 ......... 0.517 1.54 0.377 1.9741

42 ......... 1,733.411 17,746.07 120.132 9.2377 97 ......... 0.357 1.02 0.264 1.8620

43 ......... 1,571.828 16,012.66 116.131 9.1873 95 ......... 0.241 0.66 0.181 1.7563

44 ......... 1,425.071 14,440.83 112.268 9.1334 99 ......... 0.160 0.42 0.121 1.6529

45 ......... 1,291.719 13,015.76 108.468 9.0763 100 ......... 0.103 0.26 0.079 1.5518

46 ......... 1,170.561 11,724.04 104.739 9.0157 101 ......... 0.065 0.16 0.051 1.4532

47 ......... 1,060.438 10,553.48 101.031 8.9520 102 ......... 0.040 0.10 0.032 1.3571

48 ......... 960.376 9,493.04 97.372 8.8847 103 ......... 0.024 0.05 0.019 1.2635

49 ......... 869.452 8,532.67 93.755 8.8138 104 ......... 0.014 0.03 0.011 1.1724

50 ......... 786.859 7,663.21 90.203 8.7390 105 ......... 0.008 0.02 0.006 1.0839

51 ......... 711.826 6,876.36 86.702 8.6602 106 ......... 0.004 0.01 0.004 0.9980

52 ......... 643.636 6,164.53 83.225 8.5777 107 ......... 0.002 0.00 0.002 0.9146

53 ......... 581.674 5,520.89 79.775 8.4914 108 ......... 0.001 0.00 0.001 0.8338

54 ......... 525.374 4,939.22 76.354 8.4013 109 ......... 0.001 0.00 0.000 0.7555

x x x x x x x x

13
Table 1.K. -- Actuarial Functions at 11.0 Percent Interest for 1989-91 United States 

Total Population

x D N M a x D N M a

0 ......... 100,000.000 995,734.98 1,323.560 8.9573 55 ......... 288.287 2,514.30 39.122 7.7215

1 ......... 89,246.847 895,734.98 480.317 9.0366 56 ......... 257.711 2,226.01 37.115 7.6376

2 ......... 80,344.128 806,488.13 421.880 9.0379 57 ......... 230.212 1,968.30 35.155 7.5500

3 ......... 72,347.000 726,144.01 386.783 9.0370 58 ......... 205.477 1,738.09 33.234 7.4588

4 ......... 65,153.104 653,797.01 362.410 9.0348 59 ......... 183.227 1,532.61 31.347 7.3645

5 ......... 58,678.687 588,643.90 344.607 9.0316 60 ......... 163.221 1,349.38 29.498 7.2672

6 ......... 52,849.247 529,965.22 330.171 9.0279 61 ......... 145.246 1,186.16 27.698 7.1666

7 ......... 47,600.374 477,115.97 318.611 9.0234 62 ......... 129.114 1,040.92 25.960 7.0620

8 ......... 42,873.240 429,515.59 308.631 9.0183 63 ......... 114.646 911.80 24.288 6.9532

9 ......... 38,616.722 386,642.35 300.813 9.0123 64 ......... 101.674 797.16 22.676 6.8404

10 ......... 34,783.852 348,025.63 294.826 9.0054 65 ......... 90.049 695.48 21.127 6.7234

11 ......... 31,331.727 313,241.78 289.749 8.9976 66 ......... 79.643 605.43 19.645 6.6019

12 ......... 28,222.208 281,910.05 285.176 8.9889 67 ......... 70.339 525.79 18.234 6.4751

13 ......... 25,420.005 253,687.85 279.768 8.9799 68 ......... 62.024 455.45 16.889 6.3432

14 ......... 22,893.481 228,267.84 272.344 8.9709 69 ......... 54.594 393.43 15.605 6.2065

15 ......... 20,615.144 205,374.36 262.730 8.9623 70 ......... 47.954 338.84 14.376 6.0658

16 ......... 18,560.527 184,759.22 251.056 8.9544 71 ......... 42.024 290.88 13.198 5.9218

17 ......... 16,708.304 166,198.69 238.163 8.9471 72 ......... 36.732 248.86 12.071 5.7749

18 ......... 15,039.078 149,490.38 224.715 8.9401 73 ......... 32.016 212.12 10.994 5.6256

19 ......... 13,535.639 134,451.31 211.636 8.9331 74 ......... 27.824 180.11 9.975 5.4732

20 ......... 12,181.990 120,915.67 199.356 8.9258 75 ......... 24.108 152.29 9.017 5.3167

21 ......... 10,963.368 108,733.68 187.959 8.9179 76 ......... 20.823 128.18 8.121 5.1555

22 ......... 9,866.137 97,770.31 177.187 8.9097 77 ......... 17.924 107.35 7.285 4.9895

23 ......... 8,878.435 87,904.17 167.211 8.9009 78 ......... 15.369 89.43 6.507 4.8188

24 ......... 7,989.439 79,025.74 158.060 8.8913 79 ......... 13.121 74.06 5.781 4.6445

25 ......... 7,189.375 71,036.30 149.742 8.8807 80 ......... 11.144 60.94 5.105 4.4685

26 ......... 6,469.289 63,846.92 142.116 8.8692 81 ......... 9.409 49.80 4.475 4.2922

27 ......... 5,821.318 57,377.63 135.246 8.8565 82 ......... 7.893 40.39 3.891 4.1165

28 ......... 5,238.026 51,556.32 128.841 8.8427 83 ......... 6.575 32.49 3.355 3.9418

29 ......... 4,712.978 46,318.29 122.877 8.8278 84 ......... 5.437 25.92 2.869 3.7666

30 ......... 4,240.291 41,605.31 117.242 8.8119 85 ......... 4.462 20.48 2.433 3.5897

31 ......... 3,814.730 37,365.02 111.890 8.7949 86 ......... 3.630 16.02 2.043 3.4128

32 ......... 3,431.624 33,550.29 106.820 8.7768 87 ......... 2.923 12.39 1.695 3.2387

33 ......... 3,086.794 30,118.67 102.061 8.7573 88 ......... 2.327 9.47 1.389 3.0677

34 ......... 2,776.378 27,031.87 97.543 8.7364 89 ......... 1.830 7.14 1.123 2.9001

35 ......... 2,497.015 24,255.50 93.318 8.7138 90 ......... 1.421 5.31 0.895 2.7359

36 ......... 2,245.546 21,758.48 89.301 8.6896 91 ......... 1.086 3.89 0.701 2.5785

37 ......... 2,019.207 19,512.93 85.492 8.6637 92 ......... 0.816 2.80 0.539 2.4314

38 ......... 1,815.523 17,493.73 81.910 8.6356 93 ......... 0.602 1.98 0.406 2.2947

39 ......... 1,632.208 15,678.21 78.512 8.6055 94 ......... 0.437 1.38 0.300 2.1664

40 ......... 1,467.257 14,046.00 75.312 8.5730 95 ......... 0.311 0.95 0.217 2.0435

41 ......... 1,318.846 12,578.74 72.304 8.5377 96 ......... 0.217 0.64 0.154 1.9270

42 ......... 1,185.303 11,259.89 69.457 8.4996 97 ......... 0.148 0.42 0.107 1.8190

43 ......... 1,065.129 10,074.59 66.746 8.4586 95 ......... 0.099 0.27 0.073 1.7172

44 ......... 956.981 9,009.46 64.152 8.4145 99 ......... 0.065 0.17 0.048 1.6173

45 ......... 859.616 8,052.48 61.623 8.3675 100 ......... 0.042 0.11 0.031 1.5196

46 ......... 771.970 7,192.87 59.163 8.3175 101 ......... 0.026 0.06 0.020 1.4241

47 ......... 693.045 6,420.90 56.740 8.2648 102 ......... 0.016 0.04 0.012 1.3309

48 ......... 621.995 5,727.85 54.371 8.2088 103 ......... 0.010 0.02 0.007 1.2400

49 ......... 558.035 5,105.85 52.049 8.1497 104 ......... 0.005 0.01 0.004 1.1515

50 ......... 500.475 4,547.82 49.790 8.0870 105 ......... 0.003 0.01 0.002 1.0653

51 ......... 448.672 4,047.35 47.583 8.0207 106 ......... 0.002 0.00 0.001 0.9815

52 ......... 402.036 3,598.67 45.411 7.9511 107 ......... 0.001 0.00 0.001 0.9001

53 ......... 360.060 3,196.64 43.276 7.8781 108 ......... 0.000 0.00 0.000 0.8211

54 ......... 322.279 2,836.58 41.177 7.8016 109 ......... 0.000 0.00 0.000 0.7445

x x x x x x x x

14
Table 1.L. -- Actuarial Functions at 12.0 Percent Interest for 1989-91 United States 

Total Population

x D N M a x D N M a

0 ......... 100,000.000 921,778.75 1,237.991 8.2178 55 ......... 176.035 1,444.68 21.247 7.2068

1 ......... 88,450.000 821,778.75 402.277 8.2909 56 ......... 155.959 1,268.65 20.032 7.1345

2 ......... 78,915.816 733,328.75 344.879 8.2925 57 ......... 138.073 1,112.69 18.857 7.0587

3 ......... 70,426.385 654,412.93 310.713 8.2922 58 ......... 122.138 974.61 17.715 6.9796

4 ......... 62,857.187 583,986.55 287.199 8.2907 59 ......... 107.940 852.48 16.603 6.8977

5 ......... 56,105.465 521,129.36 270.177 8.2884 60 ......... 95.296 744.54 15.524 6.8129

6 ......... 50,080.486 465,023.90 256.497 8.2855 61 ......... 84.044 649.24 14.482 6.7250

7 ......... 44,703.864 414,943.41 245.641 8.2820 62 ......... 74.043 565.20 13.486 6.6334

8 ......... 39,904.875 370,239.55 236.352 8.2781 63 ......... 65.159 491.15 12.535 6.5378

9 ......... 35,622.140 330,334.67 229.140 8.2733 64 ......... 57.270 426.00 11.627 6.4384

10 ......... 31,800.009 294,712.53 223.666 8.2677 65 ......... 50.269 368.73 10.763 6.3351

11 ......... 28,388.265 262,912.52 219.066 8.2613 66 ......... 44.063 318.46 9.942 6.2273

12 ......... 25,342.559 234,524.26 214.960 8.2542 67 ......... 38.568 274.39 9.169 6.1145

13 ......... 22,622.472 209,181.70 210.147 8.2466 68 ......... 33.705 235.83 8.438 5.9967

14 ......... 20,192.088 186,559.23 203.599 8.2392 69 ......... 29.403 202.12 7.747 5.8743

15 ......... 18,020.246 166,367.14 195.195 8.2322 70 ......... 25.596 172.72 7.091 5.7478

16 ......... 16,079.392 148,346.89 185.082 8.2259 71 ......... 22.230 147.12 6.467 5.6180

17 ......... 14,345.531 132,267.50 174.013 8.2201 72 ......... 19.258 124.89 5.876 5.4853

18 ......... 12,797.066 117,921.97 162.569 8.2148 73 ......... 16.635 105.63 5.317 5.3500

19 ......... 11,414.922 105,124.91 151.539 8.2094 74 ......... 14.328 89.00 4.792 5.2115

20 ......... 10,181.631 93,709.98 141.276 8.2038 75 ......... 12.304 74.67 4.303 5.0689

21 ......... 9,081.301 83,528.35 131.835 8.1978 76 ......... 10.532 62.37 3.850 4.9215

22 ......... 8,099.462 74,447.05 122.992 8.1916 77 ......... 8.985 51.83 3.431 4.7691

23 ......... 7,223.546 66,347.59 114.875 8.1849 78 ......... 7.636 42.85 3.044 4.6119

24 ......... 6,442.216 59,124.04 107.497 8.1776 79 ......... 6.460 35.21 2.687 4.4509

25 ......... 5,745.331 52,681.83 100.850 8.1695 80 ......... 5.438 28.75 2.357 4.2877

26 ......... 5,123.720 46,936.50 94.810 8.1606 81 ......... 4.551 23.32 2.052 4.1238

27 ......... 4,569.357 41,812.78 89.417 8.1507 82 ......... 3.783 18.77 1.773 3.9601

28 ......... 4,074.801 37,243.42 84.435 8.1399 83 ......... 3.123 14.98 1.518 3.7969

29 ......... 3,633.617 33,168.62 79.836 8.1283 84 ......... 2.560 11.86 1.289 3.6327

30 ......... 3,239.995 29,535.00 75.531 8.1158 85 ......... 2.082 9.30 1.086 3.4664

31 ......... 2,888.800 26,295.01 71.478 8.1024 86 ......... 1.679 7.22 0.905 3.2996

32 ......... 2,575.480 23,406.21 67.673 8.0881 87 ......... 1.339 5.54 0.746 3.1350

33 ......... 2,295.996 20,830.73 64.133 8.0726 88 ......... 1.057 4.20 0.607 2.9730

34 ......... 2,046.666 18,534.73 60.802 8.0561 89 ......... 0.824 3.14 0.487 2.8137

35 ......... 1,824.293 16,488.06 57.715 8.0381 90 ......... 0.634 2.32 0.385 2.6573

36 ......... 1,625.925 14,663.77 54.807 8.0187 91 ......... 0.480 1.68 0.300 2.5069

37 ......... 1,448.986 13,037.85 52.074 7.9979 92 ......... 0.358 1.20 0.229 2.3663

38 ......... 1,291.189 11,588.86 49.526 7.9753 93 ......... 0.262 0.85 0.171 2.2353

39 ......... 1,150.452 10,297.67 47.131 7.9510 94 ......... 0.188 0.58 0.125 2.1122

40 ......... 1,024.954 9,147.22 44.895 7.9245 95 ......... 0.133 0.40 0.090 1.9941

41 ......... 913.056 8,122.26 42.813 7.8957 96 ......... 0.092 0.26 0.063 1.8819

42 ......... 813.275 7,209.21 40.860 7.8644 97 ......... 0.062 0.17 0.044 1.7779

43 ......... 724.295 6,395.93 39.016 7.8306 95 ......... 0.041 0.11 0.029 1.6796

44 ......... 644.943 5,671.64 37.268 7.7940 99 ......... 0.027 0.07 0.019 1.5832

45 ......... 574.153 5,026.69 35.579 7.7550 100 ......... 0.017 0.04 0.013 1.4887

46 ......... 511.009 4,452.54 33.951 7.7132 101 ......... 0.011 0.03 0.008 1.3961

47 ......... 454.668 3,941.53 32.361 7.6690 102 ......... 0.006 0.01 0.005 1.3057

48 ......... 404.413 3,486.86 30.820 7.6220 103 ......... 0.004 0.01 0.003 1.2174

49 ......... 359.587 3,082.45 29.324 7.5722 104 ......... 0.002 0.00 0.002 1.1312

50 ......... 319.617 2,722.86 27.881 7.5191 105 ......... 0.001 0.00 0.001 1.0473

51 ......... 283.976 2,403.25 26.485 7.4629 106 ......... 0.001 0.00 0.001 0.9655

52 ......... 252.187 2,119.27 25.122 7.4036 107 ......... 0.000 0.00 0.000 0.8860

53 ......... 223.840 1,867.08 23.795 7.3412 108 ......... 0.000 0.00 0.000 0.8087

54 ......... 198.564 1,643.24 22.502 7.2757 109 ......... 0.000 0.00 0.000 0.7337

x x x x x x x x

15
Table 2.A. -- Actuarial Functions at 1.0 Percent Interest for 1989-91 United States 

Total Males

x D N M a x D N M a

0 ......... 100,000.000 5,096,485.43 49,539.748 49.9649 55 ......... 50,038.051 1,004,020.66 40,097.252 19.0651

1 ......... 97,981.188 4,996,485.43 48,511.035 49.9943 56 ......... 49,049.443 953,982.61 39,604.071 18.4494

2 ......... 96,935.595 4,898,504.25 48,435.553 49.5336 57 ......... 48,034.674 904,933.17 39,074.940 17.8392

3 ......... 95,923.424 4,801,568.65 48,383.141 49.0563 58 ......... 46,989.709 856,898.49 38,505.565 17.2359

4 ......... 94,934.287 4,705,645.23 48,343.740 48.5674 59 ......... 45,910.135 809,908.78 37,891.236 16.6412

5 ......... 93,961.043 4,610,710.94 48,310.439 48.0705 60 ......... 44,794.489 763,998.65 37,230.146 16.0556

6 ......... 93,002.474 4,516,749.90 48,282.178 47.5659 61 ......... 43,645.205 719,204.16 36,524.371 15.4784

7 ......... 92,055.541 4,423,747.42 48,256.062 47.0552 62 ......... 42,465.723 675,558.96 35,777.020 14.9083

8 ......... 91,120.090 4,331,691.88 48,232.051 46.5383 63 ......... 41,255.632 633,093.23 34,987.383 14.3456

9 ......... 90,196.881 4,240,571.79 48,211.021 46.0146 64 ......... 40,014.560 591,837.60 34,154.782 13.7906

10 ......... 89,285.736 4,150,374.91 48,192.916 45.4842 65 ......... 38,741.122 551,823.04 33,277.528 13.2439

11 ......... 88,387.378 4,061,089.18 48,178.574 44.9465 66 ......... 37,438.160 513,081.92 32,358.141 12.7048

12 ......... 87,497.169 3,972,701.80 48,163.488 44.4038 67 ......... 36,108.941 475,643.76 31,399.597 12.1725

13 ......... 86,608.894 3,885,204.63 48,141.521 43.8592 68 ......... 34,752.556 439,534.82 30,400.726 11.6476

14 ......... 85,715.711 3,798,595.74 48,105.853 43.3162 69 ......... 33,366.141 404,782.26 29,358.396 11.1315

15 ......... 84,811.915 3,712,880.02 48,050.726 42.7778 70 ......... 31,945.471 371,416.12 28,268.083 10.6266

16 ......... 83,897.144 3,628,068.11 47,975.678 42.2442 71 ......... 30,487.988 339,470.65 27,126.893 10.1346

17 ......... 82,973.598 3,544,170.97 47,882.797 41.7144 72 ......... 28,995.662 308,982.66 25,936.428 9.6562

18 ......... 82,045.067 3,461,197.37 47,775.786 41.1865 73 ......... 27,471.375 279,987.00 24,699.227 9.1920

19 ......... 81,117.684 3,379,152.30 47,660.730 40.6574 74 ......... 25,923.670 252,515.62 23,423.515 8.7407

20 ......... 80,195.705 3,298,034.62 47,541.897 40.1248 75 ......... 24,363.144 226,591.95 22,119.659 8.3006

21 ......... 79,279.162 3,217,838.91 47,419.371 39.5887 76 ......... 22,797.179 202,228.81 20,794.913 7.8708

22 ......... 78,367.283 3,138,559.75 47,292.434 39.0494 77 ......... 21,230.088 179,431.63 19,453.537 7.4518

23 ......... 77,462.508 3,060,192.47 47,163.572 38.5055 78 ......... 19,668.324 158,201.54 18,101.972 7.0435

24 ......... 76,564.816 2,982,729.96 47,032.836 37.9569 79 ......... 18,116.269 138,533.22 16,744.653 6.6469

25 ......... 75,675.748 2,906,165.14 46,901.835 37.4029 80 ......... 16,578.133 120,416.95 15,385.886 6.2636

26 ......... 74,796.007 2,830,489.39 46,771.359 36.8428 81 ......... 15,054.386 103,838.82 14,026.279 5.8976

27 ......... 73,924.739 2,755,693.39 46,640.646 36.2770 82 ......... 13,552.112 88,784.43 12,673.058 5.5513

28 ......... 73,061.122 2,681,768.65 46,508.957 35.7058 83 ......... 12,088.180 75,232.32 11,343.306 5.2236

29 ......... 72,202.863 2,608,707.53 46,374.075 35.1303 84 ......... 10,685.723 63,144.14 10,060.533 4.9092

30 ......... 71,347.759 2,536,504.66 46,233.852 34.5513 85 ......... 9,363.505 52,458.42 8,844.115 4.6024

31 ......... 70,496.634 2,465,156.91 46,089.140 33.9684 86 ......... 8,123.369 43,094.91 7,696.686 4.3051

32 ......... 69,648.823 2,394,660.27 45,939.315 33.3819 87 ......... 6,963.254 34,971.54 6,617.001 4.0223

33 ......... 68,804.409 2,325,011.45 45,784.493 32.7916 88 ......... 5,890.305 28,008.29 5,612.995 3.7550

34 ......... 67,963.471 2,256,207.04 45,624.787 32.1973 89 ......... 4,912.578 22,117.98 4,693.588 3.5023

35 ......... 67,126.087 2,188,243.57 45,460.309 31.5990 90 ......... 4,034.088 17,205.40 3,863.738 3.2650

36 ......... 66,290.236 2,121,117.48 45,289.073 30.9974 91 ......... 3,257.021 13,171.32 3,126.612 3.0440

37 ......... 65,457.436 2,054,827.25 45,112.611 30.3918 92 ......... 2,579.818 9,914.30 2,481.657 2.8430

38 ......... 64,626.406 1,989,369.81 44,929.675 29.7826 93 ......... 2,002.514 7,334.48 1,929.896 2.6626

39 ......... 63,798.632 1,924,743.40 44,741.767 29.1690 94 ......... 1,523.514 5,331.96 1,470.722 2.4998

40 ......... 62,974.870 1,860,944.77 44,549.674 28.5506 95 ......... 1,137.345 3,808.45 1,099.638 2.3485

41 ......... 62,155.180 1,797,969.90 44,353.498 27.9271 96 ......... 833.257 2,671.10 806.811 2.2056

42 ......... 61,337.648 1,735,814.72 44,151.364 27.2993 97 ......... 597.833 1,837.85 579.637 2.0742

43 ......... 60,521.085 1,674,477.07 43,942.104 26.6677 95 ......... 420.596 1,240.01 408.319 1.9482

44 ......... 59,703.060 1,613,955.99 43,723.298 26.0331 99 ......... 289.878 819.42 281.765 1.8268

45 ......... 58,881.881 1,554,252.93 43,493.238 25.3961 100 ......... 195.424 529.54 190.181 1.7097

46 ......... 58,052.761 1,495,371.05 43,247.107 24.7588 101 ......... 128.661 334.12 125.352 1.5969

47 ......... 57,215.493 1,437,318.29 42,984.619 24.1211 102 ......... 82.571 205.45 80.537 1.4882

48 ......... 56,367.405 1,380,102.79 42,703.021 23.4841 103 ......... 51.554 122.88 50.337 1.3836

49 ......... 55,509.622 1,323,735.39 42,403.331 22.8470 104 ......... 31.245 71.33 30.539 1.2829

50 ......... 54,641.409 1,268,225.77 42,084.718 22.2100 105 ......... 18.337 40.09 17.940 1.1861

51 ......... 53,759.060 1,213,584.36 41,743.374 21.5745 106 ......... 10.392 21.75 10.176 1.0929

52 ......... 52,860.813 1,159,825.30 41,377.394 20.9411 107 ......... 5.669 11.36 5.557 1.0033

53 ......... 51,942.034 1,106,964.49 40,981.989 20.3115 108 ......... 2.967 5.69 2.910 0.9171

54 ......... 51,001.792 1,055,022.45 40,556.025 19.6860 109 ......... 1.483 2.72 1.456 0.8344

x x x x x x x x

16
Table 2.B. -- Actuarial Functions at 2.0 Percent Interest for 1989-91 United States 

Total Males

x D N M a x D N M a

0 ......... 100,000.000 3,786,852.47 25,747.991 36.8685 55 ......... 29,104.926 518,932.45 18,929.779 16.8297

1 ......... 97,020.588 3,686,852.47 24,729.363 37.0007 56 ......... 28,250.192 489,827.53 18,645.730 16.3389

2 ......... 95,044.214 3,589,831.88 24,655.353 36.7701 57 ......... 27,394.499 461,577.34 18,343.963 15.8493

3 ......... 93,129.716 3,494,787.66 24,604.468 36.5260 58 ......... 26,535.817 434,182.84 18,022.428 15.3621

4 ......... 91,265.766 3,401,657.95 24,566.590 36.2720 59 ......... 25,671.987 407,647.02 17,678.908 14.8791

5 ......... 89,444.540 3,310,392.18 24,534.890 36.0106 60 ......... 24,802.571 381,975.03 17,312.865 14.4006

6 ......... 87,664.087 3,220,947.64 24,508.251 35.7419 61 ......... 23,929.292 357,172.46 16,925.911 13.9262

7 ......... 85,920.807 3,133,283.56 24,483.875 35.4671 62 ......... 23,054.359 333,243.17 16,520.179 13.4547

8 ......... 84,213.895 3,047,362.75 24,461.684 35.1860 63 ......... 22,177.826 310,188.81 16,095.693 12.9864

9 ......... 82,543.397 2,963,148.85 24,442.439 34.8981 64 ......... 21,299.773 288,010.98 15,652.499 12.5218

10 ......... 80,908.492 2,880,605.46 24,426.032 34.6033 65 ......... 20,419.746 266,711.21 15,190.114 12.0614

11 ......... 79,309.183 2,799,696.96 24,413.164 34.3010 66 ......... 19,539.517 246,291.46 14,710.273 11.6048

12 ......... 77,740.696 2,720,387.78 24,399.759 33.9931 67 ......... 18,661.016 226,751.95 14,214.899 11.1511

13 ......... 76,197.043 2,642,647.09 24,380.433 33.6818 68 ......... 17,783.961 208,090.93 13,703.746 10.7010

14 ......... 74,671.910 2,566,450.04 24,349.361 33.3697 69 ......... 16,907.092 190,306.97 13,175.583 10.2560

15 ......... 73,160.202 2,491,778.13 24,301.808 33.0592 70 ......... 16,028.520 173,399.88 12,628.523 9.8182

16 ......... 71,661.585 2,418,617.93 24,237.704 32.7506 71 ......... 15,147.261 157,371.36 12,061.548 9.3894

17 ......... 70,177.898 2,346,956.34 24,159.147 32.4430 72 ......... 14,264.599 142,224.10 11,475.891 8.9704

18 ......... 68,712.241 2,276,778.45 24,069.526 32.1350 73 ......... 13,382.220 127,959.50 10,873.210 8.5619

19 ......... 67,269.528 2,208,066.21 23,974.112 31.8242 74 ......... 12,504.474 114,577.28 10,257.861 8.1629

20 ......... 65,852.937 2,140,796.68 23,876.531 31.5088 75 ......... 11,636.530 102,072.80 9,635.102 7.7718

21 ......... 64,462.077 2,074,943.74 23,776.905 31.1886 76 ......... 10,781.829 90,436.27 9,008.569 7.3878

22 ......... 63,095.914 2,010,481.66 23,674.705 30.8639 77 ......... 9,942.242 79,654.45 8,380.391 7.0117

23 ......... 61,756.006 1,947,385.75 23,571.971 30.5335 78 ......... 9,120.552 69,712.20 7,753.646 6.6434

24 ......... 60,441.898 1,885,629.74 23,468.766 30.1974 79 ......... 8,318.475 60,591.65 7,130.404 6.2840

25 ......... 59,154.361 1,825,187.85 23,366.364 29.8547 80 ......... 7,537.577 52,273.18 6,512.613 5.9350

26 ......... 57,893.481 1,766,033.49 23,265.374 29.5049 81 ......... 6,777.670 44,735.60 5,900.501 5.6004

27 ......... 56,658.132 1,708,140.00 23,165.191 29.1482 82 ......... 6,041.511 37,957.93 5,297.237 5.2829

28 ......... 55,447.247 1,651,481.87 23,065.250 28.7847 83 ......... 5,336.060 31,916.42 4,710.248 4.9813

29 ......... 54,258.686 1,596,034.62 22,963.890 28.4153 84 ......... 4,670.731 26,580.36 4,149.548 4.6908

30 ......... 53,090.449 1,541,775.94 22,859.548 28.0406 85 ......... 4,052.664 21,909.63 3,623.064 4.4062

31 ......... 51,942.834 1,488,685.49 22,752.923 27.6601 86 ......... 3,481.445 17,856.96 3,131.308 4.1292

32 ......... 50,815.037 1,436,742.65 22,643.612 27.2740 87 ......... 2,954.995 14,375.52 2,673.123 3.8648

33 ......... 49,706.815 1,385,927.62 22,531.763 26.8820 88 ......... 2,475.162 11,420.52 2,251.230 3.6141

34 ......... 48,617.925 1,336,220.80 22,417.517 26.4841 89 ......... 2,044.073 8,945.36 1,868.674 3.3762

35 ......... 47,548.126 1,287,602.88 22,301.011 26.0800 90 ......... 1,662.086 6,901.29 1,526.767 3.1522

36 ......... 46,495.705 1,240,054.75 22,180.906 25.6703 91 ......... 1,328.770 5,239.20 1,226.041 2.9429

37 ......... 45,461.469 1,193,559.05 22,058.350 25.2543 92 ......... 1,042.173 3,910.43 965.498 2.7522

38 ......... 44,444.260 1,148,097.58 21,932.543 24.8323 93 ......... 801.027 2,868.26 744.787 2.5807

39 ......... 43,444.845 1,103,653.32 21,804.583 24.4036 94 ......... 603.447 2,067.23 562.913 2.4257

40 ......... 42,463.458 1,060,208.47 21,675.057 23.9675 95 ......... 446.073 1,463.78 417.372 2.2815

41 ......... 41,499.858 1,017,745.02 21,544.074 23.5241 96 ......... 323.604 1,017.71 303.649 2.1449

42 ......... 40,552.497 976,245.16 21,410.435 23.0736 97 ......... 229.899 694.10 216.289 2.0192

43 ......... 39,620.358 935,692.66 21,273.443 22.6165 95 ......... 160.156 464.21 151.054 1.8985

44 ......... 38,701.650 896,072.30 21,131.605 22.1533 99 ......... 109.299 304.05 103.337 1.7818

45 ......... 37,795.123 857,370.65 20,983.934 21.6847 100 ......... 72.962 194.75 69.144 1.6692

46 ......... 36,897.605 819,575.53 20,827.496 21.2122 101 ......... 47.565 121.79 45.177 1.5605

47 ......... 36,008.924 782,677.92 20,662.298 20.7357 102 ......... 30.227 74.22 28.771 1.4556

48 ......... 35,127.378 746,669.00 20,486.810 20.2560 103 ......... 18.687 44.00 17.824 1.3544

49 ......... 34,253.674 711,541.62 20,301.878 19.7727 104 ......... 11.215 25.31 10.718 1.2569

50 ......... 33,387.353 677,287.95 20,107.197 19.2858 105 ......... 6.517 14.10 6.241 1.1629

51 ......... 32,526.173 643,900.60 19,900.671 18.7964 106 ......... 3.657 7.58 3.508 1.0724

52 ......... 31,669.145 611,374.42 19,681.411 18.3050 107 ......... 1.976 3.92 1.899 0.9852

53 ......... 30,813.615 579,705.28 19,446.845 17.8133 108 ......... 1.024 1.95 0.986 0.9013

54 ......... 29,959.209 548,891.66 19,196.627 17.3213 109 ......... 0.507 0.92 0.489 0.8206

x x x x x x x x

17
Table 2.C. -- Actuarial Functions at 3.0 Percent Interest for 1989-91 United States 

Total Males

x D N M a x D N M a

0 ......... 100,000.000 2,946,045.96 14,192.836 28.4605 55 ......... 17,018.786 272,008.63 9,096.205 14.9828

1 ......... 96,078.641 2,846,045.96 13,184.098 28.6220 56 ......... 16,358.611 254,989.84 8,931.723 14.5875

2 ......... 93,207.654 2,749,967.32 13,111.518 28.5037 57 ......... 15,709.102 238,631.23 8,758.677 14.1906

3 ......... 90,443.450 2,656,759.66 13,062.101 28.3748 58 ......... 15,068.964 222,922.13 8,576.086 13.7935

4 ......... 87,772.747 2,566,316.21 13,025.673 28.2382 59 ......... 14,436.881 207,853.17 8,382.905 13.3974

5 ......... 85,186.068 2,478,543.47 12,995.482 28.0956 60 ......... 13,812.539 193,416.29 8,179.055 13.0029

6 ......... 82,679.796 2,393,357.40 12,970.357 27.9473 61 ......... 13,196.830 179,603.75 7,965.653 12.6096

7 ......... 80,248.880 2,310,677.60 12,947.590 27.7939 62 ......... 12,590.871 166,406.92 7,744.067 12.2165

8 ......... 77,891.009 2,230,428.72 12,927.066 27.6353 63 ......... 11,994.569 153,816.05 7,514.490 11.8238

9 ......... 75,604.711 2,152,537.71 12,909.438 27.4709 64 ......... 11,407.844 141,821.48 7,277.122 11.4319

10 ......... 73,387.751 2,076,933.00 12,894.556 27.3008 65 ......... 10,830.335 130,413.63 7,031.880 11.0415

11 ......... 71,238.685 2,003,545.25 12,882.998 27.1244 66 ......... 10,262.858 119,583.30 6,779.850 10.6520

12 ......... 69,151.848 1,932,306.57 12,871.074 26.9429 67 ......... 9,706.278 109,320.44 6,522.188 10.2629

13 ......... 67,120.693 1,863,154.72 12,854.050 26.7583 68 ......... 9,160.283 99,614.16 6,258.900 9.8746

14 ......... 65,138.615 1,796,034.03 12,826.945 26.5725 69 ......... 8,624.070 90,453.88 5,989.491 9.4885

15 ......... 63,200.295 1,730,895.41 12,785.865 26.3875 70 ......... 8,096.545 81,829.81 5,713.152 9.1068

16 ......... 61,304.671 1,667,695.12 12,731.027 26.2034 71 ......... 7,577.106 73,733.26 5,429.535 8.7311

17 ......... 59,452.546 1,606,390.45 12,664.475 26.0197 72 ......... 7,066.295 66,156.16 5,139.417 8.3622

18 ......... 57,645.732 1,546,937.90 12,589.288 25.8353 73 ......... 6,564.827 59,089.86 4,843.763 8.0010

19 ......... 55,887.460 1,489,292.17 12,510.019 25.6481 74 ......... 6,074.682 52,525.04 4,544.826 7.6465

20 ......... 54,179.387 1,433,404.71 12,429.736 25.4566 75 ......... 5,598.150 46,450.35 4,245.227 7.2974

21 ......... 52,520.177 1,379,225.32 12,348.566 25.2609 76 ......... 5,136.608 40,852.20 3,946.738 6.9531

22 ......... 50,908.004 1,326,705.14 12,266.107 25.0608 77 ......... 4,690.631 35,715.60 3,650.371 6.6142

23 ......... 49,343.163 1,275,797.14 12,184.023 24.8556 78 ......... 4,261.191 31,024.97 3,357.551 6.2808

24 ......... 47,824.322 1,226,453.98 12,102.362 24.6450 79 ......... 3,848.722 26,763.77 3,069.195 5.9539

25 ......... 46,351.143 1,178,629.65 12,022.124 24.4283 80 ......... 3,453.564 22,915.05 2,786.136 5.6352

26 ......... 44,922.745 1,132,278.51 11,943.759 24.2050 81 ......... 3,075.241 19,461.49 2,508.401 5.3284

27 ......... 43,537.333 1,087,355.77 11,866.777 23.9752 82 ......... 2,714.608 16,386.25 2,237.339 5.0363

28 ......... 42,193.204 1,043,818.43 11,790.726 23.7390 83 ......... 2,374.353 13,671.64 1,976.150 4.7580

29 ......... 40,887.894 1,001,625.23 11,714.343 23.4969 84 ......... 2,058.128 11,297.29 1,729.081 4.4891

30 ......... 39,619.119 960,737.33 11,636.478 23.2493 85 ......... 1,768.443 9,239.16 1,499.342 4.2245

31 ......... 38,386.366 921,118.22 11,557.680 22.9960 86 ......... 1,504.433 7,470.71 1,286.840 3.9658

32 ......... 37,188.319 882,731.85 11,477.683 22.7368 87 ......... 1,264.542 5,966.28 1,090.767 3.7181

33 ......... 36,024.104 845,543.53 11,396.622 22.4716 88 ......... 1,048.921 4,701.74 911.977 3.4825

34 ......... 34,892.864 809,519.43 11,314.628 22.2001 89 ......... 857.825 3,652.82 751.432 3.2582

35 ......... 33,793.763 774,626.56 11,231.824 21.9222 90 ......... 690.747 2,794.99 609.339 3.0463

36 ......... 32,724.945 740,832.80 11,147.291 21.6382 91 ......... 546.862 2,104.25 485.574 2.8479

37 ......... 31,686.371 708,107.85 11,061.870 21.3474 92 ......... 424.748 1,557.38 379.387 2.6666

38 ......... 30,676.632 676,421.48 10,975.035 21.0501 93 ......... 323.297 1,132.64 290.307 2.5034

39 ......... 29,695.674 645,744.85 10,887.571 20.7454 94 ......... 241.188 809.34 217.615 2.3556

40 ......... 28,743.076 616,049.18 10,799.896 20.4330 95 ......... 176.558 568.15 160.010 2.2179

41 ......... 27,818.099 587,306.10 10,712.096 20.1124 96 ......... 126.840 391.59 115.435 2.0873

42 ......... 26,919.152 559,488.00 10,623.385 19.7840 97 ......... 89.236 264.75 81.525 1.9669

43 ......... 26,045.045 532,568.85 10,533.331 19.4480 95 ......... 61.562 175.52 56.450 1.8511

44 ......... 25,194.118 506,523.81 10,440.997 19.1048 99 ......... 41.605 113.95 38.286 1.7389

45 ......... 24,365.110 481,329.69 10,345.799 18.7549 100 ......... 27.504 72.35 25.397 1.6305

46 ......... 23,555.576 456,964.58 10,245.929 18.3994 101 ......... 17.756 44.85 16.450 1.5256

47 ......... 22,765.052 433,409.00 10,141.489 18.0383 102 ......... 11.174 27.09 10.385 1.4243

48 ......... 21,992.125 410,643.95 10,031.622 17.6723 103 ......... 6.841 15.92 6.378 1.3264

49 ......... 21,236.922 388,651.82 9,916.966 17.3008 104 ......... 4.066 9.07 3.801 1.2319

50 ......... 20,498.843 367,414.90 9,797.438 16.9237 105 ......... 2.340 5.01 2.194 1.1407

51 ......... 19,776.219 346,916.06 9,671.868 16.5421 106 ......... 1.300 2.67 1.222 1.0527

52 ......... 19,068.195 327,139.84 9,539.850 16.1563 107 ......... 0.696 1.37 0.656 0.9678

53 ......... 18,372.948 308,071.64 9,399.988 15.7677 108 ......... 0.357 0.67 0.337 0.8860

54 ......... 17,690.067 289,698.70 9,252.241 15.3763 109 ......... 0.175 0.32 0.166 0.8072

x x x x x x x x

18
Table 2.D. -- Actuarial Functions at 4.0 Percent Interest for 1989-91 United States 

Total Males

x D N M a x D N M a

0 ......... 100,000.000 2,381,747.04 8,394.344 22.8175 55 ......... 10,003.277 144,474.94 4,446.548 13.4428

1 ......... 95,154.808 2,281,747.04 7,395.306 22.9793 56 ......... 9,522.786 134,471.67 4,350.799 13.1210

2 ......... 91,423.817 2,186,592.24 7,324.115 22.9171 57 ......... 9,056.759 124,948.88 4,251.033 12.7962

3 ......... 87,859.510 2,095,168.42 7,276.109 22.8468 58 ......... 8,604.165 115,892.12 4,146.776 12.4693

4 ......... 84,445.251 2,007,308.91 7,241.062 22.7705 59 ......... 8,163.993 107,287.96 4,037.533 12.1416

5 ......... 81,168.590 1,922,863.66 7,212.295 22.6898 60 ......... 7,735.825 99,123.96 3,923.365 11.8136

6 ......... 78,023.011 1,841,695.07 7,188.586 22.6045 61 ......... 7,319.925 91,388.14 3,804.997 11.4848

7 ......... 75,000.848 1,763,672.06 7,167.308 22.5154 62 ......... 6,916.664 84,068.21 3,683.271 11.1544

8 ......... 72,097.203 1,688,671.21 7,148.310 22.4221 63 ......... 6,525.735 77,151.55 3,558.368 10.8227

9 ......... 69,308.074 1,616,574.01 7,132.150 22.3245 64 ......... 6,146.845 70,625.81 3,430.467 10.4898

10 ......... 66,628.867 1,547,265.93 7,118.639 22.2222 65 ......... 5,779.555 64,478.97 3,299.595 10.1564

11 ......... 64,055.825 1,480,637.07 7,108.246 22.1148 66 ......... 5,424.064 58,699.41 3,166.394 9.8220

12 ......... 61,581.522 1,416,581.24 7,097.628 22.0033 67 ......... 5,080.577 53,275.35 3,031.525 9.4861

13 ......... 59,197.987 1,354,999.72 7,082.613 21.8893 68 ......... 4,748.682 48,194.77 2,895.037 9.1491

14 ......... 56,897.465 1,295,801.73 7,058.937 21.7743 69 ......... 4,427.722 43,446.09 2,756.719 8.8123

15 ......... 54,673.564 1,238,904.27 7,023.400 21.6600 70 ......... 4,116.913 39,018.37 2,616.207 8.4776

16 ......... 52,523.751 1,184,230.70 6,976.416 21.5466 71 ......... 3,815.744 34,901.46 2,473.380 8.1467

17 ......... 50,447.135 1,131,706.95 6,919.945 21.4335 72 ......... 3,524.289 31,085.71 2,328.685 7.8204

18 ......... 48,443.677 1,081,259.82 6,856.760 21.3199 73 ......... 3,242.701 27,561.42 2,182.646 7.4995

19 ......... 46,514.483 1,032,816.14 6,790.785 21.2042 74 ......... 2,971.742 24,318.72 2,036.406 7.1833

20 ......... 44,659.288 986,301.66 6,724.609 21.0850 75 ......... 2,712.289 21,346.98 1,891.251 6.8705

21 ......... 42,875.359 941,642.37 6,658.345 20.9623 76 ......... 2,464.743 18,634.69 1,748.025 6.5605

22 ......... 41,159.638 898,767.01 6,591.676 20.8361 77 ......... 2,229.105 16,169.95 1,607.184 6.2540

23 ......... 39,510.848 857,607.37 6,525.949 20.7056 78 ......... 2,005.553 13,940.84 1,469.366 5.9511

24 ......... 37,926.439 818,096.52 6,461.188 20.5706 79 ......... 1,794.004 11,935.29 1,334.955 5.6529

25 ......... 36,404.711 780,170.08 6,398.169 20.4305 80 ......... 1,594.331 10,141.29 1,204.281 5.3608

26 ......... 34,943.573 743,765.37 6,337.212 20.2848 81 ......... 1,406.028 8,546.96 1,077.299 5.0788

27 ......... 33,540.284 708,821.80 6,277.907 20.1334 82 ......... 1,229.209 7,140.93 954.558 4.8094

28 ......... 32,192.248 675,281.52 6,219.882 19.9765 83 ......... 1,064.799 5,911.72 837.426 4.5520

29 ......... 30,896.367 643,089.27 6,162.164 19.8144 84 ......... 914.111 4,846.92 727.691 4.3023

30 ......... 29,649.773 612,192.90 6,103.892 19.6475 85 ......... 777.896 3,932.81 626.634 4.0557

31 ......... 28,450.994 582,543.13 6,045.489 19.4753 86 ......... 655.401 3,154.91 534.058 3.8137

32 ......... 27,298.004 554,092.14 5,986.768 19.2979 87 ......... 545.596 2,499.51 449.461 3.5813

33 ......... 26,189.150 526,794.13 5,927.837 19.1150 88 ......... 448.213 1,953.92 373.063 3.3593

34 ......... 25,122.839 500,604.98 5,868.802 18.9263 89 ......... 363.032 1,505.70 305.120 3.1476

35 ......... 24,097.531 475,482.14 5,809.756 18.7316 90 ......... 289.513 1,142.67 245.564 2.9469

36 ......... 23,111.004 451,384.61 5,750.057 18.5312 91 ......... 227.003 853.16 194.189 2.7584

37 ......... 22,162.373 428,273.61 5,690.311 18.3244 92 ......... 174.618 626.15 150.535 2.5859

38 ......... 21,249.823 406,111.24 5,630.160 18.1113 93 ......... 131.632 451.54 114.266 2.4303

39 ......... 20,372.518 384,861.41 5,570.156 17.8912 94 ......... 97.257 319.90 84.953 2.2893

40 ......... 19,529.389 364,488.89 5,510.585 17.6636 95 ......... 70.511 222.65 61.947 2.1576

41 ......... 18,719.177 344,959.51 5,451.504 17.4281 96 ......... 50.168 152.14 44.317 2.0325

42 ......... 17,940.088 326,240.33 5,392.383 17.1850 97 ......... 34.956 101.97 31.034 1.9171

43 ......... 17,190.646 308,300.24 5,332.944 16.9342 95 ......... 23.883 67.01 21.306 1.8058

44 ......... 16,469.109 291,109.59 5,272.586 16.6761 99 ......... 15.986 43.13 14.327 1.6980

45 ......... 15,774.050 274,640.49 5,210.955 16.4109 100 ......... 10.466 27.14 9.422 1.5935

46 ......... 15,103.321 258,866.44 5,146.920 16.1397 101 ......... 6.692 16.68 6.050 1.4923

47 ......... 14,456.104 243,763.11 5,080.600 15.8623 102 ......... 4.171 9.99 3.787 1.3943

48 ......... 13,831.004 229,307.01 5,011.503 15.5792 103 ......... 2.529 5.82 2.305 1.2995

49 ......... 13,227.627 215,476.01 4,940.089 15.2898 104 ......... 1.488 3.29 1.362 1.2078

50 ......... 12,645.139 202,248.38 4,866.355 14.9942 105 ......... 0.848 1.80 0.779 1.1192

51 ......... 12,082.072 189,603.24 4,789.640 14.6929 106 ......... 0.467 0.95 0.430 1.0336

52 ......... 11,537.498 177,521.17 4,709.761 14.3865 107 ......... 0.247 0.48 0.229 0.9510

53 ......... 11,009.936 165,983.67 4,625.948 14.0758 108 ......... 0.126 0.24 0.117 0.8712

54 ......... 10,498.791 154,973.73 4,538.263 13.7611 109 ......... 0.061 0.11 0.057 0.7942

x x x x x x x x

19
Table 2.E. -- Actuarial Functions at 5.0 Percent Interest for 1989-91 United States 

Total Males

x D N M a x D N M a

0 ......... 100,000.000 1,987,079.21 5,377.181 18.8708 55 ......... 5,909.687 77,695.33 2,209.910 12.1471

1 ......... 94,248.571 1,887,079.21 4,387.657 19.0224 56 ......... 5,572.246 71,785.64 2,153.882 11.8827

2 ......... 89,690.703 1,792,830.64 4,317.816 18.9890 57 ......... 5,249.079 66,213.40 2,096.060 11.6143

3 ......... 85,373.070 1,703,139.93 4,271.168 18.9494 58 ......... 4,939.274 60,964.32 2,036.211 11.3428

4 ......... 81,273.955 1,617,766.86 4,237.438 18.9051 59 ......... 4,641.956 56,025.04 1,974.096 11.0693

5 ......... 77,376.343 1,536,492.91 4,210.014 18.8574 60 ......... 4,356.614 51,383.09 1,909.800 10.7943

6 ......... 73,669.369 1,459,116.56 4,187.628 18.8063 61 ......... 4,083.129 47,026.47 1,843.773 10.5173

7 ......... 70,141.405 1,385,447.20 4,167.729 18.7522 62 ......... 3,821.441 42,943.35 1,776.520 10.2375

8 ......... 66,783.740 1,315,305.79 4,150.131 18.6950 63 ......... 3,571.116 39,121.90 1,708.168 9.9551

9 ......... 63,588.736 1,248,522.05 4,135.305 18.6343 64 ......... 3,331.738 35,550.79 1,638.843 9.6703

10 ......... 60,548.422 1,184,933.32 4,123.026 18.5700 65 ......... 3,102.823 32,219.05 1,568.583 9.3838

11 ......... 57,655.809 1,124,384.89 4,113.672 18.5017 66 ......... 2,884.240 29,116.23 1,497.753 9.0949

12 ......... 54,900.828 1,066,729.08 4,104.205 18.4301 67 ......... 2,675.862 26,231.99 1,426.720 8.8032

13 ......... 52,273.245 1,011,828.26 4,090.947 18.3565 68 ......... 2,477.239 23,556.12 1,355.518 8.5090

14 ......... 49,763.335 959,555.01 4,070.240 18.2824 69 ......... 2,287.806 21,078.89 1,284.049 8.2136

15 ......... 47,362.868 909,791.67 4,039.454 18.2090 70 ......... 2,106.951 18,791.08 1,212.138 7.9186

16 ......... 45,067.179 862,428.81 3,999.141 18.1365 71 ......... 1,934.221 16,684.13 1,139.739 7.6258

17 ......... 42,873.130 817,361.63 3,951.148 18.0647 72 ......... 1,769.467 14,749.91 1,067.090 7.3358

18 ......... 40,778.366 774,488.50 3,897.961 17.9926 73 ......... 1,612.582 12,980.44 994.466 7.0495

19 ......... 38,781.532 733,710.13 3,842.954 17.9191 74 ......... 1,463.760 11,367.86 922.434 6.7662

20 ......... 36,880.143 694,928.60 3,788.305 17.8429 75 ......... 1,323.241 9,904.10 851.617 6.4847

21 ......... 35,069.746 658,048.46 3,734.105 17.7640 76 ......... 1,191.019 8,580.86 782.407 6.2046

22 ......... 33,345.746 622,978.71 3,680.093 17.6824 77 ......... 1,066.895 7,389.84 714.998 5.9265

23 ......... 31,705.110 589,632.96 3,627.350 17.5974 78 ......... 950.756 6,322.94 649.664 5.6504

24 ......... 30,143.872 557,927.85 3,575.879 17.5088 79 ......... 842.370 5,372.19 586.551 5.3775

25 ......... 28,658.839 527,783.98 3,526.268 17.4161 80 ......... 741.484 4,529.82 525.778 5.1091

26 ......... 27,246.602 499,125.14 3,478.738 17.3188 81 ......... 647.681 3,788.33 467.284 4.8491

27 ......... 25,903.343 471,878.54 3,432.936 17.2169 82 ......... 560.838 3,140.65 411.283 4.5999

28 ......... 24,625.464 445,975.20 3,388.550 17.1103 83 ......... 481.197 2,579.82 358.349 4.3612

29 ......... 23,409.093 421,349.73 3,344.820 16.9994 84 ......... 409.165 2,098.62 309.230 4.1290

30 ......... 22,250.644 397,940.64 3,301.089 16.8845 85 ......... 344.877 1,689.45 264.427 3.8987

31 ......... 21,147.678 375,690.00 3,257.679 16.7651 86 ......... 287.803 1,344.58 223.775 3.6719

32 ......... 20,097.414 354,542.32 3,214.446 16.6412 87 ......... 237.303 1,056.77 186.980 3.4533

33 ......... 19,097.421 334,444.91 3,171.474 16.5126 88 ......... 193.090 819.47 154.068 3.2440

34 ......... 18,145.381 315,347.48 3,128.834 16.3789 89 ......... 154.905 626.38 125.077 3.0437

35 ......... 17,239.075 297,202.10 3,086.593 16.2400 90 ......... 122.358 471.48 99.907 2.8533

36 ......... 16,375.865 279,963.03 3,044.292 16.0961 91 ......... 95.025 349.12 78.401 2.6740

37 ......... 15,554.131 263,587.16 3,002.361 15.9464 92 ......... 72.400 254.09 60.301 2.5096

38 ......... 14,771.644 248,033.03 2,960.548 15.7912 93 ......... 54.058 181.69 45.406 2.3611

39 ......... 14,026.919 233,261.39 2,919.234 15.6296 94 ......... 39.560 127.64 33.483 2.2263

40 ......... 13,318.345 219,234.47 2,878.609 15.4611 95 ......... 28.408 88.07 24.214 2.1004

41 ......... 12,644.230 205,916.12 2,838.701 15.2854 96 ......... 20.020 59.67 17.178 1.9804

42 ......... 12,002.570 193,271.89 2,799.147 15.1025 97 ......... 13.816 39.65 11.928 1.8696

43 ......... 11,391.631 181,269.32 2,759.759 14.9125 95 ......... 9.350 25.83 8.120 1.7627

44 ......... 10,809.557 169,877.69 2,720.143 14.7155 99 ......... 6.199 16.48 5.414 1.6588

45 ......... 10,254.749 159,068.14 2,680.076 14.5117 100 ......... 4.020 10.28 3.530 1.5580

46 ......... 9,725.195 148,813.39 2,638.843 14.3018 101 ......... 2.546 6.26 2.247 1.4603

47 ......... 9,219.793 139,088.19 2,596.545 14.0858 102 ......... 1.571 3.72 1.394 1.3655

48 ......... 8,737.106 129,868.40 2,552.897 13.8640 103 ......... 0.944 2.15 0.842 1.2736

49 ......... 8,276.371 121,131.29 2,508.214 13.6358 104 ......... 0.550 1.20 0.493 1.1847

50 ......... 7,836.563 112,854.92 2,462.519 13.4011 105 ......... 0.311 0.65 0.280 1.0986

51 ......... 7,416.303 105,018.36 2,415.429 13.1605 106 ......... 0.169 0.34 0.153 1.0153

52 ......... 7,014.581 97,602.06 2,366.864 12.9142 107 ......... 0.089 0.17 0.081 0.9347

53 ......... 6,630.082 90,587.48 2,316.393 12.6631 108 ......... 0.045 0.08 0.041 0.8568

54 ......... 6,262.063 83,957.39 2,264.092 12.4073 109 ......... 0.022 0.04 0.020 0.7816

x x x x x x x x

20
Table 2.F. -- Actuarial Functions at 6.0 Percent Interest for 1989-91 United States 

Total Males

x D N M a x D N M a

0 ......... 100,000.000 1,700,542.92 3,742.853 16.0054 55 ......... 3,508.757 42,273.32 1,115.928 11.0479

1 ......... 93,359.434 1,600,542.92 2,762.665 16.1439 56 ......... 3,277.197 38,764.57 1,082.976 10.8286

2 ......... 88,006.408 1,507,183.49 2,694.135 16.1258 57 ......... 3,058.010 35,487.37 1,049.291 10.6047

3 ......... 82,979.574 1,419,177.08 2,648.796 16.1027 58 ......... 2,850.377 32,429.36 1,014.753 10.3772

4 ......... 78,250.141 1,336,197.51 2,616.320 16.0760 59 ......... 2,653.527 29,578.98 979.245 10.1470

5 ......... 73,794.734 1,257,947.37 2,590.166 16.0466 60 ......... 2,466.920 26,925.45 942.838 9.9146

6 ......... 69,596.524 1,184,152.63 2,569.017 16.0145 61 ......... 2,290.248 24,458.53 905.803 9.6794

7 ......... 65,638.477 1,114,556.11 2,550.395 15.9802 62 ......... 2,123.245 22,168.29 868.436 9.4408

8 ......... 61,906.779 1,048,917.63 2,534.083 15.9435 63 ......... 1,965.442 20,045.04 830.817 9.1987

9 ......... 58,389.008 987,010.85 2,520.469 15.9041 64 ......... 1,816.396 18,079.60 793.023 8.9536

10 ......... 55,072.802 928,621.85 2,509.301 15.8617 65 ......... 1,675.638 16,263.20 755.080 8.7057

11 ......... 51,947.045 873,549.04 2,500.872 15.8161 66 ......... 1,542.901 14,587.57 717.190 8.4546

12 ......... 48,998.197 821,602.00 2,492.424 15.7680 67 ......... 1,417.927 13,044.66 679.550 8.1998

13 ......... 46,212.994 772,603.80 2,480.703 15.7183 68 ......... 1,300.293 11,626.74 642.176 7.9416

14 ......... 43,579.029 726,390.81 2,462.569 15.6684 69 ......... 1,189.532 10,326.44 605.016 7.6811

15 ......... 41,085.587 682,811.78 2,435.864 15.6193 70 ......... 1,085.163 9,136.91 567.979 7.4199

16 ......... 38,725.347 641,726.19 2,401.223 15.5712 71 ......... 986.802 8,051.75 531.042 7.1594

17 ......... 36,492.496 603,000.84 2,360.373 15.5240 72 ......... 894.231 7,064.95 494.328 6.9006

18 ......... 34,382.039 566,508.35 2,315.529 15.4769 73 ......... 807.258 6,170.72 457.972 6.6440

19 ......... 32,389.945 532,126.31 2,269.587 15.4288 74 ......... 725.845 5,363.46 422.253 6.3893

20 ......... 30,511.340 499,736.37 2,224.376 15.3787 75 ......... 649.975 4,637.61 387.468 6.1351

21 ......... 28,739.865 469,225.03 2,179.958 15.3266 76 ......... 579.508 3,987.64 353.793 5.8811

22 ......... 27,069.235 440,485.16 2,136.112 15.2725 77 ......... 514.216 3,408.13 321.303 5.6278

23 ......... 25,494.603 413,415.93 2,093.701 15.2158 78 ......... 453.918 2,893.91 290.111 5.3754

24 ......... 24,010.514 387,921.32 2,052.703 15.1563 79 ......... 398.377 2,440.00 260.264 5.1248

25 ......... 22,612.284 363,910.81 2,013.559 15.0935 80 ......... 347.357 2,041.62 231.794 4.8776

26 ......... 21,295.196 341,298.53 1,976.411 15.0270 81 ......... 300.552 1,694.26 204.650 4.6372

27 ......... 20,054.347 320,003.33 1,940.951 14.9568 82 ......... 257.797 1,393.71 178.908 4.4062

28 ......... 18,885.156 299,948.98 1,906.912 14.8828 83 ......... 219.103 1,135.91 154.806 4.1844

29 ......... 17,782.965 281,063.83 1,873.691 14.8052 84 ......... 184.547 916.81 132.652 3.9679

30 ......... 16,743.475 263,280.86 1,840.785 14.7244 85 ......... 154.084 732.26 112.635 3.7524

31 ......... 15,763.373 246,537.39 1,808.426 14.6399 86 ......... 127.371 578.18 94.644 3.5393

32 ......... 14,839.185 230,774.01 1,776.505 14.5517 87 ......... 104.031 450.81 78.513 3.3334

33 ......... 13,967.801 215,934.83 1,745.075 14.4595 88 ......... 83.850 346.78 64.221 3.1357

34 ......... 13,146.279 201,967.03 1,714.183 14.3631 89 ......... 66.633 262.93 51.750 2.9459

35 ......... 12,371.835 188,820.75 1,683.868 14.2621 90 ......... 52.136 196.29 41.025 2.7650

36 ......... 11,641.471 176,448.91 1,653.797 14.1569 91 ......... 40.108 144.16 31.948 2.5943

37 ......... 10,952.993 164,807.44 1,624.270 14.0468 92 ......... 30.270 104.05 24.381 2.4374

38 ......... 10,303.845 153,854.45 1,595.103 13.9318 93 ......... 22.388 73.78 18.212 2.2955

39 ......... 9,692.062 143,550.60 1,566.556 13.8112 94 ......... 16.229 51.39 13.320 2.1666

40 ......... 9,115.650 133,858.54 1,538.751 13.6845 95 ......... 11.544 35.16 9.554 2.0459

41 ......... 8,572.612 124,742.89 1,511.694 13.5513 96 ......... 8.059 23.62 6.722 1.9308

42 ......... 8,060.806 116,170.28 1,485.130 13.4117 97 ......... 5.509 15.56 4.628 1.8243

43 ......... 7,578.331 108,109.47 1,458.927 13.2656 95 ......... 3.693 10.05 3.124 1.7214

44 ......... 7,123.263 100,531.14 1,432.821 13.1131 99 ......... 2.425 6.36 2.065 1.6214

45 ......... 6,693.905 93,407.88 1,406.667 12.9542 100 ......... 1.558 3.93 1.335 1.5241

46 ......... 6,288.344 86,713.97 1,380.005 12.7896 101 ......... 0.977 2.37 0.843 1.4295

47 ......... 5,905.308 80,425.63 1,352.914 12.6192 102 ......... 0.598 1.40 0.519 1.3378

48 ......... 5,543.352 74,520.32 1,325.220 12.4432 103 ......... 0.356 0.80 0.310 1.2487

49 ......... 5,201.495 68,976.97 1,297.138 12.2610 104 ......... 0.205 0.44 0.180 1.1623

50 ......... 4,878.624 63,775.48 1,268.691 12.0724 105 ......... 0.115 0.24 0.101 1.0786

51 ......... 4,573.436 58,896.85 1,239.652 11.8780 106 ......... 0.062 0.12 0.055 0.9975

52 ......... 4,284.896 54,323.42 1,209.986 11.6779 107 ......... 0.032 0.06 0.029 0.9189

53 ......... 4,011.815 50,038.52 1,179.446 11.4728 108 ......... 0.016 0.03 0.014 0.8429

54 ......... 3,753.383 46,026.71 1,148.098 11.2627 109 ......... 0.008 0.01 0.007 0.7694

x x x x x x x x

21
Table 2.G. -- Actuarial Functions at 7.0 Percent Interest for 1989-91 United States 

Total Males

x D N M a x D N M a

0 ......... 100,000.000 1,485,501.67 2,817.648 13.8550 55 ......... 2,093.477 23,254.46 572.157 10.1081

1 ......... 92,486.916 1,385,501.67 1,846.619 13.9805 56 ......... 1,937.044 21,160.99 552.680 9.9244

2 ......... 86,369.115 1,293,014.76 1,779.365 13.9708 57 ......... 1,790.597 19,223.94 532.956 9.7361

3 ......... 80,674.719 1,206,645.64 1,735.285 13.9569 58 ......... 1,653.421 17,433.35 512.921 9.5438

4 ......... 75,365.655 1,125,970.92 1,704.006 13.9401 59 ......... 1,524.849 15,779.93 492.517 9.3485

5 ......... 70,410.237 1,050,605.27 1,679.051 13.9212 60 ......... 1,404.366 14,255.08 471.791 9.1505

6 ......... 65,783.970 980,195.03 1,659.061 13.9002 61 ......... 1,291.606 12,850.71 450.905 8.9494

7 ......... 61,462.909 914,411.06 1,641.624 13.8774 62 ......... 1,186.232 11,559.11 430.028 8.7444

8 ......... 57,426.838 852,948.15 1,626.492 13.8528 63 ......... 1,087.807 10,372.87 409.208 8.5356

9 ......... 53,657.432 795,521.31 1,613.981 13.8259 64 ......... 995.919 9,285.07 388.485 8.3231

10 ......... 50,136.966 741,863.88 1,603.814 13.7967 65 ......... 910.156 8,289.15 367.876 8.1074

11 ......... 46,849.376 691,726.92 1,596.213 13.7649 66 ......... 830.225 7,378.99 347.487 7.8879

12 ......... 43,776.915 644,877.54 1,588.665 13.7310 67 ......... 755.847 6,548.77 327.423 7.6641

13 ......... 40,902.631 601,100.63 1,578.291 13.6959 68 ......... 686.662 5,792.92 307.686 7.4363

14 ......... 38,210.857 560,198.00 1,562.390 13.6607 69 ......... 622.300 5,106.26 288.246 7.2055

15 ......... 35,687.885 521,987.14 1,539.194 13.6265 70 ......... 562.394 4,483.96 269.051 6.9730

16 ......... 33,323.355 486,299.25 1,509.385 13.5933 71 ......... 506.638 3,921.56 250.088 6.7404

17 ......... 31,108.499 452,975.90 1,474.562 13.5612 72 ......... 454.820 3,414.92 231.414 6.5083

18 ......... 29,035.493 421,867.40 1,436.691 13.5294 73 ......... 406.748 2,960.10 213.096 6.2775

19 ......... 27,097.540 392,831.91 1,398.257 13.4970 74 ......... 362.309 2,553.36 195.267 6.0475

20 ......... 25,287.333 365,734.37 1,360.786 13.4631 75 ......... 321.405 2,191.05 178.066 5.8171

21 ......... 23,596.553 340,447.03 1,324.317 13.4278 76 ......... 283.882 1,869.64 161.569 5.5860

22 ......... 22,017.191 316,850.48 1,288.655 13.3910 77 ......... 249.544 1,585.76 145.802 5.3546

23 ......... 20,542.640 294,833.29 1,254.481 13.3523 78 ......... 218.223 1,336.22 130.807 5.1232

24 ......... 19,166.003 274,290.65 1,221.755 13.3113 79 ......... 189.731 1,117.99 116.591 4.8925

25 ......... 17,881.198 255,124.65 1,190.801 13.2678 80 ......... 163.887 928.26 103.159 4.6641

26 ......... 16,682.299 237,243.45 1,161.700 13.2213 81 ......... 140.478 764.38 90.472 4.4412

27 ......... 15,563.415 220,561.15 1,134.181 13.1718 82 ......... 119.369 623.90 78.553 4.2267

28 ......... 14,519.078 204,997.73 1,108.011 13.1192 83 ......... 100.504 504.53 67.497 4.0200

29 ......... 13,543.930 190,478.66 1,082.710 13.0638 84 ......... 83.861 404.03 57.430 3.8178

30 ......... 12,633.050 176,934.73 1,057.881 13.0057 85 ......... 69.364 320.16 48.419 3.6157

31 ......... 11,782.403 164,301.68 1,033.695 12.9447 86 ......... 56.803 250.80 40.395 3.4153

32 ......... 10,987.955 152,519.27 1,010.058 12.8806 87 ......... 45.960 194.00 33.269 3.2210

33 ......... 10,246.061 141,531.32 987.003 12.8132 88 ......... 36.698 148.04 27.014 3.0339

34 ......... 9,553.309 131,285.26 964.554 12.7424 89 ......... 28.891 111.34 21.607 2.8538

35 ......... 8,906.503 121,731.95 942.730 12.6678 90 ......... 22.394 82.45 17.000 2.6817

36 ......... 8,302.388 112,825.45 921.284 12.5895 91 ......... 17.066 60.05 13.138 2.5189

37 ......... 7,738.380 104,523.06 900.423 12.5071 92 ......... 12.760 42.99 9.948 2.3690

38 ......... 7,211.717 96,784.68 880.009 12.4205 93 ......... 9.349 30.23 7.372 2.2333

39 ......... 6,720.129 89,572.96 860.216 12.3291 94 ......... 6.714 20.88 5.348 2.1098

40 ......... 6,261.395 82,852.83 841.117 12.2323 95 ......... 4.731 14.17 3.804 1.9940

41 ......... 5,833.360 76,591.44 822.705 12.1299 96 ......... 3.272 9.43 2.655 1.8834

42 ......... 5,433.831 70,758.08 804.798 12.0218 97 ......... 2.216 6.16 1.813 1.7811

43 ......... 5,060.848 65,324.25 787.300 11.9078 95 ......... 1.471 3.95 1.213 1.6820

44 ......... 4,712.494 60,263.40 770.029 11.7880 99 ......... 0.957 2.48 0.795 1.5855

45 ......... 4,387.059 55,550.90 752.888 11.6624 100 ......... 0.609 1.52 0.510 1.4915

46 ......... 4,082.745 51,163.84 735.578 11.5317 101 ......... 0.379 0.91 0.319 1.4000

47 ......... 3,798.225 47,081.10 718.153 11.3956 102 ......... 0.229 0.53 0.195 1.3111

48 ......... 3,532.097 43,282.87 700.507 11.2542 103 ......... 0.135 0.30 0.115 1.2247

49 ......... 3,283.299 39,750.78 682.781 11.1070 104 ......... 0.077 0.17 0.066 1.1408

50 ......... 3,050.715 36,467.48 664.993 10.9537 105 ......... 0.043 0.09 0.037 1.0593

51 ......... 2,833.147 33,416.76 647.003 10.7949 106 ......... 0.023 0.05 0.020 0.9803

52 ......... 2,629.595 30,583.62 628.798 10.6305 107 ......... 0.012 0.02 0.010 0.9037

53 ......... 2,438.999 27,954.02 610.231 10.4613 108 ......... 0.006 0.01 0.005 0.8295

54 ......... 2,260.558 25,515.02 591.351 10.2870 109 ......... 0.003 0.00 0.002 0.7576

x x x x x x x x

22
Table 2.H. -- Actuarial Functions at 8.0 Percent Interest for 1989-91 United States 

Total Males

x D N M a x D N M a

0 ......... 100,000.000 1,319,376.16 2,268.433 12.1938 55 ......... 1,255.074 12,925.19 297.653 9.2983

1 ......... 91,630.556 1,219,376.16 1,306.396 12.3075 56 ......... 1,150.537 11,670.12 286.084 9.1432

2 ......... 84,777.092 1,127,745.60 1,240.380 12.3025 57 ......... 1,053.705 10,519.58 274.477 8.9834

3 ......... 78,454.440 1,042,968.51 1,197.513 12.2939 58 ......... 963.972 9,465.87 262.797 8.8197

4 ......... 72,612.864 964,514.07 1,167.377 12.2830 59 ......... 880.781 8,501.90 251.011 8.6527

5 ......... 67,210.313 891,901.21 1,143.557 12.2703 60 ......... 803.677 7,621.12 239.150 8.4828

6 ......... 62,212.866 824,690.90 1,124.652 12.2560 61 ......... 732.304 6,817.44 227.308 8.3096

7 ......... 57,588.168 762,478.03 1,108.314 12.2402 62 ......... 666.332 6,085.14 215.581 8.1323

8 ......... 53,308.331 704,889.86 1,094.267 12.2229 63 ......... 605.387 5,418.81 203.994 7.9510

9 ......... 49,348.060 651,581.53 1,082.761 12.2038 64 ......... 549.118 4,813.42 192.568 7.7657

10 ......... 45,683.384 602,233.47 1,073.497 12.1828 65 ......... 497.184 4,264.30 181.310 7.5769

11 ......... 42,292.568 556,550.09 1,066.635 12.1595 66 ......... 449.322 3,767.12 170.276 7.3840

12 ......... 39,153.034 514,257.52 1,059.884 12.1346 67 ......... 405.280 3,317.80 159.517 7.1864

13 ......... 36,243.617 475,104.48 1,050.692 12.1086 68 ......... 364.775 2,912.52 149.033 6.9844

14 ......... 33,544.945 438,860.87 1,036.733 12.0828 69 ......... 327.523 2,547.74 138.801 6.7788

15 ......... 31,039.959 405,315.92 1,016.558 12.0579 70 ......... 293.253 2,220.22 128.792 6.5710

16 ......... 28,715.017 374,275.96 990.871 12.0342 71 ......... 261.734 1,926.97 118.995 6.3623

17 ......... 26,558.249 345,560.95 961.142 12.0114 72 ......... 232.789 1,665.23 109.438 6.1534

18 ......... 24,558.939 319,002.70 929.110 11.9893 73 ......... 206.256 1,432.44 100.149 5.9450

19 ......... 22,707.551 294,443.76 896.902 11.9668 74 ......... 182.020 1,226.19 91.192 5.7365

20 ......... 20,994.400 271,736.21 865.792 11.9433 75 ......... 159.976 1,044.17 82.630 5.5270

21 ......... 19,409.263 250,741.81 835.795 11.9187 76 ......... 139.991 884.19 74.495 5.3161

22 ......... 17,942.477 231,332.55 806.733 11.8930 77 ......... 121.918 744.20 66.792 5.1041

23 ......... 16,585.813 213,390.07 779.142 11.8658 78 ......... 105.629 622.28 59.534 4.8912

24 ......... 15,331.056 196,804.26 752.963 11.8370 79 ......... 90.987 516.65 52.717 4.6783

25 ......... 14,170.892 181,473.20 728.432 11.8061 80 ......... 77.866 425.67 46.335 4.4667

26 ......... 13,098.347 167,302.31 705.583 11.7728 81 ......... 66.126 347.80 40.363 4.2597

27 ......... 12,106.692 154,203.96 684.176 11.7371 82 ......... 55.669 281.68 34.804 4.0598

28 ......... 11,189.731 142,097.27 664.007 11.6989 83 ......... 46.437 226.01 29.696 3.8670

29 ......... 10,341.543 130,907.54 644.689 11.6584 84 ......... 38.389 179.57 25.087 3.6777

30 ......... 9,556.721 120,565.99 625.906 11.6158 85 ......... 31.458 141.18 21.001 3.4879

31 ......... 8,830.688 111,009.27 607.779 11.5709 86 ......... 25.523 109.72 17.395 3.2990

32 ......... 8,159.012 102,178.59 590.228 11.5234 87 ......... 20.460 84.20 14.223 3.1153

33 ......... 7,537.680 94,019.57 573.267 11.4733 88 ......... 16.186 63.74 11.464 2.9381

34 ......... 6,962.971 86,481.89 556.905 11.4203 89 ......... 12.624 47.55 9.101 2.7670

35 ......... 6,431.436 79,518.92 541.146 11.3641 90 ......... 9.695 34.93 7.107 2.6030

36 ......... 5,939.691 73,087.49 525.803 11.3049 91 ......... 7.320 25.24 5.451 2.4475

37 ......... 5,484.927 67,147.80 511.016 11.2422 92 ......... 5.422 17.92 4.095 2.3042

38 ......... 5,064.301 61,662.87 496.681 11.1760 93 ......... 3.936 12.49 3.011 2.1742

39 ......... 4,675.397 56,598.57 482.910 11.1056 94 ......... 2.800 8.56 2.167 2.0558

40 ......... 4,315.906 51,923.17 469.746 11.0307 95 ......... 1.955 5.76 1.529 1.9446

41 ......... 3,983.636 47,607.26 457.172 10.9507 96 ......... 1.340 3.80 1.058 1.8383

42 ......... 3,676.437 43,623.63 445.057 10.8657 97 ......... 0.899 2.46 0.716 1.7398

43 ......... 3,392.378 39,947.19 433.327 10.7756 95 ......... 0.591 1.56 0.476 1.6443

44 ......... 3,129.621 36,554.81 421.857 10.6803 99 ......... 0.381 0.97 0.309 1.5511

45 ......... 2,886.520 33,425.19 410.579 10.5798 100 ......... 0.240 0.59 0.197 1.4602

46 ......... 2,661.419 30,538.67 399.296 10.4746 101 ......... 0.148 0.35 0.122 1.3717

47 ......... 2,453.023 27,877.25 388.042 10.3644 102 ......... 0.089 0.20 0.074 1.2855

48 ......... 2,260.027 25,424.23 376.751 10.2495 103 ......... 0.052 0.11 0.043 1.2016

49 ......... 2,081.381 23,164.20 365.514 10.1292 104 ......... 0.029 0.06 0.025 1.1200

50 ......... 1,916.032 21,082.82 354.342 10.0034 105 ......... 0.016 0.03 0.014 1.0407

51 ......... 1,762.910 19,166.79 343.148 9.8722 106 ......... 0.009 0.02 0.007 0.9637

52 ......... 1,621.101 17,403.88 331.924 9.7358 107 ......... 0.004 0.01 0.004 0.8890

53 ......... 1,489.679 15,782.78 320.584 9.5948 108 ......... 0.002 0.00 0.002 0.8164

54 ......... 1,367.908 14,293.10 309.160 9.4489 109 ......... 0.001 0.00 0.001 0.7461

x x x x x x x x

23
Table 2.I. -- Actuarial Functions at 9.0 Percent Interest for 1989-91 United States 

Total Males

x D N M a x D N M a

0 ......... 100,000.000 1,187,786.84 1,925.858 10.8779 55 ......... 755.994 7,254.42 157.005 8.5959

1 ......... 90,789.908 1,087,786.84 972.647 10.9814 56 ......... 686.669 6,498.43 150.101 8.4637

2 ......... 83,228.684 996,996.93 907.837 10.9790 57 ......... 623.107 5,811.76 143.237 8.3271

3 ......... 76,314.893 913,768.24 866.139 10.9737 58 ......... 564.814 5,188.65 136.393 8.1865

4 ......... 69,984.618 837,453.35 837.094 10.9662 59 ......... 511.336 4,623.84 129.551 8.0427

5 ......... 64,183.324 767,468.73 814.346 10.9574 60 ......... 462.293 4,112.50 122.728 7.8959

6 ......... 58,865.896 703,285.41 796.458 10.9472 61 ......... 417.373 3,650.21 115.979 7.7457

7 ......... 53,990.092 644,419.51 781.141 10.9359 62 ......... 376.288 3,232.84 109.357 7.5914

8 ......... 49,519.146 590,429.42 768.093 10.9233 63 ......... 338.735 2,856.55 102.874 7.4330

9 ......... 45,419.819 540,910.27 757.503 10.9091 64 ......... 304.432 2,517.81 96.539 7.2705

10 ......... 41,661.111 495,490.46 749.055 10.8934 65 ......... 273.111 2,213.38 90.355 7.1043

11 ......... 38,215.002 453,829.34 742.854 10.8757 66 ......... 244.555 1,940.27 84.349 6.9339

12 ......... 35,053.591 415,614.34 736.810 10.8565 67 ......... 218.560 1,695.71 78.547 6.7586

13 ......... 32,151.103 380,560.75 728.656 10.8366 68 ......... 194.912 1,477.15 72.945 6.5786

14 ......... 29,484.156 348,409.65 716.387 10.8168 69 ......... 173.401 1,282.24 67.528 6.3946

15 ......... 27,032.114 318,925.49 698.816 10.7980 70 ......... 153.833 1,108.84 62.278 6.2081

16 ......... 24,777.940 291,893.38 676.652 10.7804 71 ......... 136.039 955.01 57.186 6.0201

17 ......... 22,706.637 267,115.44 651.234 10.7638 72 ......... 119.885 818.97 52.264 5.8313

18 ......... 20,804.642 244,408.80 624.098 10.7478 73 ......... 105.246 699.08 47.524 5.6424

19 ......... 19,059.793 223,604.16 597.064 10.7317 74 ......... 92.027 593.84 42.995 5.4528

20 ......... 17,460.176 204,544.37 571.192 10.7149 75 ......... 80.140 501.81 38.706 5.2617

21 ......... 15,993.792 187,084.19 546.473 10.6973 76 ......... 69.485 421.67 34.668 5.0685

22 ......... 14,649.475 171,090.40 522.745 10.6789 77 ......... 59.959 352.18 30.880 4.8737

23 ......... 13,417.565 156,440.92 500.424 10.6594 78 ......... 51.472 292.23 27.343 4.6774

24 ......... 12,288.709 143,023.36 479.441 10.6386 79 ......... 43.930 240.75 24.052 4.4804

25 ......... 11,254.562 130,734.65 459.958 10.6161 80 ......... 37.250 196.82 20.998 4.2838

26 ......... 10,307.306 119,480.09 441.978 10.5918 81 ......... 31.344 159.57 18.168 4.0911

27 ......... 9,439.553 109,172.78 425.287 10.5655 82 ......... 26.145 128.23 15.557 3.9046

28 ......... 8,644.559 99,733.23 409.706 10.5371 83 ......... 21.609 102.08 13.180 3.7242

29 ......... 7,916.001 91,088.67 394.918 10.5069 84 ......... 17.700 80.48 11.055 3.5466

30 ......... 7,248.141 83,172.67 380.673 10.4750 85 ......... 14.372 62.78 9.188 3.3681

31 ......... 6,636.048 75,924.53 367.050 10.4412 86 ......... 11.553 48.40 7.556 3.1897

32 ......... 6,075.049 69,288.48 353.982 10.4054 87 ......... 9.176 36.85 6.134 3.0159

33 ......... 5,560.927 63,213.43 341.469 10.3674 88 ......... 7.193 27.67 4.908 2.8477

34 ......... 5,089.807 57,652.50 329.509 10.3271 89 ......... 5.558 20.48 3.867 2.6849

35 ......... 4,658.134 52,562.70 318.095 10.2841 90 ......... 4.229 14.92 2.997 2.5285

36 ......... 4,262.507 47,904.56 307.084 10.2386 91 ......... 3.164 10.69 2.281 2.3799

37 ......... 3,900.043 43,642.06 296.570 10.1901 92 ......... 2.322 7.53 1.701 2.2426

38 ......... 3,567.921 39,742.01 286.471 10.1387 93 ......... 1.670 5.21 1.240 2.1179

39 ......... 3,263.710 36,174.09 276.858 10.0837 94 ......... 1.178 3.54 0.885 2.0043

40 ......... 2,985.124 32,910.38 267.753 10.0248 95 ......... 0.815 2.36 0.620 1.8975

41 ......... 2,730.029 29,925.26 259.136 9.9615 96 ......... 0.553 1.55 0.425 1.7951

42 ......... 2,496.387 27,195.23 250.909 9.8938 97 ......... 0.368 0.99 0.286 1.7002

43 ......... 2,282.372 24,698.84 243.018 9.8216 95 ......... 0.240 0.63 0.188 1.6081

44 ......... 2,086.273 22,416.47 235.372 9.7447 99 ......... 0.153 0.39 0.121 1.5181

45 ......... 1,906.563 20,330.20 227.922 9.6633 100 ......... 0.096 0.23 0.076 1.4302

46 ......... 1,741.755 18,423.64 220.538 9.5776 101 ......... 0.058 0.14 0.047 1.3444

47 ......... 1,590.643 16,681.88 213.240 9.4875 102 ......... 0.035 0.08 0.028 1.2608

48 ......... 1,452.052 15,091.24 205.986 9.3930 103 ......... 0.020 0.04 0.016 1.1793

49 ......... 1,325.004 13,639.18 198.833 9.2937 104 ......... 0.011 0.02 0.009 1.1000

50 ......... 1,208.553 12,314.18 191.786 9.1892 105 ......... 0.006 0.01 0.005 1.0227

51 ......... 1,101.768 11,105.63 184.790 9.0798 106 ......... 0.003 0.01 0.003 0.9477

52 ......... 1,003.847 10,003.86 177.840 8.9655 107 ......... 0.002 0.00 0.001 0.8747

53 ......... 914.002 9,000.01 170.882 8.8468 108 ......... 0.001 0.00 0.001 0.8038

54 ......... 831.589 8,086.01 163.937 8.7236 109 ......... 0.000 0.00 0.000 0.7350

x x x x x x x x

24
Table 2.J. -- Actuarial Functions at 10.0 Percent Interest for 1989-91 United States 

Total Males

x D N M a x D N M a

0 ......... 100,000.000 1,081,286.21 1,701.254 9.8129 55 ......... 457.486 4,109.31 83.912 7.9824

1 ......... 89,964.545 981,286.21 756.708 9.9075 56 ......... 411.757 3,651.83 79.772 7.8689

2 ......... 81,722.314 891,321.67 693.072 9.9067 57 ......... 370.246 3,240.07 75.694 7.7511

3 ......... 74,252.442 809,599.35 652.501 9.9033 58 ......... 332.557 2,869.82 71.664 7.6296

4 ......... 67,474.216 735,346.91 624.497 9.8982 59 ......... 298.333 2,537.27 67.672 7.5048

5 ......... 61,318.464 667,872.69 602.765 9.8919 60 ......... 267.267 2,238.93 63.728 7.3771

6 ......... 55,727.124 606,554.23 585.831 9.8844 61 ......... 239.104 1,971.67 59.861 7.2461

7 ......... 50,646.654 550,827.11 571.462 9.8759 62 ......... 213.608 1,732.56 56.102 7.1110

8 ......... 46,030.283 500,180.45 559.333 9.8663 63 ......... 190.542 1,518.96 52.455 6.9718

9 ......... 41,835.958 454,150.17 549.579 9.8555 64 ......... 169.689 1,328.41 48.924 6.8285

10 ......... 38,024.978 412,314.21 541.868 9.8432 65 ......... 150.847 1,158.72 45.509 6.6814

11 ......... 34,562.554 374,289.23 536.260 9.8293 66 ......... 133.847 1,007.88 42.222 6.5301

12 ......... 31,415.087 339,726.68 530.843 9.8141 67 ......... 118.532 874.03 39.075 6.3738

13 ......... 28,551.928 308,311.59 523.602 9.7983 68 ......... 104.746 755.50 36.064 6.2127

14 ......... 25,945.502 279,759.66 512.805 9.7826 69 ......... 92.339 650.75 33.180 6.0474

15 ......... 23,571.499 253,814.16 497.484 9.7678 70 ......... 81.174 558.41 30.409 5.8792

16 ......... 21,409.484 230,242.66 478.333 9.7542 71 ......... 71.132 477.24 27.747 5.7092

17 ......... 19,441.404 208,833.18 456.570 9.7417 72 ......... 62.115 406.11 25.196 5.5380

18 ......... 17,650.982 189,391.77 433.548 9.7298 73 ......... 54.035 343.99 22.763 5.3661

19 ......... 16,023.620 171,740.79 410.820 9.7180 74 ......... 46.819 289.96 20.459 5.1932

20 ......... 14,545.374 155,717.17 389.267 9.7056 75 ......... 40.400 243.14 18.297 5.0182

21 ......... 13,202.662 141,171.80 368.862 9.6927 76 ......... 34.711 202.74 16.280 4.8408

22 ......... 11,983.010 127,969.14 349.453 9.6792 77 ......... 29.680 168.03 14.405 4.6613

23 ......... 10,875.554 115,986.13 331.361 9.6648 78 ......... 25.247 138.35 12.670 4.4798

24 ......... 9,870.014 105,110.57 314.507 9.6495 79 ......... 21.352 113.10 11.070 4.2970

25 ......... 8,957.234 95,240.56 299.002 9.6328 80 ......... 17.940 91.75 9.600 4.1141

26 ......... 8,128.760 86,283.32 284.822 9.6146 81 ......... 14.958 73.81 8.249 3.9342

27 ......... 7,376.739 78,154.56 271.778 9.5947 82 ......... 12.364 58.85 7.014 3.7598

28 ......... 6,694.060 70,777.83 259.712 9.5732 83 ......... 10.126 46.49 5.900 3.5907

29 ......... 6,074.162 64,083.77 248.365 9.5502 84 ......... 8.219 36.36 4.913 3.4239

30 ......... 5,511.134 58,009.60 237.534 9.5259 85 ......... 6.613 28.14 4.054 3.2556

31 ......... 4,999.859 52,498.47 227.271 9.5000 86 ......... 5.267 21.53 3.310 3.0870

32 ......... 4,535.569 47,498.61 217.514 9.4725 87 ......... 4.146 16.26 2.668 2.9222

33 ......... 4,113.988 42,963.04 208.257 9.4432 88 ......... 3.220 12.11 2.119 2.7623

34 ......... 3,731.221 38,849.05 199.489 9.4119 89 ......... 2.466 8.89 1.657 2.6073

35 ......... 3,383.728 35,117.83 191.198 9.3784 90 ......... 1.859 6.43 1.275 2.4580

36 ......... 3,068.191 31,734.10 183.272 9.3429 91 ......... 1.378 4.57 0.963 2.3157

37 ......... 2,781.765 28,665.91 175.773 9.3049 92 ......... 1.002 3.19 0.712 2.1840

38 ......... 2,521.739 25,884.15 168.635 9.2644 93 ......... 0.714 2.19 0.515 2.0644

39 ......... 2,285.758 23,362.41 161.902 9.2209 94 ......... 0.499 1.47 0.365 1.9552

40 ......... 2,071.643 21,076.65 155.583 9.1739 95 ......... 0.342 0.98 0.253 1.8525

41 ......... 1,877.386 19,005.01 149.658 9.1231 96 ......... 0.230 0.63 0.173 1.7539

42 ......... 1,701.109 17,127.62 144.052 9.0685 97 ......... 0.152 0.40 0.115 1.6624

43 ......... 1,541.134 15,426.51 138.723 9.0098 95 ......... 0.098 0.25 0.075 1.5735

44 ......... 1,395.915 13,885.38 133.607 8.9472 99 ......... 0.062 0.15 0.048 1.4864

45 ......... 1,264.074 12,489.47 128.668 8.8803 100 ......... 0.038 0.09 0.030 1.4013

46 ......... 1,144.307 11,225.39 123.817 8.8098 101 ......... 0.023 0.05 0.018 1.3182

47 ......... 1,035.528 10,081.08 119.066 8.7352 102 ......... 0.014 0.03 0.011 1.2370

48 ......... 936.710 9,045.56 114.387 8.6567 103 ......... 0.008 0.02 0.006 1.1578

49 ......... 846.982 8,108.85 109.814 8.5738 104 ......... 0.004 0.01 0.004 1.0806

50 ......... 765.520 7,261.86 105.350 8.4862 105 ......... 0.002 0.00 0.002 1.0054

51 ......... 691.536 6,496.34 100.959 8.3941 106 ......... 0.001 0.00 0.001 0.9321

52 ......... 624.346 5,804.81 96.637 8.2974 107 ......... 0.001 0.00 0.001 0.8608

53 ......... 563.300 5,180.46 92.348 8.1966 108 ......... 0.000 0.00 0.000 0.7915

54 ......... 507.849 4,617.16 88.107 8.0916 109 ......... 0.000 0.00 0.000 0.7242

x x x x x x x x

25
Table 2.K. -- Actuarial Functions at 11.0 Percent Interest for 1989-91 United States 

Total Males

x D N M a x D N M a

0 ......... 100,000.000 993,483.12 1,546.718 8.9348 55 ......... 278.107 2,348.13 45.410 7.4433

1 ......... 89,154.054 893,483.12 610.682 9.0218 56 ......... 248.053 2,070.02 42.915 7.3451

2 ......... 80,256.473 804,329.06 548.187 9.0220 57 ......... 221.036 1,821.97 40.481 7.2429

3 ......... 72,263.644 724,072.59 508.703 9.0199 58 ......... 196.748 1,600.93 38.097 7.1370

4 ......... 65,075.374 651,808.95 481.695 9.0162 59 ......... 174.910 1,404.19 35.756 7.0281

5 ......... 58,605.692 586,733.57 460.924 9.0115 60 ......... 155.285 1,229.28 33.464 6.9163

6 ......... 52,781.882 528,127.88 444.885 9.0059 61 ......... 137.670 1,073.99 31.238 6.8012

7 ......... 47,537.759 475,346.00 431.398 8.9993 62 ......... 121.882 936.32 29.093 6.6822

8 ......... 42,815.527 427,808.24 420.116 8.9919 63 ......... 107.741 814.44 27.031 6.5592

9 ......... 38,563.556 384,992.71 411.125 8.9833 64 ......... 95.086 706.70 25.052 6.4322

10 ......... 34,734.899 346,429.16 404.081 8.9735 65 ......... 83.766 611.61 23.156 6.3015

11 ......... 31,287.625 311,694.26 399.005 8.9622 66 ......... 73.656 527.85 21.347 6.1664

12 ......... 28,182.190 280,406.63 394.146 8.9498 67 ......... 64.641 454.19 19.631 6.0264

13 ......... 25,382.923 252,224.44 387.708 8.9368 68 ......... 56.608 389.55 18.004 5.8816

14 ......... 22,857.986 226,841.52 378.196 8.9240 69 ......... 49.453 332.94 16.459 5.7325

15 ......... 20,579.404 203,983.53 364.820 8.9120 70 ......... 43.082 283.49 14.989 5.5802

16 ......... 18,523.434 183,404.13 348.250 8.9012 71 ......... 37.412 240.41 13.588 5.4259

17 ......... 16,669.119 164,880.70 329.590 8.8914 72 ......... 32.376 202.99 12.259 5.2700

18 ......... 14,997.663 148,211.58 310.029 8.8823 73 ......... 27.910 170.62 11.002 5.1132

19 ......... 13,492.271 133,213.91 290.892 8.8734 74 ......... 23.965 142.71 9.823 4.9549

20 ......... 12,137.214 119,721.64 272.907 8.8640 75 ......... 20.493 118.74 8.726 4.7943

21 ......... 10,917.554 107,584.43 256.034 8.8543 76 ......... 17.449 98.25 7.712 4.6309

22 ......... 9,819.728 96,666.87 240.128 8.8441 77 ......... 14.785 80.80 6.778 4.4651

23 ......... 8,831.910 86,847.15 225.436 8.8333 78 ......... 12.464 66.02 5.921 4.2968

24 ......... 7,943.113 78,015.24 211.873 8.8217 79 ......... 10.446 53.55 5.139 4.1268

25 ......... 7,143.591 70,072.12 199.507 8.8091 80 ......... 8.698 43.11 4.426 3.9562

26 ......... 6,424.461 62,928.53 188.300 8.7951 81 ......... 7.187 34.41 3.777 3.7880

27 ......... 5,777.587 56,504.07 178.084 8.7799 82 ......... 5.887 27.22 3.189 3.6245

28 ......... 5,195.668 50,726.49 168.719 8.7632 83 ......... 4.778 21.34 2.663 3.4657

29 ......... 4,672.054 45,530.82 159.991 8.7454 84 ......... 3.843 16.56 2.202 3.3088

30 ......... 4,200.802 40,858.76 151.735 8.7264 85 ......... 3.064 12.72 1.804 3.1499

31 ......... 3,776.753 36,657.96 143.982 8.7062 86 ......... 2.419 9.65 1.462 2.9902

32 ......... 3,395.177 32,881.21 136.679 8.6847 87 ......... 1.887 7.23 1.170 2.8338

33 ......... 3,051.851 29,486.03 129.812 8.6617 88 ......... 1.452 5.35 0.922 2.6817

34 ......... 2,742.970 26,434.18 123.366 8.6371 89 ......... 1.102 3.89 0.716 2.5337

35 ......... 2,465.103 23,691.21 117.326 8.6106 90 ......... 0.823 2.79 0.547 2.3910

36 ......... 2,215.092 21,226.11 111.604 8.5825 91 ......... 0.605 1.97 0.410 2.2547

37 ......... 1,990.213 19,011.01 106.239 8.5523 92 ......... 0.436 1.36 0.301 2.1283

38 ......... 1,787.924 17,020.80 101.178 8.5199 93 ......... 0.308 0.93 0.216 2.0134

39 ......... 1,606.012 15,232.88 96.447 8.4849 94 ......... 0.213 0.62 0.152 1.9084

40 ......... 1,442.458 13,626.87 92.048 8.4470 95 ......... 0.145 0.41 0.104 1.8095

41 ......... 1,295.423 12,184.41 87.959 8.4057 96 ......... 0.097 0.26 0.071 1.7144

42 ......... 1,163.214 10,888.99 84.126 8.3611 97 ......... 0.063 0.17 0.047 1.6261

43 ......... 1,044.330 9,725.77 80.515 8.3129 95 ......... 0.040 0.10 0.030 1.5402

44 ......... 937.402 8,681.44 77.079 8.2612 99 ......... 0.025 0.06 0.019 1.4560

45 ......... 841.220 7,744.04 73.792 8.2057 100 ......... 0.016 0.04 0.012 1.3736

46 ......... 754.656 6,902.82 70.593 8.1470 101 ......... 0.009 0.02 0.007 1.2929

47 ......... 676.765 6,148.16 67.488 8.0846 102 ......... 0.005 0.01 0.004 1.2141

48 ......... 606.668 5,471.40 64.457 8.0188 103 ......... 0.003 0.01 0.002 1.1371

49 ......... 543.613 4,864.73 61.522 7.9489 104 ......... 0.002 0.00 0.001 1.0619

50 ......... 486.902 4,321.12 58.683 7.8747 105 ......... 0.001 0.00 0.001 0.9885

51 ......... 435.883 3,834.22 55.916 7.7964 106 ......... 0.000 0.00 0.000 0.9170

52 ......... 389.987 3,398.33 53.216 7.7140 107 ......... 0.000 0.00 0.000 0.8474

53 ......... 348.685 3,008.35 50.561 7.6277 108 ......... 0.000 0.00 0.000 0.7796

54 ......... 311.529 2,659.66 47.959 7.5374 109 ......... 0.000 0.00 0.000 0.7136

x x x x x x x x

26
Table 2.L. -- Actuarial Functions at 12.0 Percent Interest for 1989-91 United States 

Total Males

x D N M a x D N M a

0 ......... 100,000.000 919,935.28 1,435.505 8.1994 55 ......... 169.818 1,352.90 24.865 6.9667

1 ......... 88,358.036 819,935.28 507.827 8.2797 56 ......... 150.114 1,183.08 23.356 6.8812

2 ......... 78,829.719 731,577.25 446.443 8.2805 57 ......... 132.570 1,032.97 21.895 6.7918

3 ......... 70,345.242 652,747.53 408.007 8.2792 58 ......... 116.949 900.40 20.478 6.6990

4 ......... 62,782.195 582,402.29 381.951 8.2766 59 ......... 103.040 783.45 19.099 6.6033

5 ......... 56,035.672 519,620.09 362.091 8.2730 60 ......... 90.662 680.41 17.761 6.5049

6 ......... 50,016.651 463,584.42 346.892 8.2686 61 ......... 79.660 589.75 16.473 6.4033

7 ......... 44,645.058 413,567.77 334.226 8.2635 62 ......... 69.895 510.08 15.243 6.2979

8 ......... 39,851.158 368,922.71 323.725 8.2575 63 ......... 61.234 440.19 14.071 6.1886

9 ......... 35,573.097 329,071.55 315.431 8.2506 64 ......... 53.559 378.96 12.957 6.0755

10 ......... 31,755.254 293,498.45 308.991 8.2425 65 ......... 46.762 325.40 11.898 5.9586

11 ......... 28,348.306 261,743.20 304.392 8.2331 66 ......... 40.751 278.64 10.897 5.8375

12 ......... 25,306.624 233,394.89 300.028 8.2227 67 ......... 35.444 237.88 9.956 5.7116

13 ......... 22,589.471 208,088.27 294.299 8.2117 68 ......... 30.762 202.44 9.072 5.5809

14 ......... 20,160.781 185,498.80 285.910 8.2010 69 ......... 26.634 171.68 8.240 5.4458

15 ......... 17,989.005 165,338.02 274.217 8.1911 70 ......... 22.996 145.04 7.455 5.3075

16 ......... 16,047.257 147,349.01 259.862 8.1822 71 ......... 19.791 122.05 6.714 5.1669

17 ......... 14,311.887 131,301.76 243.841 8.1743 72 ......... 16.974 102.26 6.017 5.0245

18 ......... 12,761.825 116,989.87 227.196 8.1672 73 ......... 14.502 85.28 5.364 4.8809

19 ......... 11,378.348 104,228.04 211.058 8.1602 74 ......... 12.341 70.78 4.757 4.7356

20 ......... 10,144.208 92,849.70 196.026 8.1530 75 ......... 10.459 58.44 4.197 4.5878

21 ......... 9,043.352 82,705.49 182.049 8.1454 76 ......... 8.825 47.98 3.684 4.4369

22 ......... 8,061.364 73,662.14 168.992 8.1377 77 ......... 7.412 39.16 3.216 4.2833

23 ......... 7,185.692 65,600.77 157.038 8.1294 78 ......... 6.192 31.75 2.791 4.1269

24 ......... 6,404.860 58,415.08 146.102 8.1204 79 ......... 5.143 25.55 2.405 3.9685

25 ......... 5,708.743 52,010.22 136.219 8.1106 80 ......... 4.244 20.41 2.057 3.8090

26 ......... 5,088.216 46,301.48 127.343 8.0997 81 ......... 3.476 16.17 1.744 3.6513

27 ......... 4,535.031 41,213.26 119.325 8.0878 82 ......... 2.822 12.69 1.462 3.4978

28 ......... 4,041.850 36,678.23 112.039 8.0746 83 ......... 2.270 9.87 1.212 3.3485

29 ......... 3,602.065 32,636.38 105.310 8.0605 84 ......... 1.809 7.60 0.995 3.2006

30 ......... 3,209.821 29,034.32 99.002 8.0455 85 ......... 1.430 5.79 0.809 3.0503

31 ......... 2,860.041 25,824.49 93.131 8.0294 86 ......... 1.118 4.36 0.651 2.8989

32 ......... 2,548.127 22,964.45 87.650 8.0123 87 ......... 0.865 3.24 0.517 2.7502

33 ......... 2,270.005 20,416.33 82.542 7.9940 88 ......... 0.660 2.38 0.405 2.6053

34 ......... 2,022.039 18,146.32 77.790 7.9743 89 ......... 0.496 1.72 0.312 2.4640

35 ......... 1,800.979 16,124.28 73.377 7.9531 90 ......... 0.367 1.22 0.236 2.3274

36 ......... 1,603.874 14,323.30 69.234 7.9304 91 ......... 0.267 0.85 0.176 2.1966

37 ......... 1,428.180 12,719.43 65.384 7.9060 92 ......... 0.191 0.59 0.128 2.0753

38 ......... 1,271.561 11,291.25 61.785 7.8798 93 ......... 0.134 0.40 0.091 1.9647

39 ......... 1,131.989 10,019.69 58.451 7.8514 94 ......... 0.092 0.26 0.064 1.8637

40 ......... 1,007.631 8,887.70 55.377 7.8204 95 ......... 0.062 0.17 0.043 1.7684

41 ......... 896.839 7,880.07 52.546 7.7865 96 ......... 0.041 0.11 0.029 1.6766

42 ......... 798.119 6,983.23 49.916 7.7496 97 ......... 0.026 0.07 0.019 1.5913

43 ......... 710.151 6,185.11 47.461 7.7096 95 ......... 0.017 0.04 0.012 1.5083

44 ......... 631.748 5,474.96 45.146 7.6664 99 ......... 0.010 0.03 0.008 1.4268

45 ......... 561.866 4,843.21 42.950 7.6199 100 ......... 0.006 0.01 0.005 1.3469

46 ......... 499.548 4,281.34 40.832 7.5704 101 ......... 0.004 0.01 0.003 1.2686

47 ......... 443.988 3,781.80 38.795 7.5178 102 ......... 0.002 0.00 0.002 1.1920

48 ......... 394.447 3,337.81 36.825 7.4620 103 ......... 0.001 0.00 0.001 1.1170

49 ......... 350.294 2,943.36 34.934 7.4026 104 ......... 0.001 0.00 0.001 1.0438

50 ......... 310.949 2,593.07 33.120 7.3392 105 ......... 0.000 0.00 0.000 0.9722

51 ......... 275.881 2,282.12 31.369 7.2721 106 ......... 0.000 0.00 0.000 0.9024

52 ......... 244.629 2,006.24 29.675 7.2011 107 ......... 0.000 0.00 0.000 0.8344

53 ......... 216.769 1,761.61 28.025 7.1267 108 ......... 0.000 0.00 0.000 0.7680

54 ......... 191.940 1,544.84 26.422 7.0485 109 ......... 0.000 0.00 0.000 0.7034

x x x x x x x x

27
Table 3.A. -- Actuarial Functions at 1.0 Percent Interest for 1989-91 United States 

Total Females

x D N M a x D N M a

0 ......... 100,000.000 5,444,273.66 46,096.300 53.4427 55 ......... 53,734.266 1,277,160.57 41,089.112 22.7681

1 ......... 98,190.099 5,344,273.66 45,276.498 53.4278 56 ......... 52,900.951 1,223,426.31 40,787.819 22.1267

2 ......... 97,152.240 5,246,083.56 45,210.819 52.9986 57 ......... 52,053.349 1,170,525.36 40,463.989 21.4870

3 ......... 96,149.572 5,148,931.32 45,170.054 52.5513 58 ......... 51,189.269 1,118,472.01 40,115.289 20.8497

4 ......... 95,166.844 5,052,781.75 45,139.302 52.0939 59 ......... 50,304.396 1,067,282.74 39,737.240 20.2165

5 ......... 94,200.812 4,957,614.90 45,115.516 51.6282 60 ......... 49,398.449 1,016,978.34 39,329.357 19.5873

6 ......... 93,246.464 4,863,414.09 45,093.849 51.1566 61 ......... 48,471.721 967,579.89 38,891.722 18.9617

7 ......... 92,303.644 4,770,167.63 45,074.262 50.6791 62 ......... 47,525.586 919,108.17 38,425.505 18.3392

8 ......... 91,372.200 4,677,863.98 45,056.715 50.1957 63 ......... 46,558.707 871,582.59 37,929.176 17.7201

9 ......... 90,452.896 4,586,491.78 45,042.086 49.7059 64 ......... 45,569.287 825,023.88 37,400.734 17.1048

10 ......... 89,542.838 4,496,038.89 45,027.601 49.2110 65 ......... 44,556.663 779,454.59 36,839.291 16.4936

11 ......... 88,642.830 4,406,496.05 45,014.157 48.7107 66 ......... 43,521.252 734,897.93 36,245.035 15.8860

12 ......... 87,751.867 4,317,853.22 45,000.845 48.2053 67 ......... 42,462.956 691,376.68 35,617.642 15.2819

13 ......... 86,867.221 4,230,101.35 44,985.029 47.6962 68 ......... 41,380.684 648,913.72 34,955.796 14.6816

14 ......... 85,988.880 4,143,234.13 44,966.760 47.1834 69 ......... 40,270.887 607,533.04 34,255.708 14.0862

15 ......... 85,113.387 4,057,245.25 44,942.642 46.6687 70 ......... 39,128.679 567,262.15 33,512.222 13.4973

16 ......... 84,241.684 3,972,131.86 44,913.646 46.1516 71 ......... 37,950.377 528,133.47 32,721.332 12.9164

17 ......... 83,373.833 3,887,890.18 44,879.871 45.6320 72 ......... 36,733.440 490,183.09 31,880.142 12.3443

18 ......... 82,510.729 3,804,516.35 44,842.250 45.1094 73 ......... 35,476.424 453,449.65 30,986.823 11.7817

19 ......... 81,654.059 3,722,005.62 44,802.519 44.5826 74 ......... 34,180.839 417,973.23 30,042.490 11.2283

20 ......... 80,804.626 3,640,351.56 44,761.541 44.0513 75 ......... 32,851.010 383,792.39 29,051.085 10.6828

21 ......... 79,963.197 3,559,546.93 44,720.158 43.5148 76 ......... 31,490.648 350,941.38 28,015.981 10.1443

22 ......... 79,128.099 3,479,583.74 44,676.775 42.9741 77 ......... 30,101.482 319,450.73 26,938.604 9.6125

23 ......... 78,301.699 3,400,455.64 44,633.821 42.4276 78 ......... 28,679.215 289,349.25 25,814.371 9.0892

24 ......... 77,482.331 3,322,153.94 44,589.718 41.8763 79 ......... 27,216.094 260,670.04 24,635.203 8.5778

25 ......... 76,670.732 3,244,671.61 44,545.271 41.3196 80 ......... 25,707.407 233,453.94 23,395.982 8.0812

26 ......... 75,866.837 3,168,000.87 44,500.492 40.7574 81 ......... 24,153.569 207,746.54 22,096.673 7.6011

27 ......... 75,070.581 3,092,134.04 44,455.392 40.1897 82 ......... 22,560.761 183,592.97 20,743.009 7.1377

28 ......... 74,281.141 3,017,063.46 44,409.225 39.6168 83 ......... 20,938.017 161,032.20 19,343.639 6.6909

29 ......... 73,496.976 2,942,782.32 44,360.518 39.0395 84 ......... 19,296.641 140,094.19 17,909.570 6.2600

30 ......... 72,718.091 2,869,285.34 44,309.325 38.4577 85 ......... 17,647.514 120,797.55 16,451.498 5.8450

31 ......... 71,943.751 2,796,567.25 44,254.966 37.8716 86 ......... 15,997.278 103,150.03 14,975.990 5.4480

32 ......... 71,173.980 2,724,623.50 44,197.509 37.2812 87 ......... 14,353.585 87,152.76 13,490.687 5.0718

33 ......... 70,409.518 2,653,449.52 44,137.741 36.6859 88 ......... 12,736.707 72,799.17 12,015.923 4.7157

34 ......... 69,649.653 2,583,040.00 44,074.999 36.0862 89 ......... 11,167.763 60,062.46 10,573.085 4.3782

35 ......... 68,894.402 2,513,390.35 44,009.349 35.4818 90 ......... 9,664.986 48,894.70 9,180.880 4.0590

36 ......... 68,143.086 2,444,495.95 43,940.156 34.8730 91 ......... 8,237.372 39,229.71 7,848.958 3.7624

37 ......... 67,396.433 2,376,352.86 43,868.187 34.2593 92 ......... 6,898.332 30,992.34 6,591.477 3.4927

38 ......... 66,652.405 2,308,956.43 43,791.450 33.6418 93 ......... 5,672.204 24,094.01 5,433.650 3.2477

39 ......... 65,911.076 2,242,304.02 43,710.046 33.0201 94 ......... 4,580.745 18,421.81 4,398.351 3.0216

40 ......... 65,172.519 2,176,392.95 43,624.074 32.3943 95 ......... 3,631.577 13,841.06 3,494.537 2.8113

41 ......... 64,435.476 2,111,220.43 43,532.304 31.7649 96 ......... 2,823.461 10,209.48 2,722.377 2.6159

42 ......... 63,700.055 2,046,784.95 43,434.858 31.1316 97 ......... 2,148.542 7,386.02 2,075.413 2.4377

43 ......... 62,964.406 1,983,084.90 43,329.902 30.4953 95 ......... 1,600.239 5,237.48 1,548.382 2.2729

44 ......... 62,228.688 1,920,120.49 43,217.594 29.8559 99 ......... 1,166.510 3,637.24 1,130.498 2.1181

45 ......... 61,491.142 1,857,891.80 43,096.174 29.2140 100 ......... 832.068 2,470.73 807.606 1.9694

46 ......... 60,749.446 1,796,400.66 42,963.301 28.5707 101 ......... 579.688 1,638.66 563.464 1.8268

47 ......... 60,002.001 1,735,651.21 42,817.335 27.9266 102 ......... 393.654 1,058.97 383.169 1.6901

48 ......... 59,248.514 1,675,649.21 42,657.928 27.2817 103 ......... 259.975 665.32 253.388 1.5592

49 ......... 58,488.714 1,616,400.70 42,484.747 26.6361 104 ......... 166.549 405.35 162.536 1.4338

50 ......... 57,722.342 1,557,911.98 42,297.471 25.9898 105 ......... 103.206 238.80 100.842 1.3138

51 ......... 56,947.351 1,500,189.64 42,093.988 25.3434 106 ......... 61.660 135.59 60.317 1.1990

52 ......... 56,161.782 1,443,242.29 41,872.255 24.6979 107 ......... 35.385 73.93 34.653 1.0893

53 ......... 55,364.351 1,387,080.51 41,630.881 24.0537 108 ......... 19.423 38.54 19.042 0.9845

54 ......... 54,555.585 1,331,716.16 41,370.277 23.4103 109 ......... 10.148 19.12 9.958 0.8843

x x x x x x x x

28
Table 3.B. -- Actuarial Functions at 2.0 Percent Interest for 1989-91 United States 

Total Females

x D N M a x D N M a

0 ......... 100,000.000 3,967,435.33 22,207.150 38.6744 55 ......... 31,254.851 648,387.77 18,541.366 19.7452

1 ......... 97,227.451 3,867,435.33 21,395.386 38.7772 56 ......... 30,468.480 617,132.91 18,367.835 19.2548

2 ......... 95,256.632 3,770,207.88 21,330.987 38.5795 57 ......... 29,686.376 586,664.43 18,183.152 18.7621

3 ......... 93,349.277 3,674,951.25 21,291.410 38.3678 58 ......... 28,907.374 556,978.06 17,986.236 18.2677

4 ......... 91,489.336 3,581,601.97 21,261.847 38.1478 59 ......... 28,129.166 528,070.68 17,774.839 17.7731

5 ......... 89,672.785 3,490,112.63 21,239.203 37.9205 60 ......... 27,351.770 499,941.52 17,548.995 17.2782

6 ......... 87,894.071 3,400,439.85 21,218.780 37.6879 61 ......... 26,575.520 472,589.75 17,309.054 16.7829

7 ......... 86,152.376 3,312,545.78 21,200.498 37.4498 62 ......... 25,801.325 446,014.23 17,055.948 16.2865

8 ......... 84,446.898 3,226,393.40 21,184.282 37.2062 63 ......... 25,028.605 420,212.90 16,789.136 15.7893

9 ......... 82,777.688 3,141,946.50 21,170.894 36.9564 64 ......... 24,256.557 395,184.30 16,507.846 15.2919

10 ......... 81,141.471 3,059,168.82 21,157.768 36.7017 65 ......... 23,485.012 370,927.74 16,211.919 14.7942

11 ......... 79,538.398 2,978,027.35 21,145.704 36.4414 66 ......... 22,714.371 347,442.73 15,901.768 14.2962

12 ......... 77,966.994 2,898,488.95 21,133.877 36.1758 67 ......... 21,944.756 324,728.36 15,577.533 13.7975

13 ......... 76,424.315 2,820,521.95 21,119.962 35.9061 68 ......... 21,175.779 302,783.60 15,238.846 13.2986

14 ......... 74,909.883 2,744,097.64 21,104.047 35.6320 69 ......... 20,405.824 281,607.82 14,884.102 12.8004

15 ......... 73,420.258 2,669,187.76 21,083.243 35.3549 70 ......... 19,632.668 261,202.00 14,511.061 12.3045

16 ......... 71,955.877 2,595,767.50 21,058.476 35.0744 71 ......... 18,854.778 241,569.33 14,118.125 11.8121

17 ......... 70,516.411 2,523,811.62 21,029.909 34.7904 72 ......... 18,071.248 222,714.55 13,704.296 11.3242

18 ......... 69,102.230 2,453,295.21 20,998.402 34.5024 73 ......... 17,281.744 204,643.30 13,269.131 10.8416

19 ......... 67,714.335 2,384,192.98 20,965.453 34.2096 74 ......... 16,487.381 187,361.56 12,813.625 10.3639

20 ......... 66,352.955 2,316,478.65 20,931.805 33.9115 75 ......... 15,690.576 170,874.18 12,340.102 9.8902

21 ......... 65,018.268 2,250,125.69 20,898.156 33.6076 76 ......... 14,893.369 155,183.60 11,850.553 9.4196

22 ......... 63,708.470 2,185,107.42 20,863.227 33.2985 77 ......... 14,096.797 140,290.23 11,346.008 8.9519

23 ......... 62,425.040 2,121,398.95 20,828.982 32.9831 78 ......... 13,299.062 126,193.44 10,824.681 8.4889

24 ......... 61,166.203 2,058,973.91 20,794.166 32.6620 79 ......... 12,496.856 112,894.37 10,283.241 8.0338

25 ......... 59,932.123 1,997,807.71 20,759.423 32.3345 80 ......... 11,688.383 100,397.52 9,719.804 7.5895

26 ......... 58,722.324 1,937,875.59 20,724.763 32.0007 81 ......... 10,874.234 88,709.14 9,134.839 7.1577

27 ......... 57,536.340 1,879,153.26 20,690.197 31.6603 82 ......... 10,057.553 77,834.90 8,531.378 6.7390

28 ......... 56,373.139 1,821,616.92 20,655.160 31.3136 83 ......... 9,242.625 67,777.35 7,913.657 6.3331

29 ......... 55,231.181 1,765,243.78 20,618.558 30.9610 84 ......... 8,434.565 58,534.72 7,286.825 5.9399

30 ......... 54,110.124 1,710,012.60 20,580.465 30.6025 85 ......... 7,638.106 50,100.16 6,655.750 5.5592

31 ......... 53,009.089 1,655,902.48 20,540.413 30.2381 86 ......... 6,855.979 42,462.05 6,023.389 5.1934

32 ......... 51,927.775 1,602,893.39 20,498.493 29.8677 87 ......... 6,091.230 35,606.07 5,393.071 4.8455

33 ......... 50,866.404 1,550,965.61 20,455.314 29.4910 88 ......... 5,352.084 29,514.85 4,773.362 4.5146

34 ......... 49,824.141 1,500,099.21 20,410.431 29.1079 89 ......... 4,646.791 24,162.76 4,173.012 4.1999

35 ......... 48,800.695 1,450,275.07 20,363.929 28.7183 90 ......... 3,982.075 19,515.97 3,599.409 3.9010

36 ......... 47,795.286 1,401,474.37 20,315.397 28.3224 91 ......... 3,360.609 15,533.89 3,056.023 3.6223

37 ......... 46,808.140 1,353,679.09 20,265.413 27.9197 92 ......... 2,786.729 12,173.29 2,548.037 3.3683

38 ......... 45,837.561 1,306,870.95 20,212.640 27.5109 93 ......... 2,268.943 9,386.56 2,084.893 3.1370

39 ......... 44,883.351 1,261,033.39 20,157.207 27.0958 94 ......... 1,814.384 7,117.61 1,674.823 2.9229

40 ......... 43,945.316 1,216,150.03 20,099.237 26.6742 95 ......... 1,424.326 5,303.23 1,320.341 2.7233

41 ......... 43,022.369 1,172,204.72 20,037.963 26.2464 96 ......... 1,096.522 3,878.90 1,020.465 2.5375

42 ......... 42,114.369 1,129,182.35 19,973.538 25.8123 97 ......... 826.229 2,782.38 771.673 2.3676

43 ......... 41,219.887 1,087,067.98 19,904.828 25.3724 95 ......... 609.344 1,956.15 570.988 2.2103

44 ......... 40,338.852 1,045,848.09 19,832.027 24.9266 99 ......... 439.833 1,346.81 413.425 2.0621

45 ......... 39,469.957 1,005,509.24 19,754.089 24.4753 100 ......... 310.656 906.98 292.872 1.9196

46 ......... 38,611.584 966,039.29 19,669.637 24.0194 101 ......... 214.307 596.32 202.614 1.7826

47 ......... 37,762.629 927,427.70 19,577.772 23.5594 102 ......... 144.104 382.01 136.614 1.6509

48 ......... 36,922.845 889,665.07 19,478.432 23.0952 103 ......... 94.236 237.91 89.571 1.5246

49 ......... 36,092.002 852,742.23 19,371.566 22.6269 104 ......... 59.779 143.67 56.962 1.4034

50 ......... 35,269.885 816,650.22 19,257.135 22.1543 105 ......... 36.680 83.89 35.035 1.2872

51 ......... 34,455.204 781,380.34 19,134.021 21.6782 106 ......... 21.700 47.21 20.774 1.1758

52 ......... 33,646.771 746,925.14 19,001.180 21.1990 107 ......... 12.331 25.51 11.831 1.0692

53 ......... 32,843.839 713,278.37 18,857.989 20.7173 108 ......... 6.702 13.18 6.444 0.9671

54 ......... 32,046.760 680,434.53 18,704.907 20.2326 109 ......... 3.467 6.48 3.340 0.8695

x x x x x x x x

29
Table 3.C. -- Actuarial Functions at 3.0 Percent Interest for 1989-91 United States 

Total Females

x D N M a x D N M a

0 ......... 100,000.000 3,044,225.78 11,333.230 29.4423 55 ......... 18,275.932 334,504.35 8,533.086 17.3030

1 ......... 96,283.495 2,944,225.78 10,529.346 29.5787 56 ......... 17,643.138 316,228.42 8,432.602 16.9236

2 ......... 93,415.968 2,847,942.29 10,466.192 29.4867 57 ......... 17,023.356 298,585.28 8,326.697 16.5397

3 ......... 90,656.678 2,754,526.32 10,427.756 29.3842 58 ......... 16,415.706 281,561.92 8,214.874 16.1520

4 ......... 87,987.761 2,663,869.64 10,399.325 29.2755 59 ......... 15,818.698 265,146.22 8,095.993 15.7616

5 ......... 85,403.445 2,575,881.88 10,377.760 29.1613 60 ......... 15,232.187 249,327.52 7,970.220 15.3685

6 ......... 82,896.704 2,490,478.43 10,358.497 29.0432 61 ......... 14,656.205 234,095.33 7,837.894 14.9724

7 ......... 80,465.162 2,407,581.73 10,341.422 28.9208 62 ......... 14,091.094 219,439.13 7,699.663 14.5729

8 ......... 78,106.518 2,327,116.57 10,326.424 28.7941 63 ......... 13,536.373 205,348.03 7,555.362 14.1701

9 ......... 75,819.308 2,249,010.05 10,314.161 28.6628 64 ......... 12,991.455 191,811.66 7,404.707 13.7644

10 ......... 73,599.073 2,173,190.74 10,302.255 28.5274 65 ......... 12,456.108 178,820.21 7,247.752 13.3560

11 ......... 71,444.575 2,099,591.67 10,291.419 28.3877 66 ......... 11,930.406 166,364.10 7,084.850 12.9445

12 ......... 69,353.144 2,028,147.09 10,280.898 28.2438 67 ......... 11,414.272 154,433.69 6,916.203 12.5299

13 ......... 67,320.892 1,958,793.95 10,268.641 28.0964 68 ......... 10,907.364 143,019.42 6,741.750 12.1122

14 ......... 65,346.206 1,891,473.06 10,254.758 27.9454 69 ......... 10,408.724 132,112.06 6,560.800 11.6924

15 ......... 63,424.946 1,826,126.85 10,236.786 27.7919 70 ......... 9,917.121 121,703.33 6,372.364 11.2720

16 ......... 61,556.430 1,762,701.91 10,215.598 27.6355 71 ......... 9,431.715 111,786.21 6,175.806 10.8522

17 ......... 59,739.324 1,701,145.47 10,191.397 27.4761 72 ......... 8,952.005 102,354.50 5,970.806 10.4337

18 ......... 57,972.911 1,641,406.15 10,164.965 27.3133 73 ......... 8,477.791 93,402.49 5,757.330 10.0173

19 ......... 56,257.006 1,583,433.24 10,137.591 27.1464 74 ......... 8,009.580 84,924.70 5,536.045 9.6029

20 ......... 54,590.768 1,527,176.23 10,109.907 26.9750 75 ......... 7,548.487 76,915.12 5,308.241 9.1895

21 ......... 52,973.331 1,472,585.47 10,082.492 26.7986 76 ......... 7,095.401 69,366.63 5,075.013 8.7763

22 ......... 51,402.236 1,419,612.14 10,054.310 26.6177 77 ......... 6,650.700 62,271.23 4,836.975 8.3631

23 ......... 49,877.722 1,368,209.90 10,026.949 26.4313 78 ......... 6,213.423 55,620.53 4,593.407 7.9517

24 ......... 48,397.425 1,318,332.18 9,999.400 26.2397 79 ......... 5,781.940 49,407.11 4,342.898 7.5451

25 ......... 46,960.568 1,269,934.75 9,972.177 26.0426 80 ......... 5,355.379 43,625.17 4,084.743 7.1460

26 ......... 45,565.890 1,222,974.18 9,945.282 25.8397 81 ......... 4,933.980 38,269.79 3,819.326 6.7564

27 ......... 44,212.167 1,177,408.29 9,918.721 25.6309 82 ......... 4,519.121 33,335.81 3,548.175 6.3766

28 ......... 42,897.772 1,133,196.13 9,892.060 25.4162 83 ......... 4,112.633 28,816.69 3,273.312 6.0069

29 ......... 41,620.740 1,090,298.36 9,864.477 25.1960 84 ......... 3,716.638 24,704.06 2,997.102 5.6469

30 ......... 40,380.058 1,048,677.62 9,836.050 24.9702 85 ......... 3,333.007 20,987.42 2,721.723 5.2968

31 ......... 39,174.341 1,008,297.56 9,806.451 24.7387 86 ......... 2,962.667 17,654.41 2,448.461 4.9590

32 ......... 38,002.662 969,123.22 9,775.772 24.5015 87 ......... 2,606.642 14,691.74 2,178.727 4.6363

33 ......... 36,864.495 931,120.55 9,744.479 24.2579 88 ......... 2,268.100 12,085.10 1,916.107 4.3283

34 ......... 35,758.560 894,256.06 9,712.267 24.0082 89 ......... 1,950.094 9,817.00 1,664.162 4.0341

35 ......... 34,683.998 858,497.50 9,679.217 23.7520 90 ......... 1,654.911 7,866.91 1,425.778 3.7537

36 ......... 33,639.626 823,813.50 9,645.058 23.4894 91 ......... 1,383.077 6,212.00 1,202.145 3.4914

37 ......... 32,624.993 790,173.87 9,610.220 23.2199 92 ......... 1,135.758 4,828.92 995.110 3.2517

38 ......... 31,638.325 757,548.88 9,573.795 22.9440 93 ......... 915.752 3,693.16 808.184 3.0329

39 ......... 30,678.930 725,910.56 9,535.904 22.6615 94 ......... 725.181 2,777.41 644.285 2.8300

40 ......... 29,746.130 695,231.63 9,496.665 22.3722 95 ......... 563.754 2,052.23 503.980 2.6403

41 ......... 28,838.665 665,485.50 9,455.592 22.0762 96 ......... 429.794 1,488.48 386.440 2.4632

42 ......... 27,955.938 636,646.83 9,412.826 21.7732 97 ......... 320.705 1,058.68 289.870 2.3011

43 ......... 27,096.520 608,690.89 9,367.659 21.4638 95 ......... 234.224 737.98 212.729 2.1507

44 ......... 26,259.908 581,594.37 9,320.266 21.1476 99 ......... 167.425 503.75 152.752 2.0088

45 ......... 25,444.813 555,334.46 9,270.023 20.8251 100 ......... 117.105 336.33 107.309 1.8720

46 ......... 24,649.788 529,889.65 9,216.108 20.4967 101 ......... 80.001 219.23 73.615 1.7403

47 ......... 23,873.755 505,239.86 9,158.031 20.1630 102 ......... 53.272 139.22 49.217 1.6135

48 ......... 23,116.209 481,366.11 9,095.837 19.8237 103 ......... 34.498 85.95 31.995 1.4915

49 ......... 22,376.666 458,249.90 9,029.581 19.4789 104 ......... 21.672 51.45 20.173 1.3742

50 ......... 21,654.661 435,873.23 8,959.324 19.1284 105 ......... 13.169 29.78 12.301 1.2616

51 ......... 20,949.088 414,218.57 8,884.470 18.7726 106 ......... 7.715 16.61 7.231 1.1535

52 ......... 20,258.936 393,269.48 8,804.485 18.4121 107 ......... 4.341 8.90 4.082 1.0498

53 ......... 19,583.491 373,010.55 8,719.106 18.0472 108 ......... 2.337 4.56 2.204 0.9504

54 ......... 18,922.707 353,427.06 8,628.715 17.6774 109 ......... 1.197 2.22 1.132 0.8551

x x x x x x x x

30
Table 3.D. -- Actuarial Functions at 4.0 Percent Interest for 1989-91 United States 

Total Females

x D N M a x D N M a

0 ......... 100,000.000 2,437,866.06 6,235.921 23.3787 55 ......... 10,742.200 175,189.34 4,004.148 15.3085

1 ......... 95,357.692 2,337,866.06 5,439.767 23.5168 56 ......... 10,270.543 164,447.14 3,945.653 15.0115

2 ......... 91,628.143 2,242,508.37 5,377.822 23.4740 57 ......... 9,814.465 154,176.60 3,884.596 14.7091

3 ......... 88,066.646 2,150,880.22 5,340.484 23.4233 58 ......... 9,373.136 144,362.13 3,820.746 14.4017

4 ......... 84,652.114 2,062,813.58 5,313.130 23.3681 59 ......... 8,945.404 134,989.00 3,753.520 14.0903

5 ......... 81,375.715 1,978,161.46 5,292.582 23.3090 60 ......... 8,530.911 126,043.59 3,683.080 13.7749

6 ......... 78,227.703 1,896,785.75 5,274.405 23.2470 61 ......... 8,129.401 117,512.68 3,609.682 13.4553

7 ......... 75,202.987 1,818,558.04 5,258.446 23.1820 62 ......... 7,740.796 109,383.28 3,533.747 13.1308

8 ......... 72,296.681 1,743,355.06 5,244.563 23.1139 63 ......... 7,364.565 101,642.49 3,455.238 12.8016

9 ......... 69,504.798 1,671,058.38 5,233.322 23.0423 64 ......... 7,000.135 94,277.92 3,374.062 12.4680

10 ......... 66,820.728 1,601,553.58 5,222.513 22.9679 65 ......... 6,647.141 87,277.79 3,290.303 12.1301

11 ......... 64,240.956 1,534,732.85 5,212.769 22.8903 66 ......... 6,305.386 80,630.64 3,204.207 11.7876

12 ......... 61,760.781 1,470,491.90 5,203.400 22.8095 67 ......... 5,974.596 74,325.26 3,115.932 11.4402

13 ......... 59,374.556 1,408,731.11 5,192.590 22.7262 68 ......... 5,654.367 68,350.66 3,025.496 11.0881

14 ......... 57,078.792 1,349,356.56 5,180.463 22.6402 69 ......... 5,343.989 62,696.30 2,932.593 10.7321

15 ......... 54,867.907 1,292,277.77 5,164.916 22.5525 70 ......... 5,042.636 57,352.31 2,836.778 10.3735

16 ......... 52,739.450 1,237,409.86 5,146.763 22.4627 71 ......... 4,749.704 52,309.67 2,737.794 10.0132

17 ......... 50,690.474 1,184,670.41 5,126.228 22.3707 72 ......... 4,464.780 47,559.97 2,635.551 9.6523

18 ......... 48,718.627 1,133,979.94 5,104.014 22.2761 73 ......... 4,187.611 43,095.19 2,530.104 9.2911

19 ......... 46,822.051 1,085,261.31 5,081.232 22.1784 74 ......... 3,918.296 38,907.57 2,421.851 8.9297

20 ......... 44,998.384 1,038,439.26 5,058.412 22.0773 75 ......... 3,657.222 34,989.28 2,311.480 8.5672

21 ......... 43,245.296 993,440.87 5,036.032 21.9722 76 ......... 3,404.648 31,332.06 2,199.569 8.2027

22 ......... 41,559.230 950,195.58 5,013.246 21.8636 77 ......... 3,160.578 27,927.41 2,086.447 7.8362

23 ......... 39,938.889 908,636.35 4,991.337 21.7507 78 ......... 2,924.381 24,766.83 1,971.811 7.4691

24 ......... 38,380.931 868,697.46 4,969.490 21.6336 79 ......... 2,695.135 21,842.45 1,855.041 7.1044

25 ......... 36,883.360 830,316.53 4,948.109 21.5120 80 ......... 2,472.299 19,147.31 1,735.864 6.7447

26 ......... 35,443.849 793,433.17 4,927.189 21.3856 81 ......... 2,255.860 16,675.02 1,614.513 6.3919

27 ......... 34,060.162 757,989.32 4,906.726 21.2544 82 ......... 2,046.315 14,419.16 1,491.733 6.0464

28 ......... 32,729.813 723,929.16 4,886.384 21.1183 83 ......... 1,844.346 12,372.84 1,368.468 5.7085

29 ......... 31,450.132 691,199.34 4,865.542 20.9776 84 ......... 1,650.732 10,528.49 1,245.790 5.3781

30 ......... 30,219.238 659,749.21 4,844.268 20.8321 85 ......... 1,466.110 8,877.76 1,124.657 5.0553

31 ......... 29,035.021 629,529.97 4,822.330 20.6817 86 ......... 1,290.675 7,411.65 1,005.612 4.7425

32 ......... 27,895.770 600,494.95 4,799.810 20.5264 87 ......... 1,124.655 6,120.98 889.233 4.4425

33 ......... 26,800.106 572,599.18 4,777.060 20.3656 88 ......... 969.179 4,996.32 777.013 4.1552

34 ......... 25,746.140 545,799.08 4,753.868 20.1993 89 ......... 825.280 4,027.14 670.390 3.8797

35 ......... 24,732.336 520,052.94 4,730.300 20.0272 90 ......... 693.624 3,201.86 570.476 3.6161

36 ......... 23,756.969 495,320.60 4,706.177 19.8495 91 ......... 574.116 2,508.24 477.645 3.3689

37 ......... 22,818.873 471,563.63 4,681.810 19.6655 92 ......... 466.921 1,934.12 392.532 3.1423

38 ......... 21,915.992 448,744.76 4,656.578 19.4757 93 ......... 372.854 1,467.20 316.423 2.9351

39 ......... 21,047.075 426,828.77 4,630.584 19.2797 94 ......... 292.423 1,094.35 250.333 2.7423

40 ......... 20,210.911 405,781.69 4,603.923 19.0774 95 ......... 225.143 801.92 194.300 2.5618

41 ......... 19,405.930 385,570.78 4,576.284 18.8687 96 ......... 169.994 576.78 147.810 2.3930

42 ......... 18,631.047 366,164.85 4,547.783 18.6535 97 ......... 125.627 406.79 109.981 2.2381

43 ......... 17,884.656 347,533.80 4,517.971 18.4320 95 ......... 90.868 281.16 80.054 2.0941

44 ......... 17,165.805 329,649.15 4,486.991 18.2038 99 ......... 64.329 190.29 57.010 1.9581

45 ......... 16,473.054 312,483.34 4,454.463 17.9694 100 ......... 44.562 125.96 39.717 1.8267

46 ......... 15,804.906 296,010.29 4,419.895 17.7290 101 ......... 30.150 81.40 27.019 1.6999

47 ......... 15,160.145 280,205.38 4,383.015 17.4830 102 ......... 19.884 51.25 17.912 1.5776

48 ......... 14,537.948 265,045.24 4,343.901 17.2313 103 ......... 12.753 31.37 11.546 1.4597

49 ......... 13,937.528 250,507.29 4,302.632 16.9736 104 ......... 7.934 18.62 7.218 1.3462

50 ......... 13,358.130 236,569.76 4,259.293 16.7098 105 ......... 4.775 10.68 4.364 1.2370

51 ......... 12,798.624 223,211.63 4,213.561 16.4403 106 ......... 2.770 5.91 2.543 1.1320

52 ......... 12,257.973 210,413.01 4,165.165 16.1654 107 ......... 1.544 3.14 1.423 1.0311

53 ......... 11,735.350 198,155.04 4,114.002 15.8853 108 ......... 0.823 1.59 0.762 0.9342

54 ......... 11,230.345 186,419.69 4,060.357 15.5996 109 ......... 0.418 0.77 0.388 0.8412

x x x x x x x x

31
Table 3.E. -- Actuarial Functions at 5.0 Percent Interest for 1989-91 United States 

Total Females

x D N M a x D N M a

0 ......... 100,000.000 2,020,901.83 3,766.580 19.2090 55 ......... 6,346.225 93,053.14 1,915.122 13.6628

1 ......... 94,449.524 1,920,901.83 2,978.008 19.3379 56 ......... 6,009.795 86,706.92 1,880.894 13.4276

2 ......... 89,891.156 1,826,452.31 2,917.237 19.3185 57 ......... 5,688.227 80,697.12 1,845.507 13.1867

3 ......... 85,574.344 1,736,561.15 2,880.956 19.2930 58 ......... 5,380.706 75,008.90 1,808.854 12.9403

4 ......... 81,473.049 1,650,986.81 2,854.629 19.2642 59 ......... 5,086.258 69,628.19 1,770.629 12.6895

5 ......... 77,573.792 1,569,513.76 2,835.041 19.2325 60 ......... 4,804.385 64,541.93 1,730.960 12.4340

6 ......... 73,862.639 1,491,939.97 2,817.878 19.1988 61 ......... 4,534.663 59,737.55 1,690.018 12.1735

7 ......... 70,330.446 1,418,077.33 2,802.954 19.1631 62 ......... 4,276.772 55,202.89 1,648.063 11.9076

8 ......... 66,968.517 1,347,746.88 2,790.094 19.1251 63 ......... 4,030.154 50,926.11 1,605.101 11.6363

9 ......... 63,769.226 1,280,778.36 2,779.780 19.0846 64 ......... 3,794.242 46,895.96 1,561.101 11.3598

10 ......... 60,722.774 1,217,009.14 2,769.958 19.0421 65 ......... 3,568.597 43,101.72 1,516.134 11.0781

11 ......... 57,822.443 1,156,286.36 2,761.188 18.9972 66 ......... 3,352.882 39,533.12 1,470.353 10.7908

12 ......... 55,060.641 1,098,463.92 2,752.835 18.9501 67 ......... 3,146.728 36,180.24 1,423.860 10.4977

13 ......... 52,429.160 1,043,403.28 2,743.289 18.9012 68 ......... 2,949.706 33,033.51 1,376.682 10.1989

14 ......... 49,921.927 990,974.12 2,732.683 18.8505 69 ......... 2,761.241 30,083.80 1,328.679 9.8950

15 ......... 47,531.224 941,052.19 2,719.214 18.7986 70 ......... 2,580.717 27,322.56 1,279.643 9.5872

16 ......... 45,252.256 893,520.97 2,703.639 18.7453 71 ......... 2,407.650 24,741.85 1,229.467 9.2763

17 ......... 43,079.935 848,268.71 2,686.187 18.6906 72 ......... 2,241.666 22,334.20 1,178.133 8.9632

18 ......... 41,009.811 805,188.78 2,667.488 18.6341 73 ......... 2,082.482 20,092.53 1,125.695 8.6484

19 ......... 39,037.968 764,178.97 2,648.493 18.5753 74 ......... 1,929.995 18,010.05 1,072.374 8.3317

20 ......... 37,160.172 725,141.00 2,629.649 18.5139 75 ......... 1,784.244 16,080.05 1,018.528 8.0122

21 ......... 35,372.334 687,980.83 2,611.342 18.4497 76 ......... 1,645.202 14,295.81 964.449 7.6894

22 ......... 33,669.478 652,608.49 2,592.883 18.3828 77 ......... 1,512.717 12,650.60 910.307 7.3628

23 ......... 32,048.588 618,939.02 2,575.302 18.3125 78 ......... 1,386.338 11,137.89 855.962 7.0340

24 ......... 30,505.101 586,890.43 2,557.938 18.2391 79 ......... 1,265.493 9,751.55 801.133 6.7057

25 ......... 29,035.645 556,385.33 2,541.106 18.1621 80 ......... 1,149.805 8,486.06 745.707 6.3804

26 ......... 27,636.683 527,349.68 2,524.794 18.0815 81 ......... 1,039.153 7,336.25 689.807 6.0598

27 ......... 26,304.848 499,713.00 2,508.991 17.9970 82 ......... 933.650 6,297.10 633.788 5.7446

28 ......... 25,036.675 473,408.15 2,493.430 17.9086 83 ......... 833.485 5,363.45 578.083 5.4350

29 ......... 23,828.661 448,371.48 2,477.638 17.8165 84 ......... 738.884 4,529.96 523.171 5.1308

30 ......... 22,677.998 424,542.81 2,461.673 17.7205 85 ......... 649.995 3,791.08 469.467 4.8325

31 ......... 21,581.787 401,864.82 2,445.367 17.6206 86 ......... 566.767 3,141.09 417.191 4.5421

32 ......... 20,537.503 380,283.03 2,428.787 17.5165 87 ......... 489.160 2,574.32 366.573 4.2627

33 ......... 19,542.937 359,745.53 2,412.198 17.4080 88 ......... 417.522 2,085.16 318.229 3.9941

34 ......... 18,595.570 340,202.59 2,395.447 17.2948 89 ......... 352.144 1,667.64 272.733 3.7357

35 ......... 17,693.207 321,607.02 2,378.587 17.1769 90 ......... 293.149 1,315.49 230.506 3.4875

36 ......... 16,833.580 303,913.81 2,361.494 17.0540 91 ......... 240.330 1,022.34 191.647 3.2539

37 ......... 16,014.880 287,080.23 2,344.392 16.9258 92 ......... 193.595 782.01 156.357 3.0394

38 ......... 15,234.726 271,065.35 2,326.853 16.7926 93 ......... 153.121 588.42 125.101 2.8428

39 ......... 14,491.366 255,830.63 2,308.955 16.6540 94 ......... 118.946 435.30 98.218 2.6596

40 ......... 13,783.119 241,339.26 2,290.773 16.5098 95 ......... 90.707 316.35 75.643 2.4876

41 ......... 13,108.111 227,556.14 2,272.104 16.3599 96 ......... 67.836 225.64 57.091 2.3263

42 ......... 12,464.847 214,448.03 2,253.036 16.2042 97 ......... 49.654 157.81 42.139 2.1782

43 ......... 11,851.527 201,983.18 2,233.280 16.0428 95 ......... 35.574 108.15 30.423 2.0403

44 ......... 11,266.835 190,131.66 2,212.947 15.8753 99 ......... 24.944 72.58 21.488 1.9098

45 ......... 10,709.173 178,864.82 2,191.800 15.7020 100 ......... 17.115 47.64 14.846 1.7834

46 ......... 10,176.953 168,155.65 2,169.541 15.5232 101 ......... 11.469 30.52 10.016 1.6612

47 ......... 9,668.815 157,978.70 2,146.020 15.3390 102 ......... 7.492 19.05 6.585 1.5432

48 ......... 9,183.687 148,309.88 2,121.311 15.1493 103 ......... 4.759 11.56 4.209 1.4292

49 ......... 8,720.547 139,126.20 2,095.490 14.9538 104 ......... 2.933 6.80 2.609 1.3193

50 ......... 8,278.424 130,405.65 2,068.631 14.7525 105 ......... 1.748 3.87 1.564 1.2133

51 ......... 7,856.142 122,127.22 2,040.560 14.5454 106 ......... 1.005 2.12 0.904 1.1112

52 ......... 7,452.616 114,271.08 2,011.136 14.3330 107 ......... 0.555 1.12 0.501 1.0130

53 ......... 7,066.920 106,818.47 1,980.326 14.1153 108 ......... 0.293 0.56 0.266 0.9185

54 ......... 6,698.403 99,751.55 1,948.329 13.8918 109 ......... 0.147 0.27 0.134 0.8277

x x x x x x x x

32
Table 3.F. -- Actuarial Functions at 6.0 Percent Interest for 1989-91 United States 

Total Females

x D N M a x D N M a

0 ......... 100,000.000 1,722,061.17 2,524.840 16.2206 55 ......... 3,767.943 50,080.97 933.171 12.2913

1 ......... 93,558.491 1,622,061.17 1,743.707 16.3374 56 ......... 3,534.532 46,313.03 913.040 12.1030

2 ......... 88,203.097 1,528,502.68 1,684.078 16.3294 57 ......... 3,313.849 42,778.50 892.424 11.9090

3 ......... 83,175.205 1,440,299.58 1,648.814 16.3165 58 ......... 3,105.120 39,464.65 871.272 11.7095

4 ......... 78,441.828 1,357,124.38 1,623.467 16.3010 59 ......... 2,907.508 36,359.53 849.422 11.5054

5 ......... 73,983.043 1,278,682.55 1,604.785 16.2835 60 ......... 2,720.469 33,452.02 826.959 11.2964

6 ......... 69,779.109 1,204,699.51 1,588.571 16.2645 61 ......... 2,543.516 30,731.55 803.994 11.0823

7 ......... 65,815.382 1,134,920.40 1,574.605 16.2440 62 ......... 2,376.233 28,188.04 780.684 10.8625

8 ......... 62,078.062 1,069,105.01 1,562.684 16.2219 63 ......... 2,218.084 25,811.80 757.038 10.6370

9 ......... 58,554.739 1,007,026.95 1,553.214 16.1980 64 ......... 2,068.544 23,593.72 733.051 10.4060

10 ......... 55,231.386 948,472.21 1,544.279 16.1727 65 ......... 1,927.173 21,525.18 708.767 10.1693

11 ......... 52,097.179 893,240.83 1,536.378 16.1457 66 ......... 1,793.597 19,598.00 684.276 9.9266

12 ......... 49,140.828 841,143.65 1,528.923 16.1170 67 ......... 1,667.436 17,804.41 659.640 9.6777

13 ......... 46,350.832 792,002.82 1,520.484 16.0871 68 ......... 1,548.290 16,136.97 634.876 9.4224

14 ......... 43,717.912 745,651.99 1,511.196 16.0560 69 ......... 1,435.692 14,588.68 609.918 9.1614

15 ......... 41,231.630 701,934.08 1,499.512 16.0242 70 ......... 1,329.171 13,152.99 584.662 8.8956

16 ......... 38,884.380 660,702.45 1,486.128 15.9915 71 ......... 1,228.336 11,823.82 559.063 8.6259

17 ......... 36,668.523 621,818.07 1,471.274 15.9578 72 ......... 1,132.865 10,595.48 533.121 8.3528

18 ......... 34,577.180 585,149.54 1,455.508 15.9230 73 ......... 1,042.490 9,462.62 506.870 8.0769

19 ......... 32,604.117 550,572.36 1,439.644 15.8866 74 ......... 957.041 8,420.13 480.430 7.7981

20 ......... 30,743.011 517,968.25 1,424.053 15.8483 75 ......... 876.419 7,463.08 453.980 7.5154

21 ......... 28,987.838 487,225.24 1,409.051 15.8079 76 ......... 800.498 6,586.67 427.668 7.2282

22 ......... 27,332.032 458,237.40 1,394.066 15.7656 77 ......... 729.092 5,786.17 401.573 6.9361

23 ......... 25,770.799 430,905.37 1,379.929 15.7207 78 ......... 661.876 5,057.08 375.627 6.6405

24 ......... 24,298.244 405,134.57 1,366.098 15.6734 79 ......... 598.482 4,395.20 349.697 6.3439

25 ......... 22,909.590 380,836.32 1,352.817 15.6234 80 ......... 538.640 3,796.72 323.732 6.0487

26 ......... 21,600.072 357,926.73 1,340.068 15.5706 81 ......... 482.211 3,258.08 297.792 5.7565

27 ......... 20,365.192 336,326.66 1,327.834 15.5148 82 ......... 429.166 2,775.87 272.042 5.4680

28 ......... 19,200.512 315,961.47 1,315.900 15.4559 83 ......... 379.510 2,346.70 246.678 5.1835

29 ......... 18,101.694 296,760.96 1,303.904 15.3941 84 ......... 333.261 1,967.19 221.911 4.9029

30 ......... 17,065.056 278,659.26 1,291.890 15.3292 85 ......... 290.403 1,633.93 197.917 4.6264

31 ......... 16,086.955 261,594.21 1,279.736 15.2613 86 ......... 250.830 1,343.53 174.782 4.3563

32 ......... 15,164.131 245,507.25 1,267.494 15.1900 87 ......... 214.442 1,092.70 152.591 4.0955

33 ......... 14,293.650 230,343.12 1,255.360 15.1151 88 ......... 181.310 878.25 131.598 3.8439

34 ......... 13,472.440 216,049.47 1,243.224 15.0364 89 ......... 151.477 696.94 112.027 3.6010

35 ......... 12,697.749 202,577.03 1,231.124 14.9538 90 ......... 124.910 545.47 94.034 3.3669

36 ......... 11,966.857 189,879.28 1,218.973 14.8671 91 ......... 101.438 420.56 77.633 3.1460

37 ......... 11,277.445 177,912.43 1,206.931 14.7760 92 ......... 80.941 319.12 62.878 2.9426

38 ......... 10,626.865 166,634.98 1,194.696 14.6805 93 ......... 63.415 238.18 49.934 2.7558

39 ......... 10,012.977 156,008.12 1,182.329 14.5806 94 ......... 48.797 174.76 38.905 2.5814

40 ......... 9,433.761 145,995.14 1,169.885 14.4758 95 ......... 36.861 125.97 29.731 2.4173

41 ......... 8,887.117 136,561.38 1,157.228 14.3662 96 ......... 27.307 89.10 22.263 2.2631

42 ......... 8,371.266 127,674.26 1,144.422 14.2515 97 ......... 19.799 61.80 16.301 2.1212

43 ......... 7,884.279 119,302.99 1,131.279 14.1318 95 ......... 14.051 42.00 11.674 1.9890

44 ......... 7,424.599 111,418.72 1,117.880 14.0067 99 ......... 9.759 27.95 8.178 1.8636

45 ......... 6,990.535 103,994.12 1,104.076 13.8764 100 ......... 6.633 18.19 5.604 1.7420

46 ......... 6,580.452 97,003.58 1,089.683 13.7412 101 ......... 4.403 11.55 3.749 1.6242

47 ......... 6,192.908 90,423.13 1,074.618 13.6011 102 ......... 2.849 7.15 2.444 1.5102

48 ......... 5,826.689 84,230.22 1,058.941 13.4559 103 ......... 1.793 4.30 1.549 1.3999

49 ......... 5,480.649 78,403.53 1,042.713 13.3055 104 ......... 1.094 2.51 0.952 1.2933

50 ......... 5,153.703 72,922.88 1,025.992 13.1496 105 ......... 0.646 1.42 0.566 1.1904

51 ......... 4,844.673 67,769.18 1,008.682 12.9884 106 ......... 0.368 0.77 0.324 1.0911

52 ......... 4,552.472 62,924.51 990.708 12.8221 107 ......... 0.201 0.40 0.178 0.9955

53 ......... 4,276.142 58,372.03 972.065 12.6506 108 ......... 0.105 0.20 0.094 0.9033

54 ......... 4,014.918 54,095.89 952.886 12.4737 109 ......... 0.052 0.10 0.047 0.8146

x x x x x x x x

33
Table 3.G. -- Actuarial Functions at 7.0 Percent Interest for 1989-91 United States 

Total Females

x D N M a x D N M a

0 ......... 100,000.000 1,499,938.61 1,873.175 13.9994 55 ......... 2,248.118 27,287.23 462.972 11.1378

1 ......... 92,684.112 1,399,938.61 1,099.343 14.1044 56 ......... 2,089.146 25,039.11 451.074 10.9853

2 ......... 86,562.145 1,307,254.50 1,040.823 14.1019 57 ......... 1,940.402 22,949.96 439.002 10.8274

3 ......... 80,864.917 1,220,692.35 1,006.538 14.0955 58 ......... 1,801.190 21,009.56 426.733 10.6643

4 ......... 75,550.276 1,139,827.44 982.126 14.0870 59 ......... 1,670.799 19,208.37 414.176 10.4965

5 ......... 70,589.910 1,064,277.16 964.301 14.0769 60 ......... 1,548.706 17,537.57 401.388 10.3240

6 ......... 65,956.552 993,687.25 948.975 14.0658 61 ......... 1,434.438 15,988.87 388.437 10.1464

7 ......... 61,628.560 927,730.70 935.897 14.0536 62 ......... 1,327.573 14,554.43 375.414 9.9632

8 ......... 57,585.727 866,102.14 924.839 14.0402 63 ......... 1,227.636 13,226.86 362.327 9.7743

9 ......... 53,809.733 808,516.41 916.136 14.0255 64 ......... 1,134.171 11,999.22 349.175 9.5797

10 ......... 50,281.337 754,706.68 908.003 14.0097 65 ......... 1,046.782 10,865.05 335.985 9.3795

11 ......... 46,984.777 704,425.34 900.876 13.9926 66 ......... 965.123 9,818.27 322.807 9.1731

12 ......... 43,904.347 657,440.56 894.216 13.9744 67 ......... 888.851 8,853.14 309.674 8.9602

13 ......... 41,024.630 613,536.22 886.747 13.9553 68 ......... 817.625 7,964.29 296.597 8.7408

14 ......... 38,332.632 572,511.59 878.603 13.9354 69 ......... 751.078 7,146.67 283.539 8.5152

15 ......... 35,814.741 534,178.96 868.454 13.9151 70 ......... 688.854 6,395.59 270.450 8.2844

16 ......... 33,460.204 498,364.21 856.937 13.8942 71 ......... 630.646 5,706.74 257.308 8.0490

17 ......... 31,258.555 464,904.01 844.274 13.8729 72 ......... 576.194 5,076.09 244.113 7.8097

18 ......... 29,200.289 433,645.46 830.960 13.8507 73 ......... 525.272 4,499.90 230.886 7.5668

19 ......... 27,276.718 404,445.17 817.688 13.8275 74 ......... 477.711 3,974.62 217.688 7.3202

20 ......... 25,479.338 377,168.45 804.767 13.8029 75 ......... 433.380 3,496.91 204.609 7.0689

21 ......... 23,800.149 351,689.11 792.450 13.7768 76 ......... 392.138 3,063.53 191.720 6.8124

22 ......... 22,230.941 327,888.96 780.261 13.7492 77 ......... 353.820 2,671.40 179.056 6.5502

23 ......... 20,765.189 305,658.02 768.870 13.7197 78 ......... 318.200 2,317.58 166.583 6.2834

24 ......... 19,395.679 284,892.83 757.830 13.6885 79 ......... 285.033 1,999.38 154.233 6.0145

25 ......... 18,116.300 265,497.15 747.328 13.6552 80 ......... 254.136 1,714.34 141.983 5.7458

26 ......... 16,921.135 247,380.85 737.340 13.6196 81 ......... 225.386 1,460.21 129.858 5.4787

27 ......... 15,804.650 230,459.72 727.846 13.5818 82 ......... 198.718 1,234.82 117.935 5.2139

28 ......... 14,761.526 214,655.07 718.671 13.5415 83 ......... 174.083 1,036.10 106.300 4.9518

29 ......... 13,786.682 199,893.54 709.534 13.4990 84 ......... 151.440 862.02 95.046 4.6922

30 ......... 12,875.685 186,106.86 700.470 13.4541 85 ......... 130.731 710.58 84.245 4.4354

31 ......... 12,024.266 173,231.18 691.385 13.4068 86 ......... 111.861 579.85 73.927 4.1837

32 ......... 11,228.567 161,206.91 682.320 13.3569 87 ......... 94.740 467.99 64.123 3.9397

33 ......... 10,485.087 149,978.34 673.420 13.3040 88 ......... 79.353 373.25 54.935 3.7036

34 ......... 9,790.328 139,493.26 664.601 13.2481 89 ......... 65.677 293.90 46.450 3.4749

35 ......... 9,141.128 129,702.93 655.890 13.1889 90 ......... 53.652 228.22 38.722 3.2537

36 ......... 8,534.444 120,561.80 647.224 13.1265 91 ......... 43.163 174.57 31.743 3.0444

37 ......... 7,967.608 112,027.36 638.716 13.0603 92 ......... 34.120 131.40 25.523 2.8513

38 ......... 7,437.800 104,059.75 630.153 12.9907 93 ......... 26.482 97.28 20.117 2.6736

39 ......... 6,942.640 96,621.95 621.578 12.9172 94 ......... 20.187 70.80 15.555 2.5074

40 ......... 6,479.901 89,679.31 613.030 12.8396 95 ......... 15.107 50.62 11.795 2.3506

41 ......... 6,047.369 83,199.41 604.417 12.7580 96 ......... 11.086 35.51 8.763 2.2030

42 ......... 5,643.114 77,152.04 595.785 12.6719 97 ......... 7.963 24.42 6.365 2.0670

43 ......... 5,265.162 71,508.92 587.008 12.5815 95 ......... 5.598 16.46 4.522 1.9401

44 ......... 4,911.847 66,243.76 578.143 12.4865 99 ......... 3.852 10.86 3.142 1.8195

45 ......... 4,581.465 61,331.91 569.097 12.3870 100 ......... 2.594 7.01 2.135 1.7024

46 ......... 4,272.398 56,750.45 559.752 12.2830 101 ......... 1.706 4.42 1.417 1.5887

47 ......... 3,983.206 52,478.05 550.062 12.1748 102 ......... 1.093 2.71 0.916 1.4785

48 ......... 3,712.633 48,494.84 540.074 12.0621 103 ......... 0.682 1.62 0.576 1.3717

49 ......... 3,459.508 44,782.21 529.830 11.9447 104 ......... 0.412 0.93 0.351 1.2683

50 ......... 3,222.729 41,322.70 519.374 11.8223 105 ......... 0.241 0.52 0.207 1.1684

51 ......... 3,001.172 38,099.98 508.651 11.6950 106 ......... 0.136 0.28 0.118 1.0718

52 ......... 2,793.804 35,098.80 497.620 11.5631 107 ......... 0.074 0.15 0.064 0.9786

53 ......... 2,599.697 32,305.00 486.286 11.4264 108 ......... 0.038 0.07 0.033 0.8886

54 ......... 2,418.073 29,705.30 474.736 11.2847 109 ......... 0.019 0.03 0.017 0.8019

x x x x x x x x

34
Table 3.H. -- Actuarial Functions at 8.0 Percent Interest for 1989-91 United States 

Total Females

x D N M a x D N M a

0 ......... 100,000.000 1,329,559.68 1,514.098 12.2956 55 ......... 1,347.784 15,039.90 233.717 10.1590

1 ......... 91,825.926 1,229,559.68 747.431 12.3901 56 ......... 1,240.881 13,692.12 226.650 10.0342

2 ......... 84,966.564 1,137,733.75 689.990 12.3904 57 ......... 1,141.860 12,451.24 219.546 9.9043

3 ......... 78,639.403 1,052,767.19 656.649 12.3873 58 ......... 1,050.124 11,309.38 212.393 9.7696

4 ......... 72,790.741 974,127.78 633.128 12.3826 59 ......... 965.085 10,259.25 205.140 9.6304

5 ......... 67,381.820 901,337.04 616.113 12.3766 60 ......... 886.279 9,294.17 197.822 9.4867

6 ......... 62,376.080 833,955.22 601.619 12.3698 61 ......... 813.286 8,407.89 190.479 9.3382

7 ......... 57,743.376 771,579.14 589.366 12.3622 62 ......... 745.727 7,594.60 183.164 9.1842

8 ......... 53,455.824 713,835.77 579.101 12.3538 63 ......... 683.205 6,848.88 175.880 9.0246

9 ......... 49,488.130 660,379.94 571.097 12.3442 64 ......... 625.345 6,165.67 168.629 8.8596

10 ......... 45,814.931 610,891.81 563.686 12.3339 65 ......... 571.818 5,540.33 161.423 8.6890

11 ......... 42,414.799 565,076.88 557.253 12.3226 66 ......... 522.329 4,968.51 154.291 8.5122

12 ......... 39,267.006 522,662.08 551.296 12.3105 67 ......... 476.596 4,446.18 147.250 8.3290

13 ......... 36,351.720 483,395.08 544.677 12.2977 68 ......... 434.346 3,969.58 140.303 8.1392

14 ......... 33,651.850 447,043.36 537.528 12.2844 69 ......... 395.300 3,535.24 133.431 7.9432

15 ......... 31,150.294 413,391.51 528.701 12.2709 70 ......... 359.193 3,139.94 126.605 7.7416

16 ......... 28,832.940 382,241.21 518.777 12.2571 71 ......... 325.797 2,780.74 119.816 7.5352

17 ......... 26,686.356 353,408.27 507.966 12.2430 72 ......... 294.910 2,454.95 113.062 7.3244

18 ......... 24,698.328 326,721.92 496.705 12.2285 73 ......... 266.358 2,160.04 106.355 7.1095

19 ......... 22,857.700 302,023.59 485.582 12.2132 74 ......... 239.997 1,893.68 99.725 6.8904

20 ......... 21,153.810 279,165.89 474.855 12.1970 75 ......... 215.710 1,653.68 93.215 6.6662

21 ......... 19,576.729 258,012.08 464.724 12.1795 76 ......... 193.375 1,437.97 86.859 6.4362

22 ......... 18,116.668 238,435.35 454.791 12.1611 77 ......... 172.864 1,244.60 80.672 6.1999

23 ......... 16,765.496 220,318.68 445.594 12.1412 78 ......... 154.022 1,071.73 74.634 5.9583

24 ......... 15,514.776 203,553.18 436.763 12.1200 79 ......... 136.690 917.71 68.712 5.7138

25 ......... 14,357.211 188,038.41 428.440 12.0971 80 ......... 120.745 781.02 62.891 5.4684

26 ......... 13,285.872 173,681.20 420.598 12.0726 81 ......... 106.093 660.28 57.184 5.2235

27 ......... 12,294.347 160,395.33 413.212 12.0463 82 ......... 92.674 554.18 51.624 4.9799

28 ......... 11,376.584 148,100.98 406.141 12.0181 83 ......... 80.434 461.51 46.248 4.7378

29 ......... 10,526.898 136,724.39 399.165 11.9881 84 ......... 69.324 381.08 41.096 4.4970

30 ......... 9,740.270 126,197.50 392.308 11.9563 85 ......... 59.290 311.75 36.197 4.2581

31 ......... 9,011.960 116,457.23 385.499 11.9225 86 ......... 50.262 252.46 31.561 4.0229

32 ......... 8,337.676 107,445.27 378.768 11.8867 87 ......... 42.175 202.20 27.197 3.7943

33 ......... 7,713.523 99,107.59 372.220 11.8486 88 ......... 34.998 160.02 23.145 3.5723

34 ......... 7,135.723 91,394.07 365.792 11.8080 89 ......... 28.698 125.03 19.437 3.3566

35 ......... 6,600.861 84,258.34 359.502 11.7648 90 ......... 23.227 96.33 16.091 3.1473

36 ......... 6,105.708 77,657.48 353.302 11.7188 91 ......... 18.513 73.10 13.098 2.9487

37 ......... 5,647.403 71,551.78 347.272 11.6699 92 ......... 14.499 54.59 10.455 2.7651

38 ......... 5,223.064 65,904.37 341.258 11.6180 93 ......... 11.149 40.09 8.179 2.5959

39 ......... 4,830.204 60,681.31 335.293 11.5629 94 ......... 8.420 28.94 6.276 2.4372

40 ......... 4,466.520 55,851.10 329.401 11.5044 95 ......... 6.243 20.52 4.723 2.2873

41 ......... 4,129.785 51,384.58 323.519 11.4424 96 ......... 4.539 14.28 3.481 2.1458

42 ......... 3,818.034 47,254.80 317.678 11.3767 97 ......... 3.230 9.74 2.509 2.0153

43 ......... 3,529.333 43,436.77 311.795 11.3074 95 ......... 2.250 6.51 1.768 1.8934

44 ......... 3,262.014 39,907.43 305.908 11.2340 99 ......... 1.534 4.26 1.218 1.7773

45 ......... 3,014.431 36,645.42 299.956 11.1567 100 ......... 1.023 2.73 0.821 1.6644

46 ......... 2,785.049 33,630.99 293.864 11.0755 101 ......... 0.667 1.70 0.540 1.5547

47 ......... 2,572.491 30,845.94 287.606 10.9907 102 ......... 0.423 1.04 0.347 1.4480

48 ......... 2,375.544 28,273.45 281.215 10.9019 103 ......... 0.261 0.61 0.216 1.3446

49 ......... 2,193.085 25,897.90 274.721 10.8089 104 ......... 0.157 0.35 0.131 1.2443

50 ......... 2,024.067 23,704.82 268.154 10.7115 105 ......... 0.091 0.19 0.076 1.1471

51 ......... 1,867.463 21,680.75 261.482 10.6097 106 ......... 0.051 0.10 0.043 1.0531

52 ......... 1,722.333 19,813.29 254.682 10.5038 107 ......... 0.027 0.05 0.023 0.9622

53 ......... 1,587.830 18,090.96 247.759 10.3935 108 ......... 0.014 0.03 0.012 0.8744

54 ......... 1,463.223 16,503.13 240.769 10.2786 109 ......... 0.007 0.01 0.006 0.7896

x x x x x x x x

35
Table 3.I. -- Actuarial Functions at 9.0 Percent Interest for 1989-91 United States 

Total Females

x D N M a x D N M a

0 ......... 100,000.000 1,195,304.86 1,305.104 10.9530 55 ......... 811.838 8,379.37 119.964 9.3215

1 ......... 90,983.486 1,095,304.86 545.471 11.0385 56 ......... 740.588 7,567.53 115.746 9.2183

2 ......... 83,414.696 1,004,321.37 489.078 11.0401 57 ......... 675.238 6,826.95 111.545 9.1104

3 ......... 76,494.812 920,906.67 456.646 11.0388 58 ......... 615.293 6,151.71 107.353 8.9980

4 ......... 70,156.057 844,411.86 433.977 11.0362 59 ......... 560.278 5,536.42 103.143 8.8815

5 ......... 64,347.107 774,255.80 417.728 11.0325 60 ......... 509.807 4,976.14 98.933 8.7608

6 ......... 59,020.329 709,908.70 404.014 11.0282 61 ......... 463.528 4,466.33 94.748 8.6355

7 ......... 54,135.603 650,888.37 392.527 11.0233 62 ......... 421.124 4,002.80 90.617 8.5050

8 ......... 49,656.155 596,752.77 382.991 11.0177 63 ......... 382.277 3,581.68 86.542 8.3693

9 ......... 45,548.739 547,096.61 375.624 11.0112 64 ......... 346.692 3,199.40 82.522 8.2284

10 ......... 41,781.075 501,547.87 368.866 11.0042 65 ......... 314.108 2,852.71 78.564 8.0819

11 ......... 38,325.449 459,766.80 363.053 10.9964 66 ......... 284.291 2,538.60 74.682 7.9296

12 ......... 35,155.629 421,441.35 357.720 10.9879 67 ......... 257.020 2,254.31 70.884 7.7710

13 ......... 32,247.000 386,285.72 351.849 10.9790 68 ......... 232.086 1,997.29 67.172 7.6058

14 ......... 29,578.119 354,038.72 345.564 10.9696 69 ......... 209.285 1,765.20 63.534 7.4345

15 ......... 27,128.202 324,460.60 337.877 10.9603 70 ......... 188.424 1,555.92 59.954 7.2575

16 ......... 24,879.695 297,332.40 329.314 10.9508 71 ......... 169.337 1,367.49 56.425 7.0756

17 ......... 22,816.165 272,452.70 320.071 10.9412 72 ......... 151.877 1,198.16 52.947 6.8890

18 ......... 20,922.722 249,636.54 310.531 10.9314 73 ......... 135.914 1,046.28 49.524 6.6981

19 ......... 19,185.822 228,713.81 301.196 10.9210 74 ......... 121.340 910.37 46.172 6.5026

20 ......... 17,592.750 209,527.99 292.274 10.9099 75 ......... 108.060 789.03 42.911 6.3017

21 ......... 16,131.789 191,935.24 283.925 10.8980 76 ......... 95.983 680.97 39.756 6.0947

22 ......... 14,791.697 175,803.45 275.816 10.8853 77 ......... 85.015 584.98 36.713 5.8810

23 ......... 13,562.924 161,011.76 268.375 10.8715 78 ......... 75.053 499.97 33.771 5.6616

24 ......... 12,435.971 147,448.83 261.297 10.8566 79 ......... 65.997 424.92 30.912 5.4385

25 ......... 11,402.537 135,012.86 254.687 10.8406 80 ......... 57.763 358.92 28.127 5.2137

26 ......... 10,454.873 123,610.32 248.516 10.8232 81 ......... 50.288 301.16 25.422 4.9886

27 ......... 9,585.868 113,155.45 242.757 10.8044 82 ......... 43.524 250.87 22.811 4.7638

28 ......... 8,788.911 103,569.58 237.294 10.7841 83 ......... 37.429 207.34 20.309 4.5396

29 ......... 8,057.881 94,780.67 231.954 10.7625 84 ......... 31.963 169.91 17.934 4.3159

30 ......... 7,387.351 86,722.79 226.754 10.7394 85 ......... 27.086 137.95 15.696 4.0931

31 ......... 6,772.269 79,335.44 221.637 10.7147 86 ......... 22.751 110.87 13.597 3.8729

32 ......... 6,208.080 72,563.17 216.625 10.6885 87 ......... 18.915 88.11 11.640 3.6583

33 ......... 5,690.655 66,355.09 211.795 10.6604 88 ......... 15.553 69.20 9.839 3.4493

34 ......... 5,216.086 60,664.43 207.096 10.6303 89 ......... 12.636 53.65 8.207 3.2455

35 ......... 4,780.844 55,448.35 202.540 10.5980 90 ......... 10.133 41.01 6.747 3.0471

36 ......... 4,381.646 50,667.50 198.091 10.5636 91 ......... 8.002 30.88 5.453 2.8584

37 ......... 4,015.571 46,285.86 193.803 10.5266 92 ......... 6.210 22.87 4.321 2.6836

38 ......... 3,679.774 42,270.29 189.566 10.4872 93 ......... 4.731 16.66 3.355 2.5223

39 ......... 3,371.775 38,590.51 185.402 10.4452 94 ......... 3.540 11.93 2.555 2.3706

40 ......... 3,089.296 35,218.74 181.327 10.4002 95 ......... 2.601 8.39 1.908 2.2271

41 ......... 2,830.186 32,129.44 177.296 10.3524 96 ......... 1.874 5.79 1.395 2.0914

42 ......... 2,592.535 29,299.26 173.330 10.3014 97 ......... 1.321 3.92 0.998 1.9660

43 ......... 2,374.514 26,706.72 169.372 10.2472 95 ......... 0.912 2.60 0.697 1.8487

44 ......... 2,174.529 24,332.21 165.448 10.1896 99 ......... 0.616 1.69 0.477 1.7370

45 ......... 1,991.049 22,157.68 161.516 10.1286 100 ......... 0.407 1.07 0.319 1.6281

46 ......... 1,822.664 20,166.63 157.529 10.0644 101 ......... 0.263 0.66 0.208 1.5220

47 ......... 1,668.111 18,343.97 153.471 9.9969 102 ......... 0.165 0.40 0.132 1.4188

48 ......... 1,526.270 16,675.85 149.365 9.9259 103 ......... 0.101 0.23 0.082 1.3185

49 ......... 1,396.114 15,149.58 145.231 9.8512 104 ......... 0.060 0.13 0.049 1.2211

50 ......... 1,276.697 13,753.47 141.089 9.7727 105 ......... 0.034 0.07 0.028 1.1266

51 ......... 1,167.111 12,476.77 136.919 9.6903 106 ......... 0.019 0.04 0.016 1.0350

52 ......... 1,066.533 11,309.66 132.708 9.6041 107 ......... 0.010 0.02 0.009 0.9463

53 ......... 974.224 10,243.13 128.461 9.5141 108 ......... 0.005 0.01 0.004 0.8606

54 ......... 889.534 9,268.91 124.211 9.4200 109 ......... 0.002 0.00 0.002 0.7777

x x x x x x x x

36
Table 3.J. -- Actuarial Functions at 10.0 Percent Interest for 1989-91 United States 

Total Females

x D N M a x D N M a

0 ......... 100,000.000 1,087,064.09 1,175.992 9.8706 55 ......... 491.280 4,715.93 62.559 8.5993

1 ......... 90,156.364 987,064.09 423.265 9.9484 56 ......... 444.089 4,224.65 60.030 8.5131

2 ......... 81,904.959 896,907.73 367.893 9.9506 57 ......... 401.221 3,780.56 57.534 8.4226

3 ......... 74,427.498 815,002.77 336.337 9.9503 58 ......... 362.279 3,379.34 55.066 8.3280

4 ......... 67,639.505 740,575.27 314.481 9.9489 59 ......... 326.888 3,017.06 52.609 8.2297

5 ......... 61,474.937 672,935.76 298.958 9.9465 60 ......... 294.737 2,690.18 50.175 8.1274

6 ......... 55,873.323 611,460.83 285.975 9.9437 61 ......... 265.545 2,395.44 47.778 8.0208

7 ......... 50,783.154 555,587.50 275.199 9.9404 62 ......... 239.060 2,129.89 45.433 7.9095

8 ......... 46,157.640 504,804.35 266.335 9.9365 63 ......... 215.035 1,890.84 43.140 7.7932

9 ......... 41,954.705 458,646.71 259.550 9.9319 64 ......... 193.245 1,675.80 40.900 7.6719

10 ......... 38,134.472 416,692.01 253.381 9.9269 65 ......... 173.491 1,482.56 38.713 7.5454

11 ......... 34,662.445 378,557.53 248.123 9.9213 66 ......... 155.595 1,309.06 36.589 7.4133

12 ......... 31,506.534 343,895.09 243.344 9.9150 67 ......... 139.390 1,153.47 34.529 7.2751

13 ......... 28,637.090 312,388.55 238.130 9.9085 68 ......... 124.724 1,014.08 32.535 7.1306

14 ......... 26,028.188 283,751.47 232.600 9.9017 69 ......... 111.448 889.36 30.597 6.9800

15 ......... 23,655.286 257,723.28 225.897 9.8950 70 ......... 99.427 777.91 28.708 6.8239

16 ......... 21,497.406 234,067.99 218.498 9.8882 71 ......... 88.543 678.48 26.863 6.6628

17 ......... 19,535.183 212,570.59 210.584 9.8814 72 ......... 78.691 589.94 25.061 6.4969

18 ......... 17,751.163 193,035.40 202.490 9.8745 73 ......... 69.781 511.25 23.303 6.3265

19 ......... 16,129.573 175,284.24 194.642 9.8673 74 ......... 61.731 441.47 21.598 6.1514

20 ......... 14,655.816 159,154.67 187.210 9.8595 75 ......... 54.475 379.74 19.954 5.9708

21 ......... 13,316.577 144,498.85 180.318 9.8511 76 ......... 47.947 325.26 18.378 5.7837

22 ......... 12,099.346 131,182.27 173.684 9.8421 77 ......... 42.082 277.31 16.872 5.5898

23 ......... 10,993.374 119,082.93 167.654 9.8322 78 ......... 36.813 235.23 15.429 5.3898

24 ......... 9,988.291 108,089.55 161.968 9.8216 79 ......... 32.077 198.42 14.039 5.1857

25 ......... 9,075.004 98,101.26 156.707 9.8101 80 ......... 27.820 166.34 12.698 4.9792

26 ......... 8,245.137 89,026.26 151.841 9.7974 81 ......... 24.000 138.52 11.407 4.7718

27 ......... 7,491.079 80,781.12 147.341 9.7836 82 ......... 20.583 114.52 10.172 4.5639

28 ......... 6,805.842 73,290.04 143.111 9.7687 83 ......... 17.539 93.94 9.000 4.3558

29 ......... 6,183.031 66,484.20 139.013 9.7527 84 ......... 14.842 76.40 7.897 4.1475

30 ......... 5,616.983 60,301.17 135.059 9.7355 85 ......... 12.463 61.56 6.867 3.9392

31 ......... 5,102.493 54,684.19 131.203 9.7172 86 ......... 10.373 49.09 5.910 3.7328

32 ......... 4,634.888 49,581.69 127.462 9.6975 87 ......... 8.546 38.72 5.026 3.5309

33 ......... 4,209.961 44,946.80 123.888 9.6763 88 ......... 6.963 30.17 4.220 3.3338

34 ......... 3,823.793 40,736.84 120.444 9.6535 89 ......... 5.606 23.21 3.495 3.1409

35 ......... 3,472.866 36,913.05 117.134 9.6290 90 ......... 4.454 17.61 2.854 2.9527

36 ......... 3,153.948 33,440.18 113.932 9.6026 91 ......... 3.486 13.15 2.290 2.7731

37 ......... 2,864.167 30,286.24 110.873 9.5742 92 ......... 2.680 9.67 1.802 2.6065

38 ......... 2,600.794 27,422.07 107.879 9.5437 93 ......... 2.024 6.99 1.388 2.4524

39 ......... 2,361.442 24,821.27 104.962 9.5111 94 ......... 1.500 4.96 1.049 2.3074

40 ......... 2,143.937 22,459.83 102.134 9.4760 95 ......... 1.092 3.46 0.778 2.1698

41 ......... 1,946.262 20,315.90 99.362 9.4384 96 ......... 0.780 2.37 0.564 2.0395

42 ......... 1,766.626 18,369.63 96.660 9.3981 97 ......... 0.545 1.59 0.400 1.9190

43 ......... 1,603.351 16,603.01 93.987 9.3552 95 ......... 0.373 1.05 0.278 1.8061

44 ......... 1,454.966 14,999.66 91.361 9.3093 99 ......... 0.249 0.67 0.188 1.6984

45 ......... 1,320.090 13,544.69 88.755 9.2604 100 ......... 0.163 0.42 0.125 1.5932

46 ......... 1,197.463 12,224.60 86.136 9.2088 101 ......... 0.104 0.26 0.081 1.4906

47 ......... 1,085.961 11,027.14 83.494 9.1543 102 ......... 0.065 0.16 0.051 1.3906

48 ......... 984.588 9,941.18 80.845 9.0968 103 ......... 0.039 0.09 0.031 1.2933

49 ......... 892.438 8,956.59 78.202 9.0361 104 ......... 0.023 0.05 0.019 1.1987

50 ......... 808.683 8,064.15 75.579 8.9720 105 ......... 0.013 0.03 0.011 1.1067

51 ......... 732.549 7,255.47 72.961 8.9044 106 ......... 0.007 0.01 0.006 1.0175

52 ......... 663.335 6,522.92 70.342 8.8335 107 ......... 0.004 0.01 0.003 0.9310

53 ......... 600.414 5,859.58 67.724 8.7592 108 ......... 0.002 0.00 0.002 0.8472

54 ......... 543.236 5,259.17 65.130 8.6812 109 ......... 0.001 0.00 0.001 0.7661

x x x x x x x x

37
Table 3.K. -- Actuarial Functions at 11.0 Percent Interest for 1989-91 United States 

Total Females

x D N M a x D N M a

0 ......... 100,000.000 998,080.41 1,091.131 8.9808 55 ......... 298.650 2,679.47 33.117 7.9719

1 ......... 89,344.144 898,080.41 345.185 9.0519 56 ......... 267.531 2,380.82 31.594 7.8992

2 ......... 80,435.841 808,736.26 290.806 9.0544 57 ......... 239.528 2,113.29 30.103 7.8227

3 ......... 72,434.012 728,300.42 260.096 9.0547 58 ......... 214.331 1,873.76 28.643 7.7424

4 ......... 65,234.787 655,866.41 239.017 9.0539 59 ......... 191.651 1,659.43 27.203 7.6586

5 ......... 58,755.242 590,631.62 224.181 9.0524 60 ......... 171.245 1,467.78 25.789 7.5712

6 ......... 52,920.354 531,876.38 211.884 9.0505 61 ......... 152.894 1,296.53 24.409 7.4800

7 ......... 47,665.880 478,956.03 201.769 9.0482 62 ......... 136.404 1,143.64 23.071 7.3842

8 ......... 42,933.989 431,290.15 193.524 9.0454 63 ......... 121.591 1,007.24 21.774 7.2838

9 ......... 38,673.015 388,356.16 187.270 9.0420 64 ......... 108.285 885.64 20.519 7.1788

10 ......... 34,834.919 349,683.14 181.635 9.0383 65 ......... 96.340 777.36 19.305 7.0689

11 ......... 31,378.051 314,848.22 176.875 9.0340 66 ......... 85.624 681.02 18.136 6.9536

12 ......... 28,264.226 283,470.17 172.588 9.0293 67 ......... 76.016 595.40 17.012 6.8325

13 ......... 25,458.632 255,205.95 167.953 9.0243 68 ......... 67.404 519.38 15.934 6.7054

14 ......... 22,930.832 229,747.31 163.081 9.0191 69 ......... 59.687 451.98 14.897 6.5724

15 ......... 20,652.556 206,816.48 157.229 9.0141 70 ......... 52.769 392.29 13.894 6.4340

16 ......... 18,599.504 186,163.93 150.827 9.0091 71 ......... 46.570 339.52 12.924 6.2906

17 ......... 16,749.525 167,564.42 144.041 9.0041 72 ......... 41.015 292.95 11.984 6.1424

18 ......... 15,082.785 150,814.90 137.164 8.9991 73 ......... 36.043 251.93 11.077 5.9898

19 ......... 13,581.486 135,732.11 130.556 8.9939 74 ......... 31.598 215.89 10.204 5.8323

20 ......... 12,229.371 122,150.63 124.354 8.9883 75 ......... 27.633 184.29 9.370 5.6693

21 ......... 11,011.753 109,921.26 118.655 8.9822 76 ......... 24.102 156.66 8.578 5.4997

22 ......... 9,915.062 98,909.50 113.219 8.9757 77 ......... 20.964 132.56 7.827 5.3232

23 ......... 8,927.591 88,994.44 108.322 8.9685 78 ......... 18.174 111.59 7.115 5.1404

24 ......... 8,038.299 80,066.85 103.746 8.9607 79 ......... 15.693 93.42 6.435 4.9531

25 ......... 7,237.515 72,028.55 99.551 8.9521 80 ......... 13.487 77.73 5.785 4.7629

26 ......... 6,516.438 64,791.04 95.704 8.9427 81 ......... 11.531 64.24 5.165 4.5712

27 ......... 5,867.140 58,274.60 92.180 8.9324 82 ......... 9.800 52.71 4.577 4.3785

28 ......... 5,282.428 52,407.46 88.897 8.9211 83 ......... 8.276 42.91 4.023 4.1850

29 ......... 4,755.793 47,125.03 85.745 8.9090 84 ......... 6.940 34.63 3.508 3.9905

30 ......... 4,281.484 42,369.24 82.731 8.8959 85 ......... 5.775 27.69 3.031 3.7955

31 ......... 3,854.281 38,087.75 79.819 8.8819 86 ......... 4.763 21.92 2.591 3.6016

32 ......... 3,469.524 34,233.47 77.018 8.8669 87 ......... 3.889 17.16 2.189 3.4114

33 ......... 3,123.046 30,763.95 74.367 8.8506 88 ......... 3.140 13.27 1.825 3.2251

34 ......... 2,811.023 27,640.90 71.834 8.8330 89 ......... 2.505 10.13 1.502 3.0424

35 ......... 2,530.042 24,829.88 69.423 8.8140 90 ......... 1.973 7.62 1.217 2.8635

36 ......... 2,277.005 22,299.84 67.111 8.7935 91 ......... 1.530 5.65 0.970 2.6925

37 ......... 2,049.168 20,022.83 64.923 8.7712 92 ......... 1.166 4.12 0.758 2.5334

38 ......... 1,843.974 17,973.66 62.800 8.7472 93 ......... 0.872 2.95 0.580 2.3861

39 ......... 1,659.189 16,129.69 60.751 8.7214 94 ......... 0.641 2.08 0.435 2.2472

40 ......... 1,492.795 14,470.50 58.782 8.6936 95 ......... 0.462 1.44 0.320 2.1152

41 ......... 1,342.948 12,977.71 56.869 8.6636 96 ......... 0.327 0.98 0.230 1.9900

42 ......... 1,208.015 11,634.76 55.021 8.6313 97 ......... 0.226 0.65 0.162 1.8740

43 ......... 1,086.491 10,426.74 53.210 8.5967 95 ......... 0.153 0.42 0.111 1.7652

44 ......... 977.057 9,340.25 51.447 8.5596 99 ......... 0.102 0.27 0.075 1.6613

45 ......... 878.497 8,363.19 49.712 8.5199 100 ......... 0.066 0.17 0.049 1.5597

46 ......... 789.712 7,484.70 47.985 8.4778 101 ......... 0.042 0.10 0.032 1.4604

47 ......... 709.725 6,694.99 46.258 8.4332 102 ......... 0.026 0.06 0.020 1.3635

48 ......... 637.677 5,985.26 44.543 8.3860 103 ......... 0.016 0.04 0.012 1.2690

49 ......... 572.787 5,347.58 42.847 8.3361 104 ......... 0.009 0.02 0.007 1.1771

50 ......... 514.356 4,774.80 41.178 8.2831 105 ......... 0.005 0.01 0.004 1.0875

51 ......... 461.734 4,260.44 39.528 8.2270 106 ......... 0.003 0.01 0.002 1.0006

52 ......... 414.341 3,798.71 37.892 8.1681 107 ......... 0.001 0.00 0.001 0.9161

53 ......... 371.659 3,384.37 36.272 8.1061 108 ......... 0.001 0.00 0.001 0.8342

54 ......... 333.236 3,012.71 34.680 8.0407 109 ......... 0.000 0.00 0.000 0.7548

x x x x x x x x

38
Table 3.L. -- Actuarial Functions at 12.0 Percent Interest for 1989-91 United States 

Total Females

x D N M a x D N M a

0 ......... 100,000.000 923,702.74 1,031.849 8.2370 55 ......... 182.363 1,536.08 17.782 7.4232

1 ......... 88,546.429 823,702.74 292.563 8.3025 56 ......... 161.902 1,353.72 16.860 7.3614

2 ......... 79,005.899 735,156.31 239.151 8.3051 57 ......... 143.661 1,191.82 15.966 7.2960

3 ......... 70,511.087 656,150.41 209.257 8.3056 58 ......... 127.401 1,048.16 15.098 7.2272

4 ......... 62,935.991 585,639.33 188.920 8.3053 59 ......... 112.903 920.76 14.250 7.1553

5 ......... 56,178.663 522,703.34 174.734 8.3043 60 ......... 99.980 807.85 13.424 7.0801

6 ......... 50,147.868 466,524.67 163.082 8.3030 61 ......... 88.469 707.87 12.626 7.0013

7 ......... 44,765.383 416,376.81 153.582 8.3013 62 ......... 78.223 619.40 11.858 6.9184

8 ......... 39,961.418 371,611.42 145.909 8.2993 63 ......... 69.105 541.18 11.122 6.8312

9 ......... 35,674.068 331,650.00 140.139 8.2967 64 ......... 60.994 472.08 10.414 6.7397

10 ......... 31,846.695 295,975.94 134.987 8.2938 65 ......... 53.781 411.08 9.737 6.6436

11 ......... 28,430.237 264,129.24 130.675 8.2904 66 ......... 47.372 357.30 9.090 6.5424

12 ......... 25,380.290 235,699.00 126.825 8.2867 67 ......... 41.681 309.93 8.474 6.4358

13 ......... 22,656.848 210,318.71 122.700 8.2828 68 ......... 36.629 268.25 7.888 6.3234

14 ......... 20,225.032 187,661.87 118.403 8.2787 69 ......... 32.146 231.62 7.329 6.2053

15 ......... 18,052.948 167,436.84 113.287 8.2748 70 ......... 28.166 199.47 6.794 6.0820

16 ......... 16,113.158 149,383.89 107.741 8.2709 71 ......... 24.635 171.31 6.281 5.9538

17 ......... 14,380.922 133,270.73 101.916 8.2672 72 ......... 21.503 146.67 5.788 5.8209

18 ......... 12,834.257 118,889.81 96.064 8.2635 73 ......... 18.728 125.17 5.317 5.6836

19 ......... 11,453.585 106,055.55 90.491 8.2596 74 ......... 16.272 106.44 4.867 5.5415

20 ......... 10,221.232 94,601.96 85.307 8.2554 75 ......... 14.103 90.17 4.442 5.3938

21 ......... 9,121.379 84,380.73 80.587 8.2509 76 ......... 12.191 76.07 4.041 5.2396

22 ......... 8,139.626 75,259.35 76.124 8.2460 77 ......... 10.509 63.88 3.665 5.0784

23 ......... 7,263.539 67,119.73 72.139 8.2406 78 ......... 9.029 53.37 3.311 4.9108

24 ......... 6,481.613 59,856.19 68.450 8.2348 79 ......... 7.727 44.34 2.976 4.7384

25 ......... 5,783.802 53,374.58 65.097 8.2283 80 ......... 6.582 36.61 2.659 4.5629

26 ......... 5,161.062 47,590.77 62.051 8.2211 81 ......... 5.576 30.03 2.359 4.3853

27 ......... 4,605.325 42,429.71 59.284 8.2132 82 ......... 4.697 24.45 2.077 4.2062

28 ......... 4,109.343 37,824.39 56.730 8.2045 83 ......... 3.931 19.76 1.814 4.0258

29 ......... 3,666.626 33,715.04 54.300 8.1951 84 ......... 3.267 15.83 1.571 3.8440

30 ......... 3,271.470 30,048.42 51.997 8.1850 85 ......... 2.694 12.56 1.349 3.6610

31 ......... 2,918.750 26,776.95 49.792 8.1741 86 ......... 2.203 9.86 1.146 3.4785

32 ......... 2,603.925 23,858.20 47.690 8.1624 87 ......... 1.782 7.66 0.961 3.2991

33 ......... 2,322.961 21,254.27 45.718 8.1496 88 ......... 1.426 5.88 0.796 3.1228

34 ......... 2,072.206 18,931.31 43.851 8.1358 89 ......... 1.128 4.45 0.650 2.9495

35 ......... 1,848.422 16,859.10 42.090 8.1208 90 ......... 0.880 3.33 0.524 2.7792

36 ......... 1,648.703 15,010.68 40.416 8.1045 91 ......... 0.676 2.45 0.414 2.6161

37 ......... 1,470.486 13,361.98 38.845 8.0868 92 ......... 0.511 1.77 0.321 2.4641

38 ......... 1,311.424 11,891.49 37.336 8.0676 93 ......... 0.379 1.26 0.244 2.3231

39 ......... 1,169.470 10,580.07 35.891 8.0469 94 ......... 0.276 0.88 0.182 2.1900

40 ......... 1,042.794 9,410.60 34.516 8.0244 95 ......... 0.197 0.60 0.132 2.0632

41 ......... 929.742 8,367.80 33.192 8.0001 96 ......... 0.138 0.41 0.095 1.9427

42 ......... 828.859 7,438.06 31.924 7.9739 97 ......... 0.095 0.27 0.066 1.8310

43 ......... 738.821 6,609.20 30.692 7.9456 95 ......... 0.064 0.17 0.045 1.7261

44 ......... 658.473 5,870.38 29.504 7.9151 99 ......... 0.042 0.11 0.030 1.6258

45 ......... 586.764 5,211.91 28.345 7.8825 100 ......... 0.027 0.07 0.020 1.5275

46 ......... 522.753 4,625.15 27.202 7.8477 101 ......... 0.017 0.04 0.013 1.4314

47 ......... 465.611 4,102.39 26.069 7.8108 102 ......... 0.010 0.02 0.008 1.3374

48 ......... 414.609 3,636.78 24.953 7.7716 103 ......... 0.006 0.01 0.005 1.2457

49 ......... 369.093 3,222.17 23.861 7.7300 104 ......... 0.004 0.01 0.003 1.1562

50 ......... 328.482 2,853.08 22.795 7.6857 105 ......... 0.002 0.00 0.002 1.0690

51 ......... 292.243 2,524.60 21.751 7.6387 106 ......... 0.001 0.00 0.001 0.9842

52 ......... 259.905 2,232.35 20.724 7.5891 107 ......... 0.001 0.00 0.000 0.9017

53 ......... 231.051 1,972.45 19.717 7.5369 108 ......... 0.000 0.00 0.000 0.8216

54 ......... 205.315 1,741.40 18.736 7.4816 109 ......... 0.000 0.00 0.000 0.7439

x x x x x x x x

39
Table 4.A. -- Actuarial Functions at 1.0 Percent Interest for 1989-91 United States 

Total White Population

x D N M a x D N M a

0 ......... 100,000.000 5,314,867.67 47,377.548 52.1487 55 ......... 52,549.441 1,168,508.36 40,980.051 21.2364

1 ......... 98,250.495 5,214,867.67 46,618.142 52.0773 56 ......... 51,658.548 1,115,958.92 40,609.450 20.6026

2 ......... 97,216.940 5,116,617.18 46,557.363 51.6309 57 ......... 50,747.818 1,064,300.37 40,210.191 19.9723

3 ......... 96,212.660 5,019,400.24 46,515.628 51.1699 58 ......... 49,813.561 1,013,552.55 39,778.387 19.3469

4 ......... 95,228.347 4,923,187.58 46,483.916 50.6988 59 ......... 48,850.576 963,738.99 39,308.606 18.7283

5 ......... 94,259.803 4,827,959.23 46,458.226 50.2197 60 ......... 47,857.741 914,888.41 38,799.440 18.1168

6 ......... 93,303.928 4,733,699.43 46,435.617 49.7342 61 ......... 46,836.722 867,030.67 38,252.260 17.5118

7 ......... 92,359.607 4,640,395.50 46,415.097 49.2427 62 ......... 45,789.681 820,193.95 37,668.949 16.9122

8 ......... 91,425.763 4,548,035.89 46,395.704 48.7457 63 ......... 44,716.041 774,404.27 37,048.672 16.3183

9 ......... 90,503.184 4,456,610.13 46,378.332 48.2426 64 ......... 43,615.267 729,688.23 36,390.632 15.7301

10 ......... 89,592.629 4,366,106.95 46,363.847 47.7329 65 ......... 42,486.867 686,072.96 35,694.065 15.1479

11 ......... 88,692.128 4,276,514.32 46,350.402 47.2175 66 ......... 41,331.422 643,586.09 34,959.282 14.5714

12 ......... 87,799.789 4,187,822.19 46,336.203 46.6974 67 ......... 40,151.052 602,254.67 34,188.134 13.9997

13 ......... 86,912.911 4,100,022.40 46,318.630 46.1739 68 ......... 38,944.253 562,103.62 33,378.871 13.4335

14 ......... 86,027.158 4,013,109.49 46,293.401 45.6493 69 ......... 37,705.073 523,159.37 32,525.278 12.8750

15 ......... 85,138.366 3,927,082.33 46,256.363 45.1259 70 ......... 36,429.806 485,454.29 31,623.328 12.3257

16 ......... 84,245.948 3,841,943.97 46,206.899 44.6039 71 ......... 35,113.929 449,024.49 30,668.142 11.7876

17 ......... 83,351.879 3,757,698.02 46,146.948 44.0823 72 ......... 33,758.010 413,910.56 29,659.886 11.2611

18 ......... 82,458.896 3,674,346.14 46,079.231 43.5597 73 ......... 32,363.107 380,152.55 28,599.221 10.7465

19 ......... 81,569.630 3,591,887.24 46,006.390 43.0346 74 ......... 30,934.095 347,789.44 27,490.635 10.2429

20 ......... 80,688.251 3,510,317.61 45,932.631 42.5047 75 ......... 29,479.001 316,855.35 26,341.819 9.7485

21 ......... 79,814.706 3,429,629.36 45,857.979 41.9699 76 ......... 28,003.214 287,376.34 25,157.904 9.2623

22 ......... 78,948.138 3,349,814.66 45,781.657 41.4306 77 ......... 26,509.142 259,373.13 23,941.091 8.7843

23 ......... 78,088.520 3,270,866.52 45,703.703 40.8866 78 ......... 24,997.732 232,863.99 22,692.148 8.3154

24 ......... 77,238.185 3,192,778.00 45,626.522 40.3368 79 ......... 23,467.178 207,866.26 21,409.096 7.8577

25 ......... 76,395.474 3,115,539.81 45,548.545 39.7817 80 ......... 21,916.663 184,399.08 20,090.929 7.4136

26 ......... 75,561.878 3,039,144.34 45,471.340 39.2206 81 ......... 20,348.099 162,482.42 18,739.362 6.9851

27 ......... 74,737.300 2,963,582.46 45,394.900 38.6533 82 ......... 18,769.089 142,134.32 17,361.818 6.5728

28 ......... 73,919.373 2,888,845.16 45,316.946 38.0810 83 ......... 17,191.329 123,365.23 15,969.891 6.1760

29 ......... 73,108.068 2,814,925.79 45,237.516 37.5036 84 ......... 15,630.400 106,173.90 14,579.174 5.7928

30 ......... 72,301.130 2,741,817.72 45,154.420 36.9222 85 ......... 14,099.983 90,543.50 13,203.513 5.4215

31 ......... 71,499.332 2,669,516.59 45,068.475 36.3362 86 ......... 12,604.289 76,443.52 11,847.423 5.0649

32 ......... 70,701.959 2,598,017.26 44,979.016 35.7460 87 ......... 11,149.033 63,839.23 10,516.961 4.7260

33 ......... 69,909.767 2,527,315.30 44,886.843 35.1511 88 ......... 9,748.436 52,690.19 9,226.751 4.4050

34 ......... 69,122.052 2,457,405.53 44,791.305 34.5517 89 ......... 8,419.854 42,941.76 7,994.688 4.1001

35 ......... 68,339.554 2,388,283.48 44,693.183 33.9473 90 ......... 7,175.842 34,521.90 6,834.040 3.8109

36 ......... 67,560.182 2,319,943.92 44,590.441 33.3389 91 ......... 6,023.163 27,346.06 5,752.410 3.5401

37 ......... 66,785.393 2,252,383.74 44,484.564 32.7257 92 ......... 4,967.472 21,322.90 4,756.354 3.2925

38 ......... 66,013.157 2,185,598.35 44,373.569 32.1085 93 ......... 4,021.676 16,355.43 3,859.741 3.0668

39 ......... 65,244.238 2,119,585.19 44,258.246 31.4869 94 ......... 3,196.553 12,333.75 3,074.437 2.8585

40 ......... 64,478.701 2,054,340.95 44,138.692 30.8608 95 ......... 2,493.066 9,137.20 2,402.599 2.6650

41 ......... 63,715.278 1,989,862.25 44,013.671 30.2305 96 ......... 1,906.579 6,644.13 1,840.795 2.4848

42 ......... 62,953.408 1,926,146.97 43,882.646 29.5964 97 ......... 1,426.838 4,737.55 1,379.932 2.3203

43 ......... 62,192.556 1,863,193.57 43,745.095 28.9585 95 ......... 1,045.279 3,310.71 1,012.500 2.1673

44 ......... 61,430.918 1,801,001.01 43,599.224 28.3175 99 ......... 749.931 2,265.44 727.501 2.0209

45 ......... 60,666.761 1,739,570.09 43,443.295 27.6742 100 ......... 526.177 1,515.50 511.172 1.8802

46 ......... 59,897.162 1,678,903.33 43,274.357 27.0298 101 ......... 360.384 989.33 350.589 1.7452

47 ......... 59,121.194 1,619,006.17 43,091.430 26.3845 102 ......... 240.451 628.94 234.224 1.6157

48 ......... 58,337.352 1,559,884.98 42,892.946 25.7390 103 ......... 155.927 388.49 152.080 1.4915

49 ......... 57,545.427 1,501,547.62 42,678.619 25.0933 104 ......... 98.025 232.57 95.723 1.3725

50 ......... 56,745.831 1,444,002.20 42,448.780 24.4468 105 ......... 59.570 134.54 58.238 1.2585

51 ......... 55,936.562 1,387,256.37 42,201.350 23.8005 106 ......... 34.880 74.97 34.138 1.1494

52 ......... 55,113.912 1,331,319.80 41,932.528 23.1558 107 ......... 19.605 40.09 19.208 1.0449

53 ......... 54,276.102 1,276,205.89 41,640.401 22.5132 108 ......... 10.532 20.49 10.329 0.9451

54 ......... 53,421.433 1,221,929.79 41,323.118 21.8734 109 ......... 5.381 9.95 5.283 0.8496

x x x x x x x x

40
Table 4.B. -- Actuarial Functions at 2.0 Percent Interest for 1989-91 United States 

Total White Population

x D N M a x D N M a

0 ......... 100,000.000 3,902,843.90 23,473.649 38.0284 55 ......... 30,565.690 597,421.51 18,851.543 18.5455

1 ......... 97,287.255 3,802,843.90 22,721.688 38.0888 56 ......... 29,752.914 566,855.82 18,638.094 18.0521

2 ......... 95,320.069 3,705,556.65 22,662.096 37.8749 57 ......... 28,941.824 537,102.90 18,410.394 17.5580

3 ......... 93,410.528 3,610,236.58 22,621.576 37.6491 58 ......... 28,130.490 508,161.08 18,166.548 17.0644

4 ......... 91,548.462 3,516,826.05 22,591.089 37.4149 59 ......... 27,316.220 480,030.59 17,903.856 16.5731

5 ......... 89,728.940 3,425,277.59 22,566.634 37.1736 60 ......... 26,498.685 452,714.37 17,621.932 16.0844

6 ......... 87,948.238 3,335,548.65 22,545.323 36.9263 61 ......... 25,679.101 426,215.69 17,321.931 15.5978

7 ......... 86,204.610 3,247,600.41 22,526.171 36.6732 62 ......... 24,858.913 400,536.58 17,005.255 15.1124

8 ......... 84,496.400 3,161,395.80 22,508.247 36.4146 63 ......... 24,038.041 375,677.67 16,671.812 14.6285

9 ......... 82,823.710 3,076,899.40 22,492.349 36.1500 64 ......... 23,216.432 351,639.63 16,321.537 14.1462

10 ......... 81,186.590 2,994,075.69 22,479.223 35.8789 65 ......... 22,394.060 328,423.20 15,954.389 13.6656

11 ......... 79,582.632 2,912,889.10 22,467.159 35.6021 66 ......... 21,571.467 306,029.14 15,570.896 13.1868

12 ......... 78,009.572 2,833,306.47 22,454.544 35.3200 67 ......... 20,749.969 284,457.67 15,172.368 12.7088

13 ......... 76,464.512 2,755,296.89 22,439.083 35.0337 68 ......... 19,928.982 263,707.70 14,758.243 12.2324

14 ......... 74,943.230 2,678,832.38 22,417.105 34.7448 69 ......... 19,105.690 243,778.72 14,325.715 11.7595

15 ......... 73,441.805 2,603,889.15 22,385.155 34.4551 70 ......... 18,278.519 224,673.03 13,873.165 11.2916

16 ......... 71,959.520 2,530,447.35 22,342.905 34.1649 71 ......... 17,445.554 206,394.51 13,398.603 10.8308

17 ......... 70,497.843 2,458,487.83 22,292.200 33.8732 72 ......... 16,607.467 188,948.96 12,902.585 10.3773

18 ......... 69,058.820 2,387,989.99 22,235.487 33.5791 73 ......... 15,765.145 172,341.49 12,385.900 9.9318

19 ......... 67,644.319 2,318,931.17 22,175.081 33.2812 74 ......... 14,921.290 156,576.35 11,851.165 9.4935

20 ......... 66,257.393 2,251,286.85 22,114.513 32.9779 75 ......... 14,080.008 141,655.06 11,302.458 9.0607

21 ......... 64,897.529 2,185,029.45 22,053.814 32.6689 76 ......... 13,244.002 127,575.05 10,742.530 8.6327

22 ......... 63,563.578 2,120,131.92 21,992.364 32.3545 77 ......... 12,414.471 114,331.05 10,172.686 8.2095

23 ......... 62,255.086 2,056,568.35 21,930.217 32.0345 78 ......... 11,591.893 101,916.57 9,593.529 7.7921

24 ......... 60,973.470 1,994,313.26 21,869.288 31.7079 79 ......... 10,775.460 90,324.68 9,004.388 7.3824

25 ......... 59,716.958 1,933,339.79 21,808.335 31.3751 80 ......... 9,964.846 79,549.22 8,405.057 6.9830

26 ......... 58,486.280 1,873,622.83 21,748.577 31.0353 81 ......... 9,160.965 69,584.38 7,796.565 6.5957

27 ......... 57,280.904 1,815,136.55 21,689.991 30.6883 82 ......... 8,367.231 60,423.41 7,182.458 6.2214

28 ......... 56,098.588 1,757,855.65 21,630.830 30.3351 83 ......... 7,588.732 52,056.18 6,568.023 5.8597

29 ......... 54,938.926 1,701,757.06 21,571.140 29.9754 84 ......... 6,832.051 44,467.45 5,960.140 5.5087

30 ......... 53,799.860 1,646,818.13 21,509.309 29.6101 85 ......... 6,102.682 37,635.40 5,364.734 5.1670

31 ......... 52,681.635 1,593,018.27 21,445.983 29.2386 86 ......... 5,401.840 31,532.71 4,783.552 4.8374

32 ......... 51,583.394 1,540,336.64 21,380.715 28.8611 87 ......... 4,731.314 26,130.87 4,218.944 4.5230

33 ......... 50,505.366 1,488,753.24 21,314.126 28.4771 88 ......... 4,096.385 21,399.56 3,676.786 4.2240

34 ......... 49,446.721 1,438,247.88 21,245.782 28.0868 89 ......... 3,503.415 17,303.18 3,164.137 3.9389

35 ......... 48,407.673 1,388,801.16 21,176.278 27.6897 90 ......... 2,956.521 13,799.76 2,685.938 3.6676

36 ......... 47,386.440 1,340,393.49 21,104.215 27.2864 91 ......... 2,457.277 10,843.24 2,244.664 3.4127

37 ......... 46,383.761 1,293,007.04 21,030.682 26.8763 92 ......... 2,006.716 8,385.96 1,842.286 3.1789

38 ......... 45,397.943 1,246,623.28 20,954.349 26.4599 93 ......... 1,608.714 6,379.25 1,483.631 2.9654

39 ......... 44,429.256 1,201,225.34 20,875.818 26.0368 94 ......... 1,266.120 4,770.53 1,172.580 2.7678

40 ......... 43,477.480 1,156,796.08 20,795.204 25.6068 95 ......... 977.796 3,504.41 909.082 2.5840

41 ......... 42,541.506 1,113,318.60 20,711.730 25.1702 96 ......... 740.440 2,526.62 690.899 2.4123

42 ......... 41,620.734 1,070,777.10 20,625.104 24.7270 97 ......... 548.695 1,786.18 513.672 2.2553

43 ......... 40,714.593 1,029,156.36 20,535.056 24.2773 95 ......... 398.025 1,237.48 373.760 2.1091

44 ......... 39,821.709 988,441.77 20,440.497 23.8217 99 ......... 282.761 839.46 266.302 1.9688

45 ......... 38,940.803 948,620.06 20,340.409 23.3606 100 ......... 196.450 556.69 185.534 1.8338

46 ......... 38,069.883 909,679.26 20,233.034 22.8950 101 ......... 133.232 360.24 126.168 1.7039

47 ......... 37,208.288 871,609.38 20,117.908 22.4251 102 ......... 88.022 227.01 83.570 1.5791

48 ......... 36,355.022 834,401.09 19,994.216 21.9515 103 ......... 56.520 138.99 53.795 1.4591

49 ......... 35,509.922 798,046.07 19,861.960 21.4739 104 ......... 35.184 82.47 33.567 1.3440

50 ......... 34,673.211 762,536.15 19,721.522 20.9921 105 ......... 21.172 47.29 20.245 1.2335

51 ......... 33,843.640 727,862.94 19,571.818 20.5066 106 ......... 12.275 26.12 11.763 1.1276

52 ......... 33,018.987 694,019.29 19,410.766 20.0188 107 ......... 6.832 13.84 6.560 1.0260

53 ......... 32,198.257 661,000.31 19,237.467 19.5291 108 ......... 3.634 7.01 3.497 0.9287

54 ......... 31,380.542 628,802.05 19,051.090 19.0380 109 ......... 1.839 3.37 1.773 0.8355

x x x x x x x x

41
Table 4.C. -- Actuarial Functions at 3.0 Percent Interest for 1989-91 United States 

Total White Population

x D N M a x D N M a

0 ......... 100,000.000 3,010,871.57 12,304.712 29.1087 55 ......... 17,872.952 310,154.56 8,839.324 16.3533

1 ......... 96,342.718 2,910,871.57 11,560.051 29.2137 56 ......... 17,228.781 292,281.61 8,715.724 15.9647

2 ......... 93,478.179 2,814,528.85 11,501.611 29.1089 57 ......... 16,596.399 275,052.83 8,585.152 15.5730

3 ......... 90,716.162 2,721,050.67 11,462.259 28.9952 58 ......... 15,974.535 258,456.43 8,446.678 15.1793

4 ......... 88,044.624 2,630,334.51 11,432.939 28.8750 59 ......... 15,361.530 242,481.90 8,298.951 14.7850

5 ......... 85,456.927 2,542,289.88 11,409.649 28.7494 60 ......... 14,757.104 227,120.37 8,141.948 14.3906

6 ......... 82,947.791 2,456,832.95 11,389.549 28.6190 61 ......... 14,161.837 212,363.26 7,976.499 13.9955

7 ......... 80,513.948 2,373,885.16 11,371.661 28.4841 62 ......... 13,576.407 198,201.42 7,803.550 13.5990

8 ......... 78,152.304 2,293,371.22 11,355.084 28.3449 63 ......... 13,000.640 184,625.02 7,623.212 13.2012

9 ......... 75,861.461 2,215,218.91 11,340.522 28.2008 64 ......... 12,434.378 171,624.38 7,435.610 12.8024

10 ......... 73,639.998 2,139,357.45 11,328.616 28.0516 65 ......... 11,877.482 159,190.00 7,240.881 12.4027

11 ......... 71,484.308 2,065,717.45 11,317.780 27.8975 66 ......... 11,330.112 147,312.52 7,039.456 12.0019

12 ......... 69,391.018 1,994,233.15 11,306.558 27.7391 67 ......... 10,792.819 135,982.40 6,832.167 11.5993

13 ......... 67,356.302 1,924,842.13 11,292.939 27.5770 68 ......... 10,265.155 125,189.59 6,618.857 11.1956

14 ......... 65,375.295 1,857,485.83 11,273.766 27.4127 69 ......... 9,745.544 114,924.43 6,398.230 10.7925

15 ......... 63,443.560 1,792,110.53 11,246.166 27.2473 70 ......... 9,233.095 105,178.89 6,169.632 10.3915

16 ......... 61,559.546 1,728,666.97 11,210.023 27.0812 71 ......... 8,726.780 95,945.79 5,932.242 9.9944

17 ......... 59,723.593 1,667,107.42 11,167.067 26.9137 72 ......... 8,226.888 87,219.01 5,686.528 9.6017

18 ......... 57,936.492 1,607,383.83 11,119.488 26.7439 73 ......... 7,733.803 78,992.12 5,433.061 9.2139

19 ......... 56,198.837 1,549,447.34 11,069.302 26.5708 74 ......... 7,248.772 71,258.32 5,173.287 8.8304

20 ......... 54,512.146 1,493,248.50 11,019.472 26.3930 75 ......... 6,773.669 64,009.55 4,909.313 8.4498

21 ......... 52,874.959 1,438,736.36 10,970.017 26.2102 76 ......... 6,309.620 57,235.88 4,642.556 8.0712

22 ......... 51,285.332 1,385,861.40 10,920.437 26.0226 77 ......... 5,856.999 50,926.26 4,373.710 7.6949

23 ......... 49,741.929 1,334,576.06 10,870.781 25.8300 78 ......... 5,415.820 45,069.26 4,103.123 7.3218

24 ......... 48,244.925 1,284,834.13 10,822.572 25.6315 79 ......... 4,985.499 39,653.44 3,830.544 6.9538

25 ......... 46,791.973 1,236,589.21 10,774.811 25.4274 80 ......... 4,565.689 34,667.94 3,555.943 6.5931

26 ......... 45,382.730 1,189,797.24 10,728.442 25.2170 81 ......... 4,156.616 30,102.25 3,279.851 6.2420

27 ......... 44,015.884 1,144,414.51 10,683.423 25.0000 82 ......... 3,759.615 25,945.64 3,003.917 5.9011

28 ......... 42,688.849 1,100,398.62 10,638.404 24.7772 83 ......... 3,376.711 22,186.02 2,730.516 5.5703

29 ......... 41,400.504 1,057,709.77 10,593.423 24.5482 84 ......... 3,010.500 18,809.31 2,462.656 5.2479

30 ......... 40,148.522 1,016,309.27 10,547.281 24.3137 85 ......... 2,663.001 15,798.81 2,202.841 4.9327

31 ......... 38,932.349 976,160.75 10,500.482 24.0733 86 ......... 2,334.292 13,135.81 1,951.696 4.6273

32 ......... 37,750.631 937,228.40 10,452.717 23.8268 87 ......... 2,024.688 10,801.52 1,710.081 4.3349

33 ......... 36,602.839 899,477.77 10,404.458 23.5740 88 ......... 1,735.961 8,776.83 1,480.326 4.0559

34 ......... 35,487.687 862,874.93 10,355.408 23.3148 89 ......... 1,470.259 7,040.87 1,265.185 3.7889

35 ......... 34,404.667 827,387.24 10,306.009 23.0487 90 ......... 1,228.701 5,570.61 1,066.450 3.5337

36 ......... 33,351.869 792,982.57 10,255.290 22.7763 91 ......... 1,011.305 4,341.91 884.842 3.2934

37 ......... 32,329.203 759,630.70 10,204.037 22.4967 92 ......... 817.857 3,330.60 720.849 3.0724

38 ......... 31,334.889 727,301.50 10,151.350 22.2106 93 ......... 649.281 2,512.75 576.095 2.8700

39 ......... 30,368.545 695,966.61 10,097.672 21.9174 94 ......... 506.048 1,863.47 451.773 2.6824

40 ......... 29,429.457 665,598.07 10,043.105 21.6167 95 ......... 387.015 1,357.42 347.479 2.5074

41 ......... 28,516.334 636,168.61 9,987.151 21.3089 96 ......... 290.224 970.40 261.960 2.3436

42 ......... 27,628.258 607,652.28 9,929.648 20.9939 97 ......... 212.979 680.18 193.168 2.1936

43 ......... 26,764.357 580,024.02 9,870.454 20.6715 95 ......... 152.996 467.20 139.388 2.0537

44 ......... 25,923.257 553,259.66 9,808.898 20.3422 99 ......... 107.635 314.20 98.483 1.9192

45 ......... 25,103.687 527,336.40 9,744.375 20.0063 100 ......... 74.054 206.57 68.037 1.7894

46 ......... 24,303.963 502,232.72 9,675.826 19.6646 101 ......... 49.735 132.52 45.876 1.6644

47 ......... 23,523.297 477,928.75 9,603.042 19.3173 102 ......... 32.539 82.78 30.128 1.5440

48 ......... 22,760.713 454,405.46 9,525.603 18.9645 103 ......... 20.691 50.24 19.228 1.4281

49 ......... 22,015.782 431,644.74 9,443.605 18.6062 104 ......... 12.755 29.55 11.895 1.3166

50 ......... 21,288.321 409,628.96 9,357.381 18.2420 105 ......... 7.601 16.79 7.112 1.2095

51 ......... 20,577.252 388,340.64 9,266.359 17.8723 106 ......... 4.364 9.19 4.096 1.1065

52 ......... 19,880.944 367,763.39 9,169.389 17.4983 107 ......... 2.405 4.83 2.265 1.0077

53 ......... 19,198.556 347,882.44 9,066.057 17.1202 108 ......... 1.267 2.42 1.196 0.9128

54 ......... 18,529.324 328,683.89 8,956.007 16.7386 109 ......... 0.635 1.16 0.601 0.8219

x x x x x x x x

42
Table 4.D. -- Actuarial Functions at 4.0 Percent Interest for 1989-91 United States 

Total White Population

x D N M a x D N M a

0 ......... 100,000.000 2,420,044.35 6,921.371 23.2004 55 ......... 10,505.337 163,345.78 4,222.807 14.5488

1 ......... 95,416.346 2,320,044.35 6,183.871 23.3150 56 ......... 10,029.335 152,840.44 4,150.856 14.2393

2 ......... 91,689.164 2,224,628.00 6,126.549 23.2627 57 ......... 9,568.312 142,811.11 4,075.577 13.9254

3 ......... 88,124.431 2,132,938.84 6,088.322 23.2037 58 ......... 9,121.234 133,242.80 3,996.511 13.6080

4 ......... 84,706.821 2,044,814.41 6,060.113 23.1399 59 ......... 8,686.878 124,121.56 3,912.972 13.2884

5 ......... 81,426.675 1,960,107.59 6,037.921 23.0721 60 ......... 8,264.836 115,434.69 3,825.041 12.9670

6 ......... 78,275.912 1,878,680.91 6,018.954 23.0008 61 ......... 7,855.188 107,169.85 3,733.271 12.6432

7 ......... 75,248.582 1,800,405.00 6,002.236 22.9261 62 ......... 7,458.058 99,314.66 3,638.263 12.3164

8 ......... 72,339.061 1,725,156.42 5,986.891 22.8482 63 ......... 7,073.095 91,856.60 3,540.149 11.9868

9 ......... 69,543.440 1,652,817.36 5,973.542 22.7667 64 ......... 6,699.968 84,783.51 3,439.064 11.6543

10 ......... 66,857.884 1,583,273.92 5,962.733 22.6812 65 ......... 6,338.361 78,083.54 3,335.148 11.3192

11 ......... 64,276.683 1,516,416.03 5,952.989 22.5920 66 ......... 5,988.122 71,745.18 3,228.692 10.9812

12 ......... 61,794.509 1,452,139.35 5,942.996 22.4995 67 ......... 5,649.308 65,757.06 3,120.190 10.6398

13 ......... 59,405.786 1,390,344.84 5,930.984 22.4042 68 ......... 5,321.447 60,107.75 3,009.610 10.2954

14 ......... 57,104.201 1,330,939.05 5,914.237 22.3072 69 ......... 5,003.503 54,786.30 2,896.338 9.9496

15 ......... 54,884.009 1,273,834.85 5,890.361 22.2096 70 ......... 4,694.824 49,782.80 2,780.100 9.6038

16 ......... 52,742.119 1,218,950.84 5,859.394 22.1115 71 ......... 4,394.706 45,087.98 2,660.554 9.2596

17 ......... 50,677.127 1,166,208.73 5,822.945 22.0125 72 ......... 4,103.130 40,693.27 2,538.005 8.9176

18 ......... 48,688.022 1,115,531.60 5,782.961 21.9118 73 ......... 3,820.118 36,590.14 2,412.805 8.5783

19 ......... 46,773.638 1,066,843.58 5,741.192 21.8087 74 ......... 3,546.108 32,770.02 2,285.723 8.2411

20 ......... 44,933.577 1,020,069.94 5,700.118 21.7017 75 ......... 3,281.824 29,223.91 2,157.828 7.9048

21 ......... 43,164.990 975,136.36 5,659.745 21.5909 76 ......... 3,027.600 25,942.09 2,029.827 7.5685

22 ......... 41,464.712 931,971.37 5,619.659 21.4763 77 ......... 2,783.392 22,914.49 1,902.065 7.2326

23 ......... 39,830.154 890,506.66 5,579.898 21.3576 78 ......... 2,548.985 20,131.10 1,774.712 6.8977

24 ......... 38,259.993 850,676.51 5,541.666 21.2341 79 ......... 2,323.890 17,582.11 1,647.655 6.5658

25 ......... 36,750.943 812,416.51 5,504.154 21.1060 80 ......... 2,107.741 15,258.22 1,520.886 6.2391

26 ......... 35,301.377 775,665.57 5,468.085 20.9727 81 ......... 1,900.442 13,150.48 1,394.654 5.9197

27 ......... 33,908.950 740,364.19 5,433.404 20.8339 82 ......... 1,702.402 11,250.04 1,269.708 5.6083

28 ......... 32,570.411 706,455.24 5,399.056 20.6901 83 ......... 1,514.315 9,547.64 1,147.099 5.3049

29 ......... 31,283.714 673,884.83 5,365.067 20.5411 84 ......... 1,337.103 8,033.32 1,028.129 5.0080

30 ......... 30,045.963 642,601.12 5,330.535 20.3873 85 ......... 1,171.390 6,696.22 913.843 4.7165

31 ......... 28,855.663 612,555.16 5,295.849 20.2282 86 ......... 1,016.926 5,524.83 804.433 4.4329

32 ......... 27,710.767 583,699.49 5,260.787 20.0640 87 ......... 873.567 4,507.90 700.186 4.1603

33 ......... 26,609.885 555,988.73 5,225.703 19.8941 88 ......... 741.792 3,634.34 602.010 3.8994

34 ......... 25,551.112 529,378.84 5,190.387 19.7184 89 ......... 622.214 2,892.54 510.962 3.6488

35 ......... 24,533.152 503,827.73 5,155.162 19.5366 90 ......... 514.987 2,270.33 427.666 3.4085

36 ......... 23,553.750 479,294.58 5,119.343 19.3490 91 ......... 419.794 1,755.34 352.280 3.1814

37 ......... 22,611.989 455,740.83 5,083.495 19.1548 92 ......... 336.229 1,335.55 284.861 2.9721

38 ......... 21,705.801 433,128.84 5,046.999 18.9545 93 ......... 264.359 999.32 225.924 2.7802

39 ......... 20,834.137 411,423.04 5,010.174 18.7475 94 ......... 204.060 734.96 175.792 2.6017

40 ......... 19,995.748 390,588.90 4,973.098 18.5336 95 ......... 154.560 530.90 134.141 2.4349

41 ......... 19,189.029 370,593.15 4,935.446 18.3128 96 ......... 114.791 376.34 100.316 2.2785

42 ......... 18,412.667 351,404.12 4,897.124 18.0849 97 ......... 83.428 261.55 73.369 2.1350

43 ......... 17,665.417 332,991.46 4,858.053 17.8499 95 ......... 59.355 178.12 52.504 2.0010

44 ......... 16,945.739 315,326.04 4,817.815 17.6080 99 ......... 41.356 118.77 36.788 1.8719

45 ......... 16,252.208 298,380.30 4,776.042 17.3594 100 ......... 28.180 77.41 25.202 1.7471

46 ......... 15,583.171 282,128.09 4,732.090 17.1047 101 ......... 18.744 49.23 16.850 1.6266

47 ......... 14,937.600 266,544.92 4,685.872 16.8439 102 ......... 12.145 30.49 10.973 1.5104

48 ......... 14,314.374 251,607.32 4,637.169 16.5772 103 ......... 7.649 18.34 6.943 1.3983

49 ......... 13,712.748 237,292.95 4,586.096 16.3046 104 ......... 4.670 10.70 4.258 1.2903

50 ......... 13,132.146 223,580.20 4,532.907 16.0254 105 ......... 2.756 6.03 2.524 1.1863

51 ......... 12,571.454 210,448.06 4,477.298 15.7402 106 ......... 1.567 3.27 1.441 1.0862

52 ......... 12,029.263 197,876.60 4,418.625 15.4496 107 ......... 0.855 1.70 0.790 0.9900

53 ......... 11,504.678 185,847.34 4,356.704 15.1541 108 ......... 0.446 0.85 0.414 0.8975

54 ......... 10,996.878 174,342.66 4,291.391 14.8538 109 ......... 0.221 0.40 0.206 0.8087

x x x x x x x x

43
Table 4.E. -- Actuarial Functions at 5.0 Percent Interest for 1989-91 United States 

Total White Population

x D N M a x D N M a

0 ......... 100,000.000 2,011,064.20 4,235.038 19.1106 55 ......... 6,206.292 87,191.51 2,054.316 13.0489

1 ......... 94,507.619 1,911,064.20 3,504.562 19.2213 56 ......... 5,868.652 80,985.21 2,012.214 12.7996

2 ......... 89,951.020 1,816,556.58 3,448.326 19.1950 57 ......... 5,545.563 75,116.56 1,968.584 12.5453

3 ......... 85,630.493 1,726,605.56 3,411.181 19.1634 58 ......... 5,236.100 69,571.00 1,923.195 12.2868

4 ......... 81,525.702 1,640,975.06 3,384.032 19.1283 59 ......... 4,939.262 64,334.90 1,875.696 12.0252

5 ......... 77,622.370 1,559,449.36 3,362.877 19.0902 60 ......... 4,654.539 59,395.64 1,826.175 11.7608

6 ......... 73,908.158 1,481,826.99 3,344.968 19.0496 61 ......... 4,381.704 54,741.10 1,774.985 11.4931

7 ......... 70,373.087 1,407,918.83 3,329.333 19.0065 62 ......... 4,120.560 50,359.39 1,722.494 11.2215

8 ......... 67,007.774 1,337,545.75 3,315.119 18.9611 63 ......... 3,870.651 46,238.83 1,668.802 10.9460

9 ......... 63,804.680 1,270,537.97 3,302.871 18.9129 64 ......... 3,631.544 42,368.18 1,614.012 10.6667

10 ......... 60,756.539 1,206,733.29 3,293.049 18.8618 65 ......... 3,402.825 38,736.64 1,558.223 10.3837

11 ......... 57,854.600 1,145,976.76 3,284.279 18.8079 66 ......... 3,184.178 35,333.81 1,501.615 10.0967

12 ......... 55,090.710 1,088,122.15 3,275.369 18.7515 67 ......... 2,975.404 32,149.64 1,444.469 9.8051

13 ......... 52,456.736 1,033,031.44 3,264.763 18.6930 68 ......... 2,776.032 29,174.23 1,386.783 9.5093

14 ......... 49,944.150 980,574.71 3,250.116 18.6334 69 ......... 2,585.312 26,398.20 1,328.255 9.2108

15 ......... 47,545.173 930,630.56 3,229.432 18.5736 70 ......... 2,402.714 23,812.89 1,268.767 8.9108

16 ......... 45,254.547 883,085.39 3,202.862 18.5137 71 ......... 2,227.700 21,410.17 1,208.168 8.6109

17 ......... 43,068.591 837,830.84 3,171.885 18.4534 72 ......... 2,060.090 19,182.47 1,146.639 8.3115

18 ......... 40,984.049 794,762.25 3,138.227 18.3920 73 ......... 1,899.729 17,122.38 1,084.378 8.0131

19 ......... 38,997.603 753,778.20 3,103.403 18.3288 74 ......... 1,746.670 15,222.65 1,021.782 7.7152

20 ......... 37,106.654 714,780.60 3,069.483 18.2629 75 ......... 1,601.100 13,475.98 959.386 7.4167

21 ......... 35,306.648 677,673.94 3,036.460 18.1939 76 ......... 1,463.004 11,874.88 897.533 7.1168

22 ......... 33,592.903 642,367.29 3,003.984 18.1221 77 ......... 1,332.188 10,411.88 836.384 6.8156

23 ......... 31,961.335 608,774.39 2,972.078 18.0472 78 ......... 1,208.377 9,079.69 776.011 6.5140

24 ......... 30,408.980 576,813.06 2,941.692 17.9685 79 ......... 1,091.176 7,871.32 716.351 6.2136

25 ......... 28,931.403 546,404.08 2,912.161 17.8862 80 ......... 980.258 6,780.14 657.394 5.9167

26 ......... 27,525.593 517,472.67 2,884.037 17.7997 81 ......... 875.431 5,799.88 599.246 5.6252

27 ......... 26,188.066 489,947.08 2,857.253 17.7088 82 ......... 776.736 4,924.45 542.238 5.3399

28 ......... 24,914.740 463,759.01 2,830.978 17.6138 83 ......... 684.340 4,147.71 486.829 5.0609

29 ......... 23,702.572 438,844.27 2,805.226 17.5146 84 ......... 598.500 3,463.37 433.578 4.7868

30 ......... 22,547.964 415,141.70 2,779.311 17.4115 85 ......... 519.332 2,864.87 382.909 4.5165

31 ......... 21,448.469 392,593.74 2,753.529 17.3040 86 ......... 446.557 2,345.54 334.864 4.2525

32 ......... 20,401.300 371,145.27 2,727.716 17.1922 87 ......... 379.951 1,898.99 289.523 3.9980

33 ......... 19,404.226 350,743.97 2,702.132 17.0756 88 ......... 319.564 1,519.03 247.229 3.7535

34 ......... 18,454.707 331,339.74 2,676.624 16.9542 89 ......... 265.497 1,199.47 208.379 3.5178

35 ......... 17,550.713 312,885.04 2,651.425 16.8275 90 ......... 217.650 933.97 173.175 3.2912

36 ......... 16,689.584 295,334.32 2,626.044 16.6957 91 ......... 175.729 716.32 141.618 3.0763

37 ......... 15,869.683 278,644.74 2,600.886 16.5583 92 ......... 139.408 540.59 113.665 2.8778

38 ......... 15,088.614 262,775.06 2,575.516 16.4155 93 ......... 108.565 401.19 89.461 2.6954

39 ......... 14,344.753 247,686.44 2,550.161 16.2667 94 ......... 83.004 292.62 69.069 2.5254

40 ......... 13,636.386 233,341.69 2,524.876 16.1117 95 ......... 62.270 209.62 52.288 2.3663

41 ......... 12,961.601 219,705.30 2,499.444 15.9505 96 ......... 45.807 147.35 38.791 2.2167

42 ......... 12,318.743 206,743.70 2,473.804 15.7829 97 ......... 32.975 101.54 28.140 2.0793

43 ......... 11,706.245 194,424.96 2,447.914 15.6087 95 ......... 23.237 68.57 19.972 1.9508

44 ......... 11,122.394 182,718.72 2,421.503 15.4280 99 ......... 16.036 45.33 13.877 1.8267

45 ......... 10,565.600 171,596.32 2,394.347 15.2410 100 ......... 10.823 29.29 9.428 1.7066

46 ......... 10,034.175 161,030.72 2,366.046 15.0482 101 ......... 7.130 18.47 6.251 1.5904

47 ......... 9,526.880 150,996.55 2,336.569 14.8495 102 ......... 4.576 11.34 4.036 1.4781

48 ......... 9,042.454 141,469.67 2,305.803 14.6451 103 ......... 2.854 6.76 2.532 1.3697

49 ......... 8,579.905 132,427.21 2,273.847 14.4346 104 ......... 1.726 3.91 1.540 1.2650

50 ......... 8,138.375 123,847.31 2,240.884 14.2177 105 ......... 1.009 2.18 0.905 1.1640

51 ......... 7,716.699 115,708.93 2,206.750 13.9946 106 ......... 0.568 1.17 0.512 1.0666

52 ......... 7,313.565 107,992.23 2,171.078 13.7660 107 ......... 0.307 0.61 0.278 0.9729

53 ......... 6,928.012 100,678.67 2,133.789 13.5321 108 ......... 0.159 0.30 0.145 0.8827

54 ......... 6,559.150 93,750.66 2,094.833 13.2931 109 ......... 0.078 0.14 0.071 0.7959

x x x x x x x x

44
Table 4.F. -- Actuarial Functions at 6.0 Percent Interest for 1989-91 United States 

Total White Population

x D N M a x D N M a

0 ......... 100,000.000 1,716,472.58 2,841.175 16.1647 55 ......... 3,684.861 47,130.77 1,017.081 11.7904

1 ......... 93,616.038 1,616,472.58 2,117.590 16.2670 56 ......... 3,451.522 43,445.91 992.320 11.5875

2 ......... 88,261.837 1,522,856.54 2,062.410 16.2539 57 ......... 3,230.735 39,994.39 966.902 11.3793

3 ......... 83,229.780 1,434,594.70 2,026.307 16.2366 58 ......... 3,021.670 36,763.65 940.709 11.1667

4 ......... 78,492.522 1,351,364.92 2,000.168 16.2165 59 ......... 2,823.480 33,741.98 913.556 10.9505

5 ......... 74,029.373 1,272,872.40 1,979.992 16.1942 60 ......... 2,635.619 30,918.50 885.515 10.7310

6 ......... 69,822.112 1,198,843.03 1,963.073 16.1700 61 ......... 2,457.721 28,282.88 856.803 10.5078

7 ......... 65,855.286 1,129,020.91 1,948.441 16.1440 62 ......... 2,289.439 25,825.16 827.638 10.2801

8 ......... 62,114.452 1,063,165.63 1,935.266 16.1162 63 ......... 2,130.298 23,535.72 798.087 10.0481

9 ......... 58,587.294 1,001,051.18 1,924.020 16.0865 64 ......... 1,979.845 21,405.43 768.217 9.8117

10 ......... 55,262.097 942,463.88 1,915.085 16.0544 65 ......... 1,837.650 19,425.58 738.089 9.5709

11 ......... 52,126.152 887,201.79 1,907.183 16.0203 66 ......... 1,703.350 17,587.93 707.807 9.3255

12 ......... 49,167.664 835,075.63 1,899.232 15.9842 67 ......... 1,576.653 15,884.58 677.525 9.0749

13 ......... 46,375.212 785,907.97 1,889.855 15.9467 68 ......... 1,457.129 14,307.93 647.246 8.8193

14 ......... 43,737.373 739,532.76 1,877.028 15.9085 69 ......... 1,344.219 12,850.80 616.815 8.5601

15 ......... 41,243.730 695,795.38 1,859.086 15.8703 70 ......... 1,237.492 11,506.58 586.176 8.2983

16 ......... 38,886.348 654,551.65 1,836.255 15.8324 71 ......... 1,136.529 10,269.09 555.260 8.0355

17 ......... 36,658.867 615,665.31 1,809.888 15.7944 72 ......... 1,041.102 9,132.56 524.165 7.7720

18 ......... 34,555.459 579,006.44 1,781.510 15.7559 73 ......... 951.004 8,091.46 492.997 7.5083

19 ......... 32,570.405 544,450.98 1,752.425 15.7161 74 ......... 866.134 7,140.45 461.957 7.2441

20 ......... 30,698.734 511,880.57 1,724.362 15.6743 75 ......... 786.459 6,274.32 431.308 6.9779

21 ......... 28,934.008 481,181.84 1,697.300 15.6303 76 ......... 711.847 5,487.86 401.213 6.7093

22 ......... 27,269.871 452,247.83 1,670.937 15.5842 77 ......... 642.081 4,776.02 371.741 6.4383

23 ......... 25,700.637 424,977.96 1,645.281 15.5357 78 ......... 576.913 4,133.93 342.917 6.1656

24 ......... 24,221.680 399,277.32 1,621.077 15.4843 79 ......... 516.043 3,557.02 314.702 5.8929

25 ......... 22,827.342 375,055.64 1,597.777 15.4301 80 ......... 459.214 3,040.98 287.083 5.6221

26 ......... 21,513.247 352,228.30 1,575.796 15.3726 81 ......... 406.238 2,581.76 260.100 5.3553

27 ......... 20,274.779 330,715.06 1,555.059 15.3116 82 ......... 357.038 2,175.53 233.895 5.0933

28 ......... 19,107.000 310,440.28 1,534.909 15.2475 83 ......... 311.599 1,818.49 208.666 4.8360

29 ......... 18,005.909 291,333.28 1,515.346 15.1799 84 ......... 269.943 1,506.89 184.648 4.5822

30 ......... 16,967.206 273,327.37 1,495.846 15.1092 85 ......... 232.026 1,236.95 162.010 4.3311

31 ......... 15,987.581 256,360.16 1,476.628 15.0350 86 ......... 197.630 1,004.92 140.747 4.0849

32 ......... 15,063.563 240,372.58 1,457.568 14.9572 87 ......... 166.566 807.29 120.870 3.8467

33 ......... 14,192.197 225,309.02 1,438.857 14.8756 88 ......... 138.771 640.72 102.504 3.6171

34 ......... 13,370.385 211,116.82 1,420.376 14.7899 89 ......... 114.205 501.95 85.793 3.3952

35 ......... 12,595.486 197,746.43 1,402.292 14.6998 90 ......... 92.740 387.75 70.792 3.1810

36 ......... 11,864.491 185,150.95 1,384.249 14.6055 91 ......... 74.171 295.01 57.473 2.9774

37 ......... 11,175.200 173,286.46 1,366.533 14.5063 92 ......... 58.286 220.84 45.786 2.7888

38 ......... 10,524.945 162,111.26 1,348.836 14.4026 93 ......... 44.962 162.55 35.761 2.6152

39 ......... 9,911.674 151,586.31 1,331.316 14.2937 94 ......... 34.052 117.59 27.396 2.4532

40 ......... 9,333.330 141,674.64 1,314.011 14.1794 95 ......... 25.305 83.54 20.577 2.3011

41 ......... 8,787.785 132,341.31 1,296.768 14.0597 96 ......... 18.439 58.23 15.143 2.1580

42 ......... 8,273.144 123,553.52 1,279.549 13.9343 97 ......... 13.149 39.79 10.896 2.0263

43 ......... 7,787.629 115,280.38 1,262.325 13.8030 95 ......... 9.178 26.64 7.670 1.9029

44 ......... 7,329.416 107,492.75 1,244.921 13.6659 99 ......... 6.274 17.46 5.286 1.7836

45 ......... 6,896.817 100,163.33 1,227.194 13.5231 100 ......... 4.195 11.19 3.561 1.6679

46 ......... 6,488.131 93,266.52 1,208.895 13.3749 101 ......... 2.737 7.00 2.341 1.5557

47 ......... 6,101.998 86,778.38 1,190.014 13.2213 102 ......... 1.740 4.26 1.499 1.4472

48 ......... 5,737.083 80,676.39 1,170.495 13.0623 103 ......... 1.075 2.52 0.933 1.3421

49 ......... 5,392.259 74,939.30 1,150.412 12.8976 104 ......... 0.644 1.44 0.562 1.2406

50 ......... 5,066.516 69,547.04 1,129.891 12.7268 105 ......... 0.373 0.80 0.328 1.1424

51 ......... 4,758.682 64,480.53 1,108.841 12.5501 106 ......... 0.208 0.43 0.184 1.0477

52 ......... 4,467.532 59,721.85 1,087.050 12.3680 107 ......... 0.111 0.22 0.099 0.9564

53 ......... 4,192.090 55,254.31 1,064.487 12.1806 108 ......... 0.057 0.11 0.051 0.8683

54 ......... 3,931.452 51,062.22 1,041.138 11.9881 109 ......... 0.028 0.05 0.025 0.7835

x x x x x x x x

45
Table 4.G. -- Actuarial Functions at 7.0 Percent Interest for 1989-91 United States 

Total White Population

x D N M a x D N M a

0 ......... 100,000.000 1,496,693.13 2,085.496 13.9669 55 ......... 2,198.548 25,778.18 512.125 10.7251

1 ......... 92,741.121 1,396,693.13 1,368.674 14.0601 56 ......... 2,040.082 23,579.63 497.489 10.5582

2 ......... 86,619.792 1,303,952.01 1,314.521 14.0537 57 ......... 1,891.735 21,539.55 482.606 10.3861

3 ......... 80,917.976 1,217,332.21 1,279.420 14.0440 58 ......... 1,752.783 19,647.82 467.412 10.2095

4 ......... 75,599.101 1,136,414.24 1,254.244 14.0321 59 ......... 1,622.512 17,895.03 451.809 10.0292

5 ......... 70,634.115 1,060,815.14 1,234.994 14.0185 60 ......... 1,500.403 16,272.52 435.846 9.8454

6 ......... 65,997.199 990,181.02 1,219.002 14.0034 61 ......... 1,386.053 14,772.12 419.653 9.6577

7 ......... 61,665.925 924,183.82 1,205.301 13.9869 62 ......... 1,279.083 13,386.07 403.359 9.4654

8 ......... 57,619.483 862,517.90 1,193.079 13.9692 63 ......... 1,179.049 12,106.98 387.003 9.2684

9 ......... 53,839.650 804,898.41 1,182.744 13.9499 64 ......... 1,085.537 10,927.93 370.626 9.0668

10 ......... 50,309.296 751,058.76 1,174.611 13.9288 65 ......... 998.156 9,842.40 354.261 8.8606

11 ......... 47,010.907 700,749.47 1,167.484 13.9061 66 ......... 916.562 8,844.24 337.966 8.6494

12 ......... 43,928.323 653,738.56 1,160.380 13.8819 67 ......... 840.458 7,927.68 321.824 8.4326

13 ......... 41,046.208 609,810.24 1,152.081 13.8567 68 ......... 769.485 7,087.22 305.835 8.2103

14 ......... 38,349.696 568,764.03 1,140.834 13.8310 69 ......... 703.224 6,317.74 289.914 7.9840

15 ......... 35,825.252 530,414.33 1,125.249 13.8056 70 ......... 641.340 5,614.51 274.036 7.7543

16 ......... 33,461.897 494,589.08 1,105.602 13.7807 71 ......... 583.511 4,973.17 258.163 7.5228

17 ......... 31,250.324 461,127.18 1,083.125 13.7559 72 ......... 529.522 4,389.66 242.348 7.2899

18 ......... 29,181.946 429,876.86 1,059.160 13.7309 73 ......... 479.176 3,860.14 226.643 7.0558

19 ......... 27,248.514 400,694.91 1,034.828 13.7052 74 ......... 432.334 3,380.96 211.150 6.8203

20 ......... 25,442.643 373,446.40 1,011.570 13.6780 75 ......... 388.895 2,948.63 195.994 6.5821

21 ......... 23,755.952 348,003.76 989.351 13.6491 76 ......... 348.711 2,559.74 181.251 6.3406

22 ......... 22,180.381 324,247.81 967.908 13.6187 77 ......... 311.595 2,211.02 166.949 6.0958

23 ......... 20,708.656 302,067.42 947.235 13.5865 78 ......... 277.353 1,899.43 153.091 5.8484

24 ......... 19,334.563 281,358.77 927.915 13.5521 79 ......... 245.771 1,622.08 139.654 5.5999

25 ......... 18,051.260 262,024.21 909.490 13.5156 80 ......... 216.662 1,376.31 126.623 5.3523

26 ......... 16,853.117 243,972.95 892.270 13.4764 81 ......... 189.876 1,159.64 114.011 5.1074

27 ......... 15,734.484 227,119.83 876.177 13.4345 82 ......... 165.320 969.77 101.878 4.8660

28 ......... 14,689.634 211,385.34 860.686 13.3901 83 ......... 142.932 804.45 90.305 4.6282

29 ......... 13,713.730 196,695.71 845.786 13.3430 84 ......... 122.667 661.52 79.390 4.3928

30 ......... 12,801.857 182,981.98 831.073 13.2934 85 ......... 104.451 538.85 69.200 4.1588

31 ......... 11,949.988 170,180.12 816.709 13.2410 86 ......... 88.136 434.40 59.717 3.9287

32 ......... 11,154.100 158,230.14 802.596 13.1858 87 ......... 73.588 346.26 50.936 3.7054

33 ......... 10,410.666 147,076.04 788.870 13.1274 88 ......... 60.736 272.67 42.897 3.4895

34 ......... 9,716.165 136,665.37 775.440 13.0658 89 ......... 49.517 211.94 35.652 3.2801

35 ......... 9,067.509 126,949.20 762.421 13.0004 90 ......... 39.834 162.42 29.209 3.0774

36 ......... 8,461.440 117,881.70 749.553 12.9316 91 ......... 31.561 122.59 23.541 2.8842

37 ......... 7,895.371 109,420.26 737.036 12.8588 92 ......... 24.569 91.03 18.614 2.7049

38 ......... 7,366.465 101,524.88 724.650 12.7820 93 ......... 18.776 66.46 14.428 2.5394

39 ......... 6,872.400 94,158.42 712.503 12.7010 94 ......... 14.087 47.68 10.968 2.3847

40 ......... 6,410.917 87,286.02 700.616 12.6152 95 ......... 10.371 33.59 8.173 2.2393

41 ......... 5,979.777 80,875.10 688.883 12.5248 96 ......... 7.486 23.22 5.967 2.1021

42 ......... 5,576.970 74,895.33 677.275 12.4294 97 ......... 5.288 15.74 4.259 1.9757

43 ......... 5,200.619 69,318.36 665.773 12.3289 95 ......... 3.657 10.45 2.973 1.8572

44 ......... 4,848.878 64,117.74 654.259 12.2232 99 ......... 2.477 6.79 2.032 1.7423

45 ......... 4,520.044 59,268.86 642.642 12.1125 100 ......... 1.640 4.31 1.358 1.6308

46 ......... 4,212.459 54,748.82 630.761 11.9969 101 ......... 1.060 2.67 0.885 1.5225

47 ......... 3,924.734 50,536.36 618.617 11.8764 102 ......... 0.668 1.61 0.562 1.4174

48 ......... 3,655.538 46,611.62 606.180 11.7510 103 ......... 0.409 0.95 0.347 1.3156

49 ......... 3,403.714 42,956.08 593.503 11.6204 104 ......... 0.243 0.54 0.207 1.2170

50 ......... 3,168.209 39,552.37 580.670 11.4841 105 ......... 0.139 0.30 0.120 1.1217

51 ......... 2,947.903 36,384.16 567.631 11.3424 106 ......... 0.077 0.16 0.067 1.0294

52 ......... 2,741.677 33,436.26 554.258 11.1956 107 ......... 0.041 0.08 0.036 0.9404

53 ......... 2,548.597 30,694.58 540.541 11.0437 108 ......... 0.021 0.04 0.018 0.8544

54 ......... 2,367.804 28,145.99 526.478 10.8870 109 ......... 0.010 0.02 0.009 0.7715

x x x x x x x x

46
Table 4.H. -- Actuarial Functions at 8.0 Percent Interest for 1989-91 United States 

Total White Population

x D N M a x D N M a

0 ......... 100,000.000 1,327,652.77 1,655.350 12.2765 55 ......... 1,318.066 14,255.98 262.068 9.8158

1 ......... 91,882.407 1,227,652.77 945.165 12.3611 56 ......... 1,211.738 12,937.91 253.375 9.6771

2 ......... 85,023.148 1,135,770.36 892.010 12.3584 57 ......... 1,113.222 11,726.17 244.616 9.5335

3 ......... 78,691.002 1,050,747.22 857.875 12.3528 58 ......... 1,021.902 10,612.95 235.758 9.3855

4 ......... 72,837.783 972,056.21 833.619 12.3455 59 ......... 937.193 9,591.05 226.745 9.2338

5 ......... 67,424.016 899,218.43 815.243 12.3368 60 ......... 858.636 8,653.85 217.610 9.0786

6 ......... 62,414.521 831,794.41 800.119 12.3269 61 ......... 785.853 7,795.22 208.429 8.9194

7 ......... 57,778.386 769,379.89 787.283 12.3161 62 ......... 718.489 7,009.37 199.276 8.7557

8 ......... 53,487.160 711,601.51 775.937 12.3042 63 ......... 656.165 6,290.88 190.175 8.5873

9 ......... 49,515.643 658,114.35 766.432 12.2910 64 ......... 598.530 5,634.71 181.144 8.4142

10 ......... 45,840.407 608,598.71 759.021 12.2765 65 ......... 545.255 5,036.18 172.205 8.2364

11 ......... 42,438.388 562,758.30 752.588 12.2606 66 ......... 496.047 4,490.93 163.386 8.0534

12 ......... 39,288.450 520,319.91 746.234 12.2436 67 ......... 450.648 3,994.88 154.731 7.8647

13 ......... 36,370.840 481,031.46 738.880 12.2257 68 ......... 408.772 3,544.23 146.237 7.6704

14 ......... 33,666.831 444,660.62 729.007 12.2077 69 ......... 370.114 3,135.46 137.858 7.4716

15 ......... 31,159.436 410,993.79 715.451 12.1900 70 ......... 334.418 2,765.34 129.578 7.2691

16 ......... 28,834.400 379,834.35 698.522 12.1730 71 ......... 301.447 2,430.93 121.378 7.0642

17 ......... 26,679.329 350,999.95 679.333 12.1563 72 ......... 271.023 2,129.48 113.283 6.8572

18 ......... 24,682.812 324,320.63 659.062 12.1395 73 ......... 242.983 1,858.46 105.320 6.6485

19 ......... 22,834.065 299,637.81 638.672 12.1224 74 ......... 217.201 1,615.47 97.536 6.4377

20 ......... 21,123.344 276,803.75 619.362 12.1042 75 ......... 193.568 1,398.27 89.993 6.2237

21 ......... 19,540.375 255,680.40 601.086 12.0847 76 ......... 171.960 1,204.70 82.722 6.0057

22 ......... 18,075.466 236,140.03 583.612 12.0641 77 ......... 152.234 1,032.74 75.735 5.7839

23 ......... 16,719.851 218,064.56 566.921 12.0423 78 ......... 134.250 880.51 69.027 5.5587

24 ......... 15,465.889 201,344.71 551.466 12.0186 79 ......... 117.862 746.26 62.583 5.3317

25 ......... 14,305.666 185,878.82 536.865 11.9934 80 ......... 102.940 628.40 56.392 5.1045

26 ......... 13,232.467 171,573.16 523.344 11.9661 81 ......... 89.378 525.46 50.455 4.8791

27 ......... 12,239.766 158,340.69 510.826 11.9366 82 ......... 77.099 436.08 44.797 4.6561

28 ......... 11,321.177 146,100.92 498.887 11.9051 83 ......... 66.041 358.98 39.449 4.4358

29 ......... 10,471.195 134,779.75 487.510 11.8715 84 ......... 56.153 292.94 34.453 4.2169

30 ......... 9,684.420 124,308.55 476.380 11.8359 85 ......... 47.371 236.79 29.832 3.9986

31 ......... 8,956.290 114,624.13 465.614 11.7982 86 ......... 39.602 189.42 25.571 3.7831

32 ......... 8,282.382 105,667.84 455.134 11.7581 87 ......... 32.759 149.82 21.662 3.5733

33 ......... 7,658.774 97,385.46 445.036 11.7155 88 ......... 26.787 117.06 18.116 3.3699

34 ......... 7,081.669 89,726.69 435.248 11.6703 89 ......... 21.637 90.27 14.950 3.1720

35 ......... 6,547.700 82,645.02 425.847 11.6220 90 ......... 17.245 68.63 12.161 2.9799

36 ......... 6,053.479 76,097.32 416.641 11.5708 91 ......... 13.537 51.39 9.730 2.7962

37 ......... 5,596.202 70,043.84 407.769 11.5163 92 ......... 10.440 37.85 7.637 2.6254

38 ......... 5,172.970 64,447.63 399.072 11.4585 93 ......... 7.905 27.41 5.874 2.4676

39 ......... 4,781.336 59,274.66 390.620 11.3971 94 ......... 5.876 19.51 4.431 2.3198

40 ......... 4,418.970 54,493.33 382.427 11.3317 95 ......... 4.286 13.63 3.276 2.1805

41 ......... 4,083.626 50,074.36 374.414 11.2622 96 ......... 3.065 9.34 2.373 2.0489

42 ......... 3,773.282 45,990.73 366.561 11.1885 97 ......... 2.145 6.28 1.680 1.9275

43 ......... 3,486.069 42,217.45 358.851 11.1103 95 ......... 1.470 4.13 1.163 1.8135

44 ......... 3,220.195 38,731.38 351.204 11.0277 99 ......... 0.986 2.67 0.789 1.7029

45 ......... 2,974.018 35,511.19 343.560 10.9405 100 ......... 0.647 1.68 0.523 1.5952

46 ......... 2,745.976 32,537.17 335.815 10.8490 101 ......... 0.414 1.03 0.338 1.4905

47 ......... 2,534.727 29,791.19 327.972 10.7532 102 ......... 0.259 0.62 0.213 1.3888

48 ......... 2,339.012 27,256.47 320.014 10.6530 103 ......... 0.157 0.36 0.130 1.2901

49 ......... 2,157.715 24,917.45 311.978 10.5481 104 ......... 0.092 0.20 0.077 1.1944

50 ......... 1,989.825 22,759.74 303.918 10.4381 105 ......... 0.052 0.11 0.044 1.1016

51 ......... 1,834.317 20,769.91 295.805 10.3230 106 ......... 0.029 0.06 0.024 1.0118

52 ......... 1,690.197 18,935.60 287.560 10.2032 107 ......... 0.015 0.03 0.013 0.9249

53 ......... 1,556.619 17,245.40 279.182 10.0788 108 ......... 0.008 0.01 0.007 0.8409

54 ......... 1,432.804 15,688.78 270.673 9.9497 109 ......... 0.004 0.01 0.003 0.7598

x x x x x x x x

47
Table 4.I. -- Actuarial Functions at 9.0 Percent Interest for 1989-91 United States 

Total White Population

x D N M a x D N M a

0 ......... 100,000.000 1,194,189.07 1,397.233 10.9419 55 ......... 793.937 7,966.07 136.188 9.0336

1 ......... 91,039.450 1,094,189.07 693.563 11.0188 56 ......... 723.195 7,172.14 131.000 8.9173

2 ......... 83,470.247 1,003,149.62 641.379 11.0181 57 ......... 658.302 6,448.94 125.821 8.7963

3 ......... 76,545.004 919,679.38 608.175 11.0149 58 ......... 598.757 5,790.64 120.630 8.6711

4 ......... 70,201.396 843,134.37 584.797 11.0102 59 ......... 544.086 5,191.88 115.398 8.5424

5 ......... 64,387.403 772,932.98 567.249 11.0044 60 ......... 493.907 4,647.80 110.143 8.4103

6 ......... 59,056.701 708,545.57 552.938 10.9977 61 ......... 447.893 4,153.89 104.911 8.2743

7 ......... 54,168.425 649,488.87 540.904 10.9902 62 ......... 405.742 3,706.00 99.742 8.1339

8 ......... 49,685.264 595,320.45 530.364 10.9818 63 ......... 367.147 3,300.26 94.649 7.9889

9 ......... 45,574.062 545,635.18 521.616 10.9725 64 ......... 331.826 2,933.11 89.643 7.8393

10 ......... 41,804.308 500,061.12 514.858 10.9620 65 ......... 299.517 2,601.28 84.732 7.6849

11 ......... 38,346.763 458,256.81 509.045 10.9503 66 ......... 269.987 2,301.77 79.933 7.5255

12 ......... 35,174.828 419,910.05 503.356 10.9378 67 ......... 243.026 2,031.78 75.265 7.3603

13 ......... 32,263.961 384,735.22 496.832 10.9246 68 ......... 218.421 1,788.75 70.726 7.1895

14 ......... 29,591.286 352,471.26 488.154 10.9113 69 ......... 195.950 1,570.33 66.290 7.0139

15 ......... 27,136.164 322,879.97 476.349 10.8985 70 ......... 175.428 1,374.38 61.947 6.8345

16 ......... 24,880.955 295,743.81 461.741 10.8864 71 ......... 156.681 1,198.95 57.685 6.6522

17 ......... 22,810.158 270,862.86 445.335 10.8747 72 ......... 139.575 1,042.27 53.516 6.4675

18 ......... 20,909.579 248,052.70 428.163 10.8631 73 ......... 123.987 902.70 49.452 6.2806

19 ......... 19,165.985 227,143.12 411.048 10.8514 74 ......... 109.814 778.71 45.517 6.0912

20 ......... 17,567.413 207,977.14 394.989 10.8388 75 ......... 96.968 668.90 41.738 5.8981

21 ......... 16,101.833 190,409.72 379.929 10.8253 76 ......... 85.353 571.93 38.130 5.7007

22 ......... 14,758.056 174,307.89 365.662 10.8110 77 ......... 74.869 486.58 34.693 5.4990

23 ......... 13,525.999 159,549.83 352.159 10.7958 78 ......... 65.419 411.71 31.424 5.2934

24 ......... 12,396.785 146,023.83 339.771 10.7792 79 ......... 56.906 346.29 28.313 5.0853

25 ......... 11,361.601 133,627.05 328.175 10.7613 80 ......... 49.245 289.38 25.351 4.8763

26 ......... 10,412.848 122,265.45 317.535 10.7418 81 ......... 42.365 240.14 22.537 4.6683

27 ......... 9,543.311 111,852.60 307.775 10.7205 82 ......... 36.210 197.77 19.880 4.4619

28 ......... 8,746.107 102,309.29 298.551 10.6977 83 ......... 30.732 161.56 17.392 4.2572

29 ......... 8,015.243 93,563.18 289.843 10.6732 84 ......... 25.890 130.83 15.088 4.0532

30 ......... 7,344.993 85,547.94 281.401 10.6471 85 ......... 21.641 104.94 12.976 3.8491

31 ......... 6,730.435 78,202.95 273.311 10.6193 86 ......... 17.926 83.30 11.048 3.6469

32 ......... 6,166.908 71,472.51 265.508 10.5897 87 ......... 14.692 65.37 9.295 3.4495

33 ......... 5,650.264 65,305.60 258.058 10.5580 88 ......... 11.904 50.68 7.719 3.2575

34 ......... 5,176.574 59,655.34 250.903 10.5241 89 ......... 9.527 38.78 6.325 3.0703

35 ......... 4,742.341 54,478.77 244.094 10.4877 90 ......... 7.523 29.25 5.108 2.8879

36 ......... 4,344.165 49,736.43 237.488 10.4490 91 ......... 5.851 21.73 4.057 2.7131

37 ......... 3,979.164 45,392.26 231.180 10.4075 92 ......... 4.472 15.88 3.161 2.5503

38 ......... 3,644.482 41,413.10 225.052 10.3632 93 ......... 3.355 11.40 2.413 2.3996

39 ......... 3,337.662 37,768.61 219.152 10.3159 94 ......... 2.471 8.05 1.806 2.2581

40 ......... 3,056.408 34,430.95 213.485 10.2652 95 ......... 1.785 5.58 1.325 2.1246

41 ......... 2,798.553 31,374.54 207.994 10.2110 96 ......... 1.265 3.79 0.952 1.9982

42 ......... 2,562.147 28,575.99 202.661 10.1531 97 ......... 0.877 2.53 0.669 1.8815

43 ......... 2,345.406 26,013.84 197.474 10.0914 95 ......... 0.596 1.65 0.459 1.7717

44 ......... 2,146.651 23,668.44 192.377 10.0257 99 ......... 0.396 1.06 0.309 1.6651

45 ......... 1,964.356 21,521.79 187.328 9.9562 100 ......... 0.257 0.66 0.203 1.5611

46 ......... 1,797.093 19,557.43 182.259 9.8828 101 ......... 0.163 0.40 0.130 1.4599

47 ......... 1,643.624 17,760.34 177.174 9.8056 102 ......... 0.101 0.24 0.081 1.3613

48 ......... 1,502.798 16,116.71 172.061 9.7245 103 ......... 0.061 0.14 0.049 1.2655

49 ......... 1,373.598 14,613.92 166.945 9.6391 104 ......... 0.035 0.08 0.029 1.1725

50 ......... 1,255.098 13,240.32 161.861 9.5492 105 ......... 0.020 0.04 0.016 1.0822

51 ......... 1,146.395 11,985.22 156.790 9.4547 106 ......... 0.011 0.02 0.009 0.9947

52 ......... 1,046.634 10,838.82 151.685 9.3559 107 ......... 0.006 0.01 0.005 0.9099

53 ......... 955.074 9,792.19 146.545 9.2528 108 ......... 0.003 0.01 0.002 0.8278

54 ......... 871.041 8,837.12 141.371 9.1455 109 ......... 0.001 0.00 0.001 0.7485

x x x x x x x x

48
Table 4.J. -- Actuarial Functions at 10.0 Percent Interest for 1989-91 United States 

Total White Population

x D N M a x D N M a

0 ......... 100,000.000 1,086,430.77 1,233.566 9.8643 55 ......... 480.448 4,494.96 71.815 8.3558

1 ......... 90,211.818 986,430.77 536.293 9.9346 56 ......... 433.659 4,014.51 68.704 8.2573

2 ......... 81,959.504 896,218.96 485.054 9.9349 57 ......... 391.158 3,580.85 65.627 8.1545

3 ......... 74,476.334 814,259.45 452.747 9.9331 58 ......... 352.543 3,189.69 62.571 8.0477

4 ......... 67,683.218 739,783.12 430.208 9.9301 59 ......... 317.440 2,837.15 59.518 7.9376

5 ......... 61,513.434 672,099.90 413.443 9.9261 60 ......... 285.544 2,519.71 56.480 7.8242

6 ......... 55,907.756 610,586.47 399.895 9.9213 61 ......... 256.588 2,234.16 53.482 7.7072

7 ......... 50,813.943 554,678.71 388.606 9.9159 62 ......... 230.328 1,977.58 50.548 7.5859

8 ......... 46,184.697 503,864.77 378.809 9.9098 63 ......... 206.524 1,747.25 47.683 7.4603

9 ......... 41,978.030 457,680.07 370.751 9.9028 64 ......... 184.959 1,540.72 44.893 7.3301

10 ......... 38,155.677 415,702.04 364.583 9.8949 65 ......... 165.432 1,355.77 42.181 7.1953

11 ......... 34,681.722 377,546.36 359.325 9.8860 66 ......... 147.766 1,190.33 39.554 7.0555

12 ......... 31,523.740 342,864.64 354.227 9.8764 67 ......... 131.801 1,042.57 37.022 6.9102

13 ......... 28,652.152 311,340.90 348.434 9.8662 68 ......... 117.380 910.77 34.583 6.7591

14 ......... 26,039.774 282,688.75 340.797 9.8560 69 ......... 104.347 793.39 32.221 6.6034

15 ......... 23,662.228 256,648.97 330.503 9.8464 70 ......... 92.569 689.04 29.929 6.4435

16 ......... 21,498.494 232,986.75 317.881 9.8374 71 ......... 81.925 596.47 27.700 6.2807

17 ......... 19,530.039 211,488.25 303.834 9.8289 72 ......... 72.317 514.55 25.540 6.1151

18 ......... 17,740.012 191,958.21 289.265 9.8206 73 ......... 63.657 442.23 23.454 5.9471

19 ......... 16,112.895 174,218.20 274.877 9.8123 74 ......... 55.868 378.57 21.452 5.7762

20 ......... 14,634.708 158,105.31 261.499 9.8034 75 ......... 48.884 322.70 19.547 5.6015

21 ......... 13,291.848 143,470.60 249.067 9.7939 76 ......... 42.637 273.82 17.744 5.4221

22 ......... 12,071.828 130,178.75 237.396 9.7837 77 ......... 37.060 231.18 16.043 5.2381

23 ......... 10,963.445 118,106.92 226.452 9.7728 78 ......... 32.088 194.12 14.440 5.0498

24 ......... 9,956.818 107,143.48 216.502 9.7608 79 ......... 27.658 162.04 12.928 4.8585

25 ......... 9,042.424 97,186.66 207.273 9.7479 80 ......... 23.718 134.38 11.501 4.6657

26 ......... 8,211.994 88,144.23 198.882 9.7336 81 ......... 20.218 110.66 10.158 4.4732

27 ......... 7,457.822 79,932.24 191.254 9.7179 82 ......... 17.124 90.44 8.902 4.2817

28 ......... 6,772.696 72,474.42 184.112 9.7010 83 ......... 14.401 73.32 7.736 4.0912

29 ......... 6,150.314 65,701.72 177.430 9.6827 84 ......... 12.022 58.92 6.666 3.9007

30 ......... 5,584.776 59,551.41 171.011 9.6632 85 ......... 9.958 46.89 5.694 3.7094

31 ......... 5,070.973 53,966.63 164.916 9.6423 86 ......... 8.173 36.94 4.815 3.5194

32 ......... 4,604.150 48,895.66 159.090 9.6199 87 ......... 6.638 28.76 4.023 3.3333

33 ......... 4,180.080 44,291.51 153.579 9.5959 88 ......... 5.329 22.13 3.318 3.1519

34 ......... 3,794.827 40,111.43 148.334 9.5700 89 ......... 4.226 16.80 2.699 2.9744

35 ......... 3,444.897 36,316.60 143.388 9.5421 90 ......... 3.307 12.57 2.164 2.8011

36 ......... 3,126.969 32,871.71 138.632 9.5123 91 ......... 2.549 9.26 1.707 2.6345

37 ......... 2,838.200 29,744.74 134.133 9.4801 92 ......... 1.930 6.71 1.320 2.4790

38 ......... 2,575.851 26,906.54 129.802 9.4457 93 ......... 1.435 4.78 1.000 2.3349

39 ......... 2,337.551 24,330.69 125.670 9.4086 94 ......... 1.047 3.35 0.743 2.1994

40 ......... 2,121.113 21,993.13 121.737 9.3687 95 ......... 0.750 2.30 0.540 2.0713

41 ......... 1,924.508 19,872.02 117.961 9.3258 96 ......... 0.527 1.55 0.385 1.9498

42 ......... 1,745.919 17,947.51 114.327 9.2797 97 ......... 0.362 1.03 0.268 1.8375

43 ......... 1,583.697 16,201.59 110.825 9.2302 95 ......... 0.243 0.66 0.183 1.7317

44 ......... 1,436.314 14,617.90 107.414 9.1774 99 ......... 0.160 0.42 0.122 1.6289

45 ......... 1,302.392 13,181.58 104.066 9.1211 100 ......... 0.103 0.26 0.080 1.5284

46 ......... 1,180.663 11,879.19 100.736 9.0615 101 ......... 0.065 0.16 0.051 1.4304

47 ......... 1,070.019 10,698.53 97.426 8.9984 102 ......... 0.040 0.09 0.031 1.3348

48 ......... 969.446 9,628.51 94.127 8.9320 103 ......... 0.024 0.05 0.019 1.2418

49 ......... 878.045 8,659.06 90.857 8.8618 104 ......... 0.014 0.03 0.011 1.1514

50 ......... 795.002 7,781.02 87.637 8.7874 105 ......... 0.008 0.02 0.006 1.0635

51 ......... 719.547 6,986.02 84.454 8.7089 106 ......... 0.004 0.01 0.003 0.9781

52 ......... 650.958 6,266.47 81.279 8.6265 107 ......... 0.002 0.00 0.002 0.8954

53 ......... 588.612 5,615.51 78.111 8.5403 108 ......... 0.001 0.00 0.001 0.8151

54 ......... 531.943 5,026.90 74.952 8.4501 109 ......... 0.000 0.00 0.000 0.7375

x x x x x x x x

49
Table 4.K. -- Actuarial Functions at 11.0 Percent Interest for 1989-91 United States 

Total White Population

x D N M a x D N M a

0 ......... 100,000.000 997,749.60 1,123.913 8.9775 55 ......... 292.065 2,559.74 38.398 7.7643

1 ......... 89,399.099 897,749.60 432.922 9.0420 56 ......... 261.248 2,267.67 36.523 7.6802

2 ......... 80,489.408 808,350.50 382.602 9.0429 57 ......... 233.521 2,006.42 34.686 7.5921

3 ......... 72,481.539 727,861.10 351.160 9.0420 58 ......... 208.571 1,772.90 32.878 7.5002

4 ......... 65,276.946 655,379.56 329.422 9.0400 59 ......... 186.112 1,564.33 31.088 7.4053

5 ......... 58,792.036 590,102.61 313.399 9.0371 60 ......... 165.904 1,378.22 29.323 7.3074

6 ......... 52,952.967 531,310.57 300.568 9.0336 61 ......... 147.737 1,212.32 27.597 7.2059

7 ......... 47,694.779 478,357.61 289.971 9.0296 62 ......... 131.422 1,064.58 25.923 7.1005

8 ......... 42,959.157 430,662.83 280.859 9.0249 63 ......... 116.778 933.16 24.303 6.9908

9 ......... 38,694.516 387,703.67 273.431 9.0196 64 ......... 103.642 816.38 22.740 6.8769

10 ......... 34,854.289 349,009.16 267.796 9.0134 65 ......... 91.865 712.74 21.233 6.7585

11 ......... 31,395.501 314,154.87 263.037 9.0064 66 ......... 81.316 620.87 19.788 6.6353

12 ......... 28,279.662 282,759.36 258.464 8.9987 67 ......... 71.877 539.56 18.407 6.5067

13 ......... 25,472.023 254,479.70 253.313 8.9906 68 ......... 63.436 467.68 17.089 6.3725

14 ......... 22,941.040 229,007.68 246.585 8.9824 69 ......... 55.884 404.24 15.824 6.2336

15 ......... 20,658.617 206,066.64 237.598 8.9749 70 ......... 49.130 348.36 14.608 6.0906

16 ......... 18,600.445 185,408.02 226.677 8.9679 71 ......... 43.089 299.23 13.435 5.9445

17 ......... 16,745.114 166,807.58 214.633 8.9616 72 ......... 37.693 256.14 12.310 5.7955

18 ......... 15,073.310 150,062.46 202.255 8.9555 73 ......... 32.880 218.45 11.232 5.6438

19 ......... 13,567.443 134,989.15 190.139 8.9495 74 ......... 28.597 185.57 10.207 5.4891

20 ......... 12,211.758 121,421.71 178.976 8.9430 75 ......... 24.797 156.97 9.241 5.3304

21 ......... 10,991.304 109,209.95 168.696 8.9360 76 ......... 21.433 132.17 8.335 5.1668

22 ......... 9,892.512 98,218.65 159.132 8.9286 77 ......... 18.462 110.74 7.487 4.9984

23 ......... 8,903.285 88,326.14 150.244 8.9206 78 ......... 15.841 92.28 6.696 4.8255

24 ......... 8,012.970 79,422.85 142.237 8.9118 79 ......... 13.531 76.44 5.956 4.6491

25 ......... 7,211.531 71,409.88 134.877 8.9022 80 ......... 11.499 62.91 5.264 4.4709

26 ......... 6,490.244 64,198.35 128.245 8.8915 81 ......... 9.714 51.41 4.619 4.2924

27 ......... 5,841.092 57,708.11 122.271 8.8797 82 ......... 8.153 41.70 4.021 4.1142

28 ......... 5,256.702 51,867.01 116.727 8.8668 83 ......... 6.795 33.54 3.471 3.9365

29 ......... 4,730.628 46,610.31 111.588 8.8529 84 ......... 5.621 26.75 2.971 3.7583

30 ......... 4,256.934 41,879.68 106.695 8.8380 85 ......... 4.614 21.13 2.520 3.5787

31 ......... 3,830.471 37,622.75 102.091 8.8220 86 ......... 3.753 16.51 2.117 3.3998

32 ......... 3,446.514 33,792.28 97.730 8.8048 87 ......... 3.021 12.76 1.756 3.2241

33 ......... 3,100.879 30,345.76 93.642 8.7862 88 ......... 2.403 9.74 1.438 3.0524

34 ......... 2,789.729 27,244.89 89.786 8.7661 89 ......... 1.889 7.34 1.162 2.8840

35 ......... 2,509.666 24,455.16 86.182 8.7444 90 ......... 1.465 5.45 0.925 2.7190

36 ......... 2,257.527 21,945.49 82.749 8.7210 91 ......... 1.119 3.98 0.724 2.5600

37 ......... 2,030.589 19,687.96 79.530 8.6957 92 ......... 0.839 2.86 0.556 2.4114

38 ......... 1,826.289 17,657.37 76.459 8.6684 93 ......... 0.618 2.02 0.418 2.2735

39 ......... 1,642.402 15,831.08 73.556 8.6390 94 ......... 0.447 1.41 0.308 2.1435

40 ......... 1,476.903 14,188.68 70.818 8.6070 95 ......... 0.317 0.96 0.222 2.0205

41 ......... 1,327.938 12,711.78 68.212 8.5726 96 ......... 0.221 0.64 0.157 1.9036

42 ......... 1,193.856 11,383.84 65.727 8.5354 97 ......... 0.150 0.42 0.109 1.7954

43 ......... 1,073.172 10,189.98 63.354 8.4952 95 ......... 0.100 0.27 0.073 1.6935

44 ......... 964.531 9,116.81 61.064 8.4521 99 ......... 0.065 0.17 0.049 1.5941

45 ......... 866.720 8,152.28 58.836 8.4059 100 ......... 0.042 0.10 0.031 1.4969

46 ......... 778.632 7,285.56 56.640 8.3569 101 ......... 0.026 0.06 0.020 1.4020

47 ......... 699.307 6,506.93 54.476 8.3048 102 ......... 0.016 0.04 0.012 1.3093

48 ......... 627.870 5,807.62 52.340 8.2497 103 ......... 0.009 0.02 0.007 1.2190

49 ......... 563.550 5,179.75 50.241 8.1913 104 ......... 0.005 0.01 0.004 1.1310

50 ......... 505.654 4,616.20 48.193 8.1292 105 ......... 0.003 0.01 0.002 1.0454

51 ......... 453.538 4,110.55 46.187 8.0633 106 ......... 0.002 0.00 0.001 0.9621

52 ......... 406.610 3,657.01 44.203 7.9939 107 ......... 0.001 0.00 0.001 0.8813

53 ......... 364.354 3,250.40 42.242 7.9210 108 ......... 0.000 0.00 0.000 0.8028

54 ......... 326.309 2,886.05 40.304 7.8445 109 ......... 0.000 0.00 0.000 0.7268

x x x x x x x x

50
Table 4.L. -- Actuarial Functions at 12.0 Percent Interest for 1989-91 United States 

Total White Population

x D N M a x D N M a

0 ......... 100,000.000 923,566.08 1,046.491 8.2357 55 ......... 178.341 1,470.39 20.800 7.2448

1 ......... 88,600.893 823,566.08 361.670 8.2952 56 ......... 158.099 1,292.04 19.666 7.1724

2 ......... 79,058.514 734,965.19 312.244 8.2965 57 ......... 140.058 1,133.95 18.564 7.0962

3 ......... 70,557.352 655,906.67 281.637 8.2961 58 ......... 123.977 993.89 17.489 7.0167

4 ......... 62,976.664 585,349.32 260.665 8.2947 59 ......... 109.640 869.91 16.435 6.9343

5 ......... 56,213.844 522,372.66 245.345 8.2926 60 ......... 96.862 760.27 15.404 6.8490

6 ......... 50,178.773 466,158.81 233.186 8.2900 61 ......... 85.485 663.41 14.406 6.7605

7 ......... 44,792.524 415,980.04 223.234 8.2868 62 ......... 75.366 577.92 13.446 6.6682

8 ......... 39,984.843 371,187.52 214.752 8.2832 63 ......... 66.370 502.56 12.525 6.5720

9 ......... 35,693.901 331,202.67 207.901 8.2790 64 ......... 58.379 436.19 11.644 6.4717

10 ......... 31,864.403 295,508.77 202.749 8.2739 65 ......... 51.283 377.81 10.803 6.3671

11 ......... 28,446.048 263,644.37 198.437 8.2682 66 ......... 44.989 326.53 10.004 6.2580

12 ......... 25,394.150 235,198.32 194.330 8.2619 67 ......... 39.411 281.54 9.247 6.1435

13 ......... 22,668.765 209,804.17 189.747 8.2552 68 ......... 34.472 242.13 8.530 6.0237

14 ......... 20,234.035 187,135.41 183.813 8.2485 69 ......... 30.098 207.65 7.849 5.8993

15 ......... 18,058.247 166,901.37 175.957 8.2424 70 ......... 26.224 177.56 7.200 5.7708

16 ......... 16,113.973 148,843.12 166.496 8.2369 71 ......... 22.794 151.33 6.580 5.6392

17 ......... 14,377.135 132,729.15 156.155 8.2320 72 ......... 19.761 128.54 5.989 5.5045

18 ......... 12,826.195 118,352.02 145.622 8.2274 73 ......... 17.084 108.78 5.430 5.3671

19 ......... 11,441.742 105,525.82 135.404 8.2229 74 ......... 14.726 91.69 4.902 5.2266

20 ......... 10,206.511 94,084.08 126.074 8.2180 75 ......... 12.655 76.97 4.409 5.0819

21 ......... 9,104.441 83,877.57 117.559 8.2128 76 ......... 10.841 64.31 3.950 4.9323

22 ......... 8,121.114 74,773.13 109.708 8.2072 77 ......... 9.255 53.47 3.526 4.7778

23 ......... 7,243.764 66,652.01 102.477 8.2013 78 ......... 7.870 44.22 3.132 4.6185

24 ......... 6,461.190 59,408.25 96.020 8.1946 79 ......... 6.662 36.35 2.768 4.4555

25 ......... 5,763.037 52,947.06 90.138 8.1874 80 ......... 5.611 29.68 2.431 4.2903

26 ......... 5,140.317 47,184.02 84.886 8.1792 81 ......... 4.698 24.07 2.119 4.1243

27 ......... 4,584.879 42,043.70 80.196 8.1701 82 ......... 3.908 19.38 1.832 3.9582

28 ......... 4,089.330 37,458.83 75.884 8.1601 83 ......... 3.228 15.47 1.570 3.7921

29 ......... 3,647.224 33,369.50 71.921 8.1493 84 ......... 2.646 12.24 1.335 3.6251

30 ......... 3,252.712 29,722.27 68.183 8.1377 85 ......... 2.153 9.59 1.125 3.4562

31 ......... 2,900.720 26,469.56 64.696 8.1252 86 ......... 1.735 7.44 0.938 3.2875

32 ......... 2,586.656 23,568.84 61.423 8.1117 87 ......... 1.384 5.71 0.773 3.1213

33 ......... 2,306.473 20,982.18 58.382 8.0971 88 ......... 1.092 4.32 0.629 2.9586

34 ......... 2,056.509 18,675.71 55.540 8.0813 89 ......... 0.850 3.23 0.504 2.7985

35 ......... 1,833.536 16,619.20 52.907 8.0640 90 ......... 0.653 2.38 0.398 2.6412

36 ......... 1,634.600 14,785.67 50.421 8.0454 91 ......... 0.495 1.73 0.310 2.4894

37 ......... 1,457.154 13,151.07 48.111 8.0252 92 ......... 0.368 1.23 0.236 2.3472

38 ......... 1,298.847 11,693.91 45.927 8.0033 93 ......... 0.269 0.86 0.176 2.2150

39 ......... 1,157.638 10,395.06 43.881 7.9795 94 ......... 0.192 0.59 0.129 2.0902

40 ......... 1,031.693 9,237.43 41.968 7.9537 95 ......... 0.135 0.40 0.092 1.9719

41 ......... 919.350 8,205.73 40.164 7.9256 96 ......... 0.093 0.27 0.065 1.8594

42 ......... 819.144 7,286.38 38.460 7.8951 97 ......... 0.063 0.17 0.044 1.7551

43 ......... 729.764 6,467.24 36.846 7.8621 95 ......... 0.042 0.11 0.030 1.6568

44 ......... 650.032 5,737.48 35.302 7.8265 99 ......... 0.027 0.07 0.020 1.5607

45 ......... 578.897 5,087.44 33.814 7.7882 100 ......... 0.017 0.04 0.013 1.4667

46 ......... 515.419 4,508.55 32.360 7.7473 101 ......... 0.011 0.02 0.008 1.3747

47 ......... 458.776 3,993.13 30.941 7.7039 102 ......... 0.006 0.01 0.005 1.2847

48 ......... 408.232 3,534.35 29.552 7.6577 103 ......... 0.004 0.01 0.003 1.1969

49 ......... 363.141 3,126.12 28.199 7.6086 104 ......... 0.002 0.00 0.002 1.1113

50 ......... 322.925 2,762.98 26.891 7.5561 105 ......... 0.001 0.00 0.001 1.0278

51 ......... 287.056 2,440.05 25.622 7.5003 106 ......... 0.001 0.00 0.000 0.9466

52 ......... 255.056 2,153.00 24.378 7.4413 107 ......... 0.000 0.00 0.000 0.8676

53 ......... 226.509 1,897.94 23.159 7.3791 108 ......... 0.000 0.00 0.000 0.7909

54 ......... 201.046 1,671.43 21.964 7.3137 109 ......... 0.000 0.00 0.000 0.7164

x x x x x x x x

51
Table 5.A. -- Actuarial Functions at 1.0 Percent Interest for 1989-91 United States 

White Males

x D N M a x D N M a

0 ......... 100,000.000 5,146,775.46 49,041.827 50.4678 55 ......... 50,923.199 1,032,736.39 40,698.086 19.2803

1 ......... 98,156.436 5,046,775.46 48,188.362 50.4156 56 ......... 49,958.477 981,813.19 40,237.555 18.6526

2 ......... 97,119.890 4,948,619.03 48,123.662 49.9537 57 ......... 48,967.601 931,854.71 39,741.317 18.0300

3 ......... 96,111.719 4,851,499.14 48,077.074 49.4777 58 ......... 47,945.405 882,887.11 39,203.948 17.4144

4 ......... 95,124.561 4,755,387.42 48,041.518 48.9912 59 ......... 46,885.834 834,941.70 38,619.085 16.8080

5 ......... 94,153.239 4,660,262.86 48,012.022 48.4966 60 ......... 45,787.500 788,055.87 37,984.967 16.2112

6 ......... 93,195.593 4,566,109.62 47,986.587 47.9949 61 ......... 44,652.909 742,268.37 37,303.717 15.6231

7 ......... 92,248.614 4,472,914.02 47,962.336 47.4876 62 ......... 43,485.034 697,615.46 36,577.950 15.0427

8 ......... 91,313.098 4,380,665.41 47,940.173 46.9741 63 ......... 42,285.153 654,130.43 35,808.614 14.4695

9 ......... 90,388.892 4,289,352.31 47,920.057 46.4544 64 ......... 41,051.344 611,845.27 34,993.470 13.9044

10 ......... 89,477.657 4,198,963.42 47,903.762 45.9275 65 ......... 39,783.876 570,793.93 34,132.451 13.3474

11 ......... 88,577.399 4,109,485.76 47,889.421 45.3943 66 ......... 38,485.109 531,010.05 33,227.584 12.7978

12 ......... 87,685.308 4,020,908.36 47,874.334 44.8561 67 ......... 37,158.360 492,524.94 32,281.875 12.2548

13 ......... 86,796.928 3,933,223.06 47,854.125 44.3152 68 ......... 35,801.243 455,366.59 31,292.663 11.7193

14 ......... 85,904.493 3,846,426.13 47,821.066 43.7756 69 ......... 34,409.478 419,565.34 30,255.366 11.1933

15 ......... 85,003.134 3,760,521.64 47,770.247 43.2398 70 ......... 32,978.976 385,155.86 29,165.551 10.6788

16 ......... 84,093.293 3,675,518.50 47,702.021 42.7076 71 ......... 31,506.820 352,176.89 28,019.920 10.1778

17 ......... 83,176.249 3,591,425.21 47,617.583 42.1785 72 ......... 29,994.637 320,670.07 26,819.685 9.6909

18 ......... 82,255.744 3,508,248.96 47,520.605 41.6505 73 ......... 28,445.949 290,675.43 25,567.975 9.2185

19 ......... 81,337.035 3,425,993.22 47,416.310 41.1210 74 ......... 26,868.961 262,229.48 24,272.629 8.7596

20 ......... 80,425.177 3,344,656.18 47,309.769 40.5872 75 ......... 25,274.895 235,360.52 22,944.593 8.3120

21 ......... 79,520.968 3,264,231.00 47,201.849 40.0487 76 ......... 23,669.858 210,085.63 21,589.803 7.8757

22 ......... 78,621.960 3,184,710.04 47,090.177 39.5066 77 ......... 22,058.804 186,415.77 20,213.103 7.4509

23 ......... 77,730.572 3,106,088.08 46,977.224 38.9597 78 ......... 20,448.799 164,356.97 18,821.502 7.0375

24 ......... 76,847.552 3,028,357.50 46,863.815 38.4073 79 ......... 18,845.276 143,908.17 17,420.443 6.6363

25 ......... 75,972.839 2,951,509.95 46,749.969 37.8495 80 ......... 17,253.006 125,062.89 16,014.759 6.2488

26 ......... 75,107.142 2,875,537.11 46,636.478 37.2858 81 ......... 15,673.445 107,809.88 14,606.021 5.8785

27 ......... 74,249.611 2,800,429.97 46,522.581 36.7164 82 ......... 14,114.185 92,136.44 13,201.943 5.5279

28 ......... 73,400.184 2,726,180.36 46,408.299 36.1413 83 ......... 12,592.146 78,022.25 11,819.649 5.1961

29 ......... 72,555.803 2,652,780.18 46,290.652 35.5619 84 ......... 11,131.810 65,430.11 10,483.987 4.8778

30 ......... 71,715.753 2,580,224.37 46,168.977 34.9785 85 ......... 9,751.952 54,298.30 9,214.345 4.5679

31 ......... 70,879.349 2,508,508.62 46,042.630 34.3912 86 ......... 8,454.423 44,546.35 8,013.370 4.2690

32 ......... 70,047.386 2,437,629.27 45,912.442 33.7997 87 ......... 7,238.856 36,091.92 6,881.510 3.9859

33 ......... 69,219.908 2,367,581.89 45,778.503 33.2038 88 ......... 6,114.019 28,853.07 5,828.345 3.7192

34 ......... 68,396.959 2,298,361.98 45,640.899 32.6033 89 ......... 5,089.118 22,739.05 4,863.979 3.4682

35 ......... 67,577.872 2,229,965.02 45,499.011 31.9984 90 ......... 4,171.308 17,649.93 3,996.556 3.2313

36 ......... 66,762.010 2,162,387.15 45,352.236 31.3895 91 ......... 3,360.938 13,478.62 3,227.486 3.0104

37 ......... 65,948.759 2,095,625.14 45,199.995 30.7766 92 ......... 2,657.085 10,117.68 2,556.910 2.8078

38 ......... 65,139.586 2,029,676.38 45,043.780 30.1589 93 ......... 2,058.007 7,460.60 1,984.140 2.6252

39 ......... 64,333.188 1,964,536.79 44,882.328 29.5369 94 ......... 1,561.190 5,402.59 1,507.699 2.4606

40 ......... 63,530.327 1,900,203.60 44,716.430 28.9102 95 ......... 1,161.048 3,841.40 1,123.014 2.3086

41 ......... 62,730.408 1,836,673.28 44,545.524 28.2788 96 ......... 846.887 2,680.36 820.348 2.1650

42 ......... 61,933.517 1,773,942.87 44,369.726 27.6427 97 ......... 604.442 1,833.47 586.289 2.0333

43 ......... 61,137.130 1,712,009.35 44,186.543 27.0028 95 ......... 422.517 1,229.03 410.349 1.9088

44 ......... 60,340.115 1,650,872.22 43,994.845 26.3594 99 ......... 289.198 806.51 281.213 1.7888

45 ......... 59,538.829 1,590,532.11 43,790.987 25.7142 100 ......... 193.525 517.31 188.403 1.6731

46 ......... 58,731.045 1,530,993.28 43,572.696 25.0679 101 ......... 126.399 323.79 123.193 1.5616

47 ......... 57,913.999 1,472,262.23 43,337.146 24.4215 102 ......... 80.426 197.39 78.472 1.4543

48 ......... 57,088.147 1,414,348.23 43,084.700 23.7748 103 ......... 49.751 116.96 48.593 1.3509

49 ......... 56,252.092 1,357,260.09 42,813.873 23.1282 104 ......... 29.852 67.21 29.186 1.2515

50 ......... 55,406.930 1,301,007.99 42,525.663 22.4810 105 ......... 17.329 37.36 16.959 1.1558

51 ......... 54,548.307 1,245,601.06 42,215.623 21.8348 106 ......... 9.705 20.03 9.507 1.0638

52 ......... 53,673.836 1,191,052.76 41,881.234 21.1906 107 ......... 5.227 10.32 5.124 0.9753

53 ......... 52,779.466 1,137,378.92 41,518.288 20.5496 108 ......... 2.697 5.10 2.646 0.8903

54 ......... 51,863.069 1,084,599.46 41,124.461 19.9128 109 ......... 1.327 2.40 1.304 0.8086

x x x x x x x x

52
Table 5.B. -- Actuarial Functions at 2.0 Percent Interest for 1989-91 United States 

White Males

x D N M a x D N M a

0 ......... 100,000.000 3,816,745.36 25,161.856 37.1675 55 ......... 29,619.777 533,461.22 19,159.753 17.0103

1 ......... 97,194.118 3,716,745.36 24,316.758 37.2404 56 ......... 28,773.753 503,841.44 18,894.509 16.5105

2 ......... 95,224.913 3,619,551.24 24,253.321 37.0105 57 ......... 27,926.554 475,067.69 18,611.501 16.0113

3 ......... 93,312.527 3,524,326.33 24,208.089 36.7691 58 ......... 27,075.514 447,141.13 18,308.041 15.5146

4 ......... 91,448.687 3,431,013.80 24,173.907 36.5185 59 ......... 26,217.578 420,065.62 17,980.997 15.0223

5 ......... 89,627.498 3,339,565.11 24,145.829 36.2605 60 ......... 25,352.398 393,848.04 17,629.888 14.5349

6 ......... 87,846.121 3,249,937.62 24,121.854 35.9958 61 ......... 24,481.785 368,495.64 17,256.380 14.0518

7 ......... 86,101.013 3,162,091.49 24,099.219 35.7254 62 ......... 23,607.736 344,013.86 16,862.366 13.5721

8 ......... 84,392.274 3,075,990.48 24,078.736 35.4487 63 ......... 22,731.267 320,406.12 16,448.794 13.0954

9 ......... 82,719.115 2,991,598.21 24,060.327 35.1657 64 ......... 21,851.654 297,674.86 16,014.892 12.6225

10 ......... 81,082.406 2,908,879.09 24,045.561 34.8756 65 ......... 20,969.362 275,823.20 15,561.064 12.1536

11 ......... 79,479.686 2,827,796.69 24,032.692 34.5789 66 ......... 20,085.935 254,853.84 15,088.801 11.6882

12 ......... 77,907.857 2,748,317.00 24,019.288 34.2765 67 ......... 19,203.353 234,767.91 14,600.061 11.2254

13 ......... 76,362.472 2,670,409.14 24,001.508 33.9702 68 ......... 18,320.606 215,564.55 14,093.850 10.7662

14 ......... 74,836.369 2,594,046.67 23,972.709 33.6629 69 ......... 17,435.766 197,243.95 13,568.237 10.3126

15 ......... 73,325.152 2,519,210.30 23,928.871 33.3567 70 ......... 16,547.078 179,808.18 13,021.427 9.8665

16 ......... 71,829.128 2,445,885.15 23,870.596 33.0514 71 ......... 15,653.445 163,261.10 12,452.246 9.4297

17 ......... 70,349.297 2,374,056.02 23,799.179 32.7467 72 ......... 14,756.051 147,607.66 11,861.783 9.0032

18 ......... 68,888.681 2,303,706.72 23,717.961 32.4410 73 ......... 13,856.967 132,851.61 11,252.033 8.5874

19 ......... 67,451.432 2,234,818.04 23,631.471 32.1323 74 ......... 12,960.442 118,994.64 10,627.214 8.1814

20 ......... 66,041.369 2,167,366.61 23,543.984 31.8183 75 ......... 12,072.008 106,034.20 9,992.906 7.7835

21 ......... 64,658.690 2,101,325.24 23,456.234 31.4987 76 ......... 11,194.560 93,962.19 9,352.164 7.3936

22 ......... 63,300.962 2,036,666.55 23,366.323 31.1743 77 ......... 10,330.337 82,767.63 8,707.443 7.0121

23 ......... 61,969.716 1,973,365.59 23,276.273 30.8440 78 ......... 9,482.472 72,437.29 8,062.133 6.6391

24 ......... 60,665.096 1,911,395.87 23,186.745 30.5073 79 ......... 8,653.214 62,954.82 7,418.806 6.2753

25 ......... 59,386.593 1,850,730.78 23,097.754 30.1641 80 ......... 7,844.422 54,301.61 6,779.684 5.9223

26 ......... 58,134.306 1,791,344.19 23,009.910 29.8139 81 ......... 7,056.378 46,457.19 6,145.453 5.5837

27 ......... 56,907.124 1,733,209.88 22,922.616 29.4568 82 ......... 6,292.082 39,400.81 5,519.517 5.2620

28 ......... 55,704.567 1,676,302.76 22,835.886 29.0927 83 ......... 5,558.525 33,108.73 4,909.334 4.9564

29 ......... 54,523.912 1,620,598.19 22,747.477 28.7227 84 ......... 4,865.716 27,550.20 4,325.516 4.6621

30 ......... 53,364.276 1,566,074.28 22,656.938 28.3469 85 ......... 4,220.790 22,684.48 3,775.996 4.3745

31 ......... 52,224.824 1,512,710.00 22,563.843 27.9653 86 ......... 3,623.325 18,463.70 3,261.292 4.0958

32 ......... 51,105.824 1,460,485.18 22,468.860 27.5777 87 ......... 3,071.952 14,840.37 2,780.965 3.8309

33 ......... 50,006.987 1,409,379.35 22,372.097 27.1836 88 ......... 2,569.168 11,768.42 2,338.415 3.5806

34 ......... 48,928.022 1,359,372.37 22,273.662 26.7831 89 ......... 2,117.530 9,199.25 1,937.152 3.3443

35 ......... 47,868.143 1,310,444.34 22,173.156 26.3761 90 ......... 1,718.622 7,081.72 1,579.765 3.1206

36 ......... 46,826.606 1,262,576.20 22,070.209 25.9628 91 ......... 1,371.166 5,363.10 1,266.007 2.9113

37 ......... 45,802.702 1,215,749.60 21,964.475 25.5432 92 ......... 1,073.386 3,991.93 995.113 2.7190

38 ......... 44,797.180 1,169,946.89 21,857.044 25.1165 93 ......... 823.225 2,918.55 765.999 2.5453

39 ......... 43,808.860 1,125,149.71 21,747.101 24.6832 94 ......... 618.370 2,095.32 577.286 2.3885

40 ......... 42,837.999 1,081,340.85 21,635.237 24.2426 95 ......... 455.370 1,476.95 426.410 2.2434

41 ......... 41,883.927 1,038,502.86 21,521.126 23.7948 96 ......... 328.898 1,021.58 308.867 2.1061

42 ......... 40,946.448 996,618.93 21,404.900 23.3396 97 ......... 232.440 692.68 218.858 1.9800

43 ......... 40,023.654 955,672.48 21,284.978 22.8777 95 ......... 160.887 460.24 151.863 1.8606

44 ......... 39,114.611 915,648.83 21,160.713 22.4094 99 ......... 109.042 299.35 103.173 1.7453

45 ......... 38,216.805 876,534.22 21,029.860 21.9358 100 ......... 72.253 190.31 68.522 1.6340

46 ......... 37,328.713 838,317.41 20,891.117 21.4577 101 ......... 46.729 118.06 44.414 1.5265

47 ......... 36,448.533 800,988.70 20,742.872 20.9759 102 ......... 29.441 71.33 28.043 1.4228

48 ......... 35,576.535 764,540.16 20,585.551 20.4900 103 ......... 18.034 41.89 17.212 1.3228

49 ......... 34,711.835 728,963.63 20,418.431 20.0004 104 ......... 10.715 23.86 10.247 1.2264

50 ......... 33,855.107 694,251.79 20,242.326 19.5066 105 ......... 6.159 13.14 5.901 1.1336

51 ......... 33,003.696 660,396.69 20,054.741 19.0098 106 ......... 3.415 6.98 3.279 1.0441

52 ......... 32,156.231 627,392.99 19,854.408 18.5108 107 ......... 1.821 3.57 1.751 0.9580

53 ......... 31,310.406 595,236.76 19,639.097 18.0108 108 ......... 0.931 1.74 0.896 0.8751

54 ......... 30,465.136 563,926.35 19,407.757 17.5105 109 ......... 0.454 0.81 0.438 0.7954

x x x x x x x x

53
Table 5.C. -- Actuarial Functions at 3.0 Percent Interest for 1989-91 United States 

White Males

x D N M a x D N M a

0 ......... 100,000.000 2,964,727.46 13,648.715 28.6473 55 ......... 17,319.840 279,465.97 9,180.054 15.1356

1 ......... 96,250.485 2,864,727.46 12,811.821 28.7633 56 ......... 16,661.786 262,146.13 9,026.461 14.7334

2 ......... 93,384.862 2,768,476.98 12,749.610 28.6459 57 ......... 16,014.203 245,484.35 8,864.173 14.3292

3 ......... 90,620.988 2,675,092.12 12,705.683 28.5196 58 ......... 15,375.443 229,470.14 8,691.846 13.9245

4 ......... 87,948.667 2,584,471.13 12,672.809 28.3861 59 ......... 14,743.699 214,094.70 8,507.931 13.5211

5 ......... 85,360.315 2,496,522.46 12,646.068 28.2469 60 ......... 14,118.738 199,351.00 8,312.398 13.1196

6 ......... 82,851.480 2,411,162.15 12,623.456 28.1022 61 ......... 13,501.526 185,232.27 8,106.411 12.7194

7 ......... 80,417.190 2,328,310.67 12,602.316 27.9529 62 ......... 12,893.091 171,730.74 7,891.225 12.3196

8 ......... 78,055.996 2,247,893.48 12,583.370 27.7985 63 ......... 12,293.889 158,837.65 7,667.550 11.9200

9 ......... 75,765.659 2,169,837.48 12,566.509 27.6388 64 ......... 11,703.423 146,543.76 7,435.159 11.5214

10 ......... 73,545.498 2,094,071.82 12,553.115 27.4731 65 ......... 11,121.844 134,840.34 7,194.455 11.1239

11 ......... 71,391.838 2,020,526.32 12,541.557 27.3019 66 ......... 10,549.857 123,718.49 6,946.406 10.7270

12 ......... 69,300.540 1,949,134.49 12,529.633 27.1258 67 ......... 9,988.368 113,168.64 6,692.194 10.3300

13 ......... 67,266.416 1,879,833.94 12,513.971 26.9461 68 ......... 9,436.702 103,180.27 6,431.452 9.9339

14 ......... 65,282.078 1,812,567.53 12,488.849 26.7652 69 ......... 8,893.739 93,743.57 6,163.344 9.5404

15 ......... 63,342.788 1,747,285.45 12,450.979 26.5846 70 ......... 8,358.486 84,849.83 5,887.131 9.1513

16 ......... 61,447.999 1,683,942.66 12,401.126 26.4044 71 ......... 7,830.314 76,491.34 5,602.411 8.7686

17 ......... 59,597.750 1,622,494.66 12,340.624 26.2241 72 ......... 7,309.747 68,661.03 5,309.911 8.3931

18 ......... 57,793.755 1,562,896.91 12,272.486 26.0427 73 ......... 6,797.721 61,351.28 5,010.790 8.0253

19 ......... 56,038.586 1,505,103.16 12,200.630 25.8583 74 ......... 6,296.191 54,553.56 4,707.252 7.6645

20 ......... 54,334.416 1,449,064.57 12,128.652 25.6694 75 ......... 5,807.651 48,257.37 4,402.097 7.3093

21 ......... 52,680.367 1,394,730.16 12,057.158 25.4753 76 ......... 5,333.238 42,449.72 4,096.839 6.9595

22 ......... 51,073.444 1,342,049.79 11,984.615 25.2769 77 ......... 4,873.730 37,116.48 3,792.667 6.6156

23 ......... 49,513.918 1,290,976.34 11,912.665 25.0730 78 ......... 4,430.283 32,242.75 3,491.173 6.2778

24 ......... 48,000.926 1,241,462.43 11,841.826 24.8633 79 ......... 4,003.596 27,812.47 3,193.524 5.9469

25 ......... 46,533.111 1,193,461.50 11,772.096 24.6476 80 ......... 3,594.154 23,808.87 2,900.692 5.6243

26 ......... 45,109.614 1,146,928.39 11,703.933 24.4254 81 ......... 3,201.699 20,214.72 2,612.921 5.3137

27 ......... 43,728.664 1,101,818.78 11,636.855 24.1967 82 ......... 2,827.197 17,013.02 2,331.672 5.0176

28 ......... 42,389.015 1,058,090.11 11,570.856 23.9614 83 ......... 2,473.342 14,185.82 2,060.163 4.7355

29 ......... 41,087.761 1,015,701.10 11,504.234 23.7203 84 ......... 2,144.047 11,712.48 1,802.907 4.4628

30 ......... 39,823.464 974,613.34 11,436.668 23.4733 85 ......... 1,841.807 9,568.43 1,563.115 4.1951

31 ......... 38,594.760 934,789.87 11,367.870 23.2206 86 ......... 1,565.744 7,726.62 1,340.697 3.9348

32 ......... 37,401.128 896,195.11 11,298.358 22.9617 87 ......... 1,314.592 6,160.88 1,135.149 3.6865

33 ......... 36,241.648 858,793.98 11,228.231 22.6963 88 ......... 1,088.759 4,846.29 947.605 3.4512

34 ......... 35,115.419 822,552.34 11,157.584 22.4242 89 ......... 888.652 3,757.53 779.209 3.2283

35 ......... 34,021.208 787,436.92 11,086.152 22.1455 90 ......... 714.242 2,868.88 630.683 3.0167

36 ......... 32,957.842 753,415.71 11,013.695 21.8600 91 ......... 564.310 2,154.63 501.554 2.8182

37 ......... 31,924.209 720,457.87 10,939.999 21.5678 92 ......... 437.469 1,590.32 391.149 2.6353

38 ......... 30,920.226 688,533.66 10,865.848 21.2681 93 ......... 332.256 1,152.86 298.678 2.4698

39 ......... 29,944.488 657,613.43 10,790.698 20.9611 94 ......... 247.153 820.60 223.252 2.3202

40 ......... 28,996.598 627,668.94 10,714.979 20.6463 95 ......... 180.237 573.45 163.535 2.1816

41 ......... 28,075.547 598,672.35 10,638.488 20.3236 96 ......... 128.915 393.21 117.462 2.0501

42 ......... 27,180.660 570,596.80 10,561.336 19.9927 97 ......... 90.223 264.29 82.525 1.9293

43 ......... 26,310.158 543,416.14 10,482.504 19.6542 95 ......... 61.843 174.07 56.773 1.8147

44 ......... 25,462.948 517,105.98 10,401.609 19.3082 99 ......... 41.507 112.23 38.239 1.7038

45 ......... 24,636.953 491,643.03 10,317.253 18.9555 100 ......... 27.237 70.72 25.177 1.5965

46 ......... 23,830.798 467,006.08 10,228.679 18.5967 101 ......... 17.444 43.48 16.177 1.4928

47 ......... 23,042.976 443,175.28 10,134.958 18.2326 102 ......... 10.884 26.04 10.125 1.3926

48 ......... 22,273.328 420,132.31 10,036.464 17.8626 103 ......... 6.602 15.16 6.160 1.2958

49 ......... 21,520.977 397,858.98 9,932.851 17.4870 104 ......... 3.884 8.55 3.635 1.2023

50 ......... 20,786.030 376,338.00 9,824.729 17.1053 105 ......... 2.211 4.67 2.075 1.1121

51 ......... 20,066.558 355,551.97 9,710.675 16.7186 106 ......... 1.214 2.46 1.143 1.0251

52 ......... 19,361.473 335,485.41 9,590.053 16.3275 107 ......... 0.641 1.24 0.605 0.9413

53 ......... 18,669.165 316,123.94 9,461.671 15.9329 108 ......... 0.324 0.60 0.307 0.8604

54 ......... 17,988.803 297,454.78 9,325.072 15.5356 109 ......... 0.157 0.28 0.148 0.7825

x x x x x x x x

54
Table 5.D. -- Actuarial Functions at 4.0 Percent Interest for 1989-91 United States 

White Males

x D N M a x D N M a

0 ......... 100,000.000 2,394,045.35 7,921.333 22.9405 55 ......... 10,180.230 148,355.64 4,474.243 13.5729

1 ......... 95,325.000 2,294,045.35 7,092.487 23.0655 56 ......... 9,699.272 138,175.41 4,384.833 13.2460

2 ......... 91,597.633 2,198,720.35 7,031.466 23.0041 57 ......... 9,232.659 128,476.14 4,291.269 12.9154

3 ......... 88,031.975 2,107,122.71 6,988.794 22.9359 58 ......... 8,779.161 119,243.48 4,192.873 12.5826

4 ......... 84,614.502 2,019,090.74 6,957.166 22.8622 59 ......... 8,337.497 110,464.32 4,088.869 12.2491

5 ......... 81,334.619 1,934,476.23 6,931.687 22.7842 60 ......... 7,907.314 102,126.83 3,979.359 11.9155

6 ......... 78,185.026 1,853,141.62 6,910.348 22.7020 61 ......... 7,488.932 94,219.51 3,865.104 11.5812

7 ......... 75,158.151 1,774,956.59 6,890.590 22.6163 62 ......... 7,082.685 86,730.58 3,746.894 11.2454

8 ......... 72,249.917 1,699,798.44 6,873.054 22.5266 63 ......... 6,688.582 79,647.89 3,625.202 10.9080

9 ......... 69,455.617 1,627,548.52 6,857.597 22.4329 64 ......... 6,306.111 72,959.31 3,499.983 10.5696

10 ......... 66,772.087 1,558,092.90 6,845.437 22.3345 65 ......... 5,935.118 66,653.20 3,371.533 10.2303

11 ......... 64,193.536 1,491,320.82 6,835.043 22.2316 66 ......... 5,575.746 60,718.08 3,240.435 9.8897

12 ......... 61,713.936 1,427,127.28 6,824.425 22.1249 67 ......... 5,228.232 55,142.34 3,107.373 9.5470

13 ......... 59,326.510 1,365,413.35 6,810.612 22.0152 68 ......... 4,891.977 49,914.11 2,972.204 9.2033

14 ......... 57,022.777 1,306,086.84 6,788.668 21.9047 69 ......... 4,566.174 45,022.13 2,834.554 8.8599

15 ......... 54,796.833 1,249,064.06 6,755.907 21.7945 70 ......... 4,250.104 40,455.95 2,694.106 8.5188

16 ......... 52,646.550 1,194,267.23 6,713.195 21.6846 71 ......... 3,943.256 36,205.85 2,550.724 8.1817

17 ......... 50,570.345 1,141,620.68 6,661.857 21.5749 72 ......... 3,645.710 32,262.59 2,404.841 7.8495

18 ......... 48,568.071 1,091,050.33 6,604.597 21.4644 73 ......... 3,357.739 28,616.88 2,257.090 7.5227

19 ......... 46,640.263 1,042,482.26 6,544.792 21.3516 74 ......... 3,080.104 25,259.14 2,108.599 7.2007

20 ......... 44,787.077 995,842.00 6,485.461 21.2350 75 ......... 2,813.792 22,179.04 1,960.752 6.8823

21 ......... 43,006.132 951,054.92 6,427.096 21.1144 76 ......... 2,559.094 19,365.25 1,814.277 6.5672

22 ......... 41,293.398 908,048.79 6,368.445 20.9902 77 ......... 2,316.118 16,806.15 1,669.727 6.2562

23 ......... 39,647.577 866,755.39 6,310.832 20.8615 78 ......... 2,085.137 14,490.04 1,527.827 5.9492

24 ......... 38,066.493 827,107.81 6,254.654 20.7280 79 ......... 1,866.196 12,404.90 1,389.084 5.6472

25 ......... 36,547.630 789,041.32 6,199.887 20.5894 80 ......... 1,659.234 10,538.70 1,253.899 5.3515

26 ......... 35,088.931 752,493.69 6,146.866 20.4453 81 ......... 1,463.846 8,879.47 1,122.327 5.0659

27 ......... 33,687.681 717,404.76 6,095.190 20.2958 82 ......... 1,280.191 7,415.62 994.974 4.7926

28 ......... 32,341.646 683,717.08 6,044.835 20.1405 83 ......... 1,109.192 6,135.43 873.213 4.5314

29 ......... 31,047.394 651,375.43 5,994.493 19.9800 84 ......... 952.271 5,026.24 758.954 4.2782

30 ......... 29,802.699 620,328.04 5,943.928 19.8145 85 ......... 810.167 4,073.97 653.476 4.0286

31 ......... 28,605.450 590,525.34 5,892.937 19.6438 86 ......... 682.111 3,263.80 556.580 3.7849

32 ......... 27,454.215 561,919.89 5,841.912 19.4675 87 ......... 567.190 2,581.69 467.895 3.5517

33 ......... 26,347.302 534,465.67 5,790.930 19.2854 88 ......... 465.237 2,014.50 387.756 3.3301

34 ......... 25,283.079 508,118.37 5,740.065 19.0972 89 ......... 376.078 1,549.27 316.491 3.1195

35 ......... 24,259.716 482,835.29 5,689.128 18.9028 90 ......... 299.361 1,173.19 254.238 2.9190

36 ......... 23,275.480 458,575.58 5,637.958 18.7021 91 ......... 234.246 873.83 200.637 2.7304

37 ......... 22,328.724 435,300.10 5,586.412 18.4951 92 ......... 179.848 639.58 155.248 2.5562

38 ......... 21,418.562 412,971.37 5,535.047 18.2810 93 ......... 135.280 459.73 117.598 2.3984

39 ......... 20,543.215 391,552.81 5,483.492 18.0600 94 ......... 99.662 324.45 87.183 2.2555

40 ......... 19,701.644 371,009.60 5,432.044 17.8314 95 ......... 71.980 224.79 63.334 2.1230

41 ......... 18,892.417 351,307.95 5,380.573 17.5952 96 ......... 50.989 152.81 45.112 1.9970

42 ......... 18,114.368 332,415.53 5,329.155 17.3509 97 ......... 35.342 101.82 31.426 1.8810

43 ......... 17,365.630 314,301.17 5,277.123 17.0990 95 ......... 23.992 66.48 21.435 1.7709

44 ......... 16,644.841 296,935.54 5,224.243 16.8395 99 ......... 15.948 42.49 14.314 1.6641

45 ......... 15,950.042 280,290.70 5,169.631 16.5730 100 ......... 10.364 26.54 9.344 1.5607

46 ......... 15,279.787 264,340.65 5,112.839 16.3000 101 ......... 6.574 16.18 5.952 1.4605

47 ......... 14,632.589 249,060.87 5,053.325 16.0210 102 ......... 4.062 9.60 3.693 1.3636

48 ......... 14,007.854 234,428.28 4,991.382 15.7355 103 ......... 2.440 5.54 2.227 1.2698

49 ......... 13,404.554 220,420.42 4,926.845 15.4437 104 ......... 1.422 3.10 1.303 1.1791

50 ......... 12,822.296 207,015.87 4,860.148 15.1450 105 ......... 0.802 1.68 0.737 1.0915

51 ......... 12,259.451 194,193.57 4,790.468 14.8403 106 ......... 0.436 0.88 0.402 1.0068

52 ......... 11,714.950 181,934.12 4,717.483 14.5301 107 ......... 0.228 0.44 0.211 0.9251

53 ......... 11,187.443 170,219.17 4,640.551 14.2152 108 ......... 0.114 0.21 0.106 0.8462

54 ......... 10,676.086 159,031.73 4,559.481 13.8961 109 ......... 0.055 0.10 0.051 0.7701

x x x x x x x x

55
Table 5.E. -- Actuarial Functions at 5.0 Percent Interest for 1989-91 United States 

White Males

x D N M a x D N M a

0 ......... 100,000.000 1,995,606.44 4,971.122 18.9561 55 ......... 6,014.227 79,741.44 2,217.015 12.2588

1 ......... 94,417.143 1,895,606.44 4,150.170 19.0769 56 ......... 5,675.516 73,727.21 2,164.697 11.9904

2 ......... 89,861.224 1,801,189.29 4,090.306 19.0441 57 ......... 5,351.026 68,051.70 2,110.469 11.7175

3 ......... 85,540.654 1,711,328.07 4,048.842 19.0060 58 ......... 5,039.731 62,700.67 2,053.984 11.4413

4 ......... 81,436.850 1,625,787.41 4,018.402 18.9638 59 ......... 4,740.608 57,660.94 1,994.849 11.1632

5 ......... 77,534.615 1,544,350.56 3,994.112 18.9182 60 ......... 4,453.192 52,920.33 1,933.176 10.8837

6 ......... 73,822.343 1,466,815.95 3,973.964 18.8695 61 ......... 4,177.402 48,467.14 1,869.443 10.6022

7 ......... 70,288.516 1,392,993.61 3,955.487 18.8182 62 ......... 3,913.168 44,289.74 1,804.132 10.3181

8 ......... 66,925.199 1,322,705.09 3,939.243 18.7639 63 ......... 3,660.232 40,376.57 1,737.538 10.0312

9 ......... 63,724.104 1,255,779.89 3,925.061 18.7065 64 ......... 3,418.064 36,716.34 1,669.667 9.7419

10 ......... 60,678.572 1,192,055.79 3,914.011 18.6454 65 ......... 3,186.339 33,298.28 1,600.707 9.4503

11 ......... 57,779.761 1,131,377.21 3,904.656 18.5809 66 ......... 2,964.897 30,111.94 1,530.996 9.1561

12 ......... 55,018.878 1,073,597.45 3,895.190 18.5133 67 ......... 2,753.630 27,147.04 1,460.914 8.8586

13 ......... 52,386.734 1,018,578.58 3,882.992 18.4434 68 ......... 2,551.991 24,393.41 1,390.400 8.5586

14 ......... 49,872.935 966,191.84 3,863.800 18.3731 69 ......... 2,359.344 21,841.42 1,319.276 8.2574

15 ......... 47,469.653 916,318.91 3,835.420 18.3033 70 ......... 2,175.116 19,482.07 1,247.398 7.9568

16 ......... 45,172.545 868,849.25 3,798.771 18.2340 71 ......... 1,998.858 17,306.96 1,174.717 7.6584

17 ......... 42,977.842 823,676.71 3,755.141 18.1651 72 ......... 1,830.429 15,308.10 1,101.472 7.3631

18 ......... 40,883.077 780,698.87 3,706.941 18.0959 73 ......... 1,669.790 13,477.67 1,027.996 7.0715

19 ......... 38,886.402 739,815.79 3,657.078 18.0251 74 ......... 1,517.136 11,807.88 954.856 6.7830

20 ......... 36,985.673 700,929.39 3,608.083 17.9514 75 ......... 1,372.761 10,290.75 882.726 6.4964

21 ......... 35,176.711 663,943.72 3,560.343 17.8745 76 ......... 1,236.612 8,917.99 811.946 6.2116

22 ......... 33,454.112 628,767.01 3,512.826 17.7949 77 ......... 1,108.541 7,681.37 742.761 5.9293

23 ......... 31,814.828 595,312.89 3,466.595 17.7118 78 ......... 988.484 6,572.83 675.492 5.6494

24 ......... 30,255.186 563,498.06 3,421.945 17.6248 79 ......... 876.267 5,584.35 610.346 5.3729

25 ......... 28,771.349 533,242.88 3,378.831 17.5338 80 ......... 771.668 4,708.08 547.474 5.1012

26 ......... 27,359.942 504,471.53 3,337.489 17.4383 81 ......... 674.315 3,936.41 486.866 4.8377

27 ......... 26,017.179 477,111.59 3,297.579 17.3383 82 ......... 584.098 3,262.10 428.760 4.5848

28 ......... 24,739.746 451,094.41 3,259.060 17.2336 83 ......... 501.259 2,678.00 373.735 4.3426

29 ......... 23,523.520 426,354.66 3,220.918 17.1246 84 ......... 426.246 2,176.74 322.591 4.1068

30 ......... 22,365.407 402,831.14 3,182.972 17.0113 85 ......... 359.185 1,750.50 275.828 3.8735

31 ......... 21,262.486 380,465.73 3,145.070 16.8938 86 ......... 299.531 1,391.31 233.279 3.6450

32 ......... 20,212.420 359,203.25 3,107.504 16.7714 87 ......... 246.695 1,091.78 194.706 3.4256

33 ......... 19,212.748 338,990.83 3,070.327 16.6441 88 ......... 200.424 845.08 160.182 3.2165

34 ......... 18,261.117 319,778.08 3,033.589 16.5114 89 ......... 160.471 644.66 129.773 3.0173

35 ......... 17,355.100 301,516.96 2,997.150 16.3734 90 ......... 126.520 484.19 103.463 2.8270

36 ......... 16,492.409 284,161.86 2,960.892 16.2299 91 ......... 98.057 357.67 81.025 2.6476

37 ......... 15,670.880 267,669.46 2,924.716 16.0807 92 ......... 74.569 259.61 62.206 2.4815

38 ......... 14,888.942 251,998.57 2,889.010 15.9252 93 ......... 55.556 185.04 46.744 2.3308

39 ......... 14,144.447 237,109.63 2,853.512 15.7634 94 ......... 40.539 129.49 34.373 2.1942

40 ......... 13,435.817 222,965.19 2,818.427 15.5948 95 ......... 29.000 88.95 24.764 2.0672

41 ......... 12,761.249 209,529.37 2,783.660 15.4192 96 ......... 20.347 59.95 17.492 1.9463

42 ......... 12,119.170 196,768.12 2,749.260 15.2361 97 ......... 13.969 39.60 12.083 1.8350

43 ......... 11,507.587 184,648.95 2,714.780 15.0458 95 ......... 9.393 25.63 8.172 1.7291

44 ......... 10,924.899 173,141.36 2,680.072 14.8483 99 ......... 6.184 16.24 5.411 1.6262

45 ......... 10,369.162 162,216.46 2,644.568 14.6441 100 ......... 3.981 10.06 3.502 1.5264

46 ......... 9,838.823 151,847.30 2,607.999 14.4335 101 ......... 2.501 6.08 2.211 1.4296

47 ......... 9,332.351 142,008.48 2,570.043 14.2168 102 ......... 1.531 3.58 1.360 1.3357

48 ......... 8,848.824 132,676.13 2,530.913 13.9936 103 ......... 0.911 2.04 0.813 1.2448

49 ......... 8,387.071 123,827.30 2,490.533 13.7641 104 ......... 0.526 1.13 0.472 1.1568

50 ......... 7,946.352 115,440.23 2,449.198 13.5274 105 ......... 0.294 0.61 0.265 1.0716

51 ......... 7,525.183 107,493.88 2,406.427 13.2846 106 ......... 0.158 0.31 0.143 0.9891

52 ......... 7,122.468 99,968.70 2,362.054 13.0357 107 ......... 0.082 0.16 0.074 0.9095

53 ......... 6,736.975 92,846.23 2,315.726 12.7816 108 ......... 0.041 0.07 0.037 0.8325

54 ......... 6,367.812 86,109.25 2,267.372 12.5226 109 ......... 0.019 0.03 0.018 0.7581

x x x x x x x x

56
Table 5.F. -- Actuarial Functions at 6.0 Percent Interest for 1989-91 United States 

White Males

x D N M a x D N M a

0 ......... 100,000.000 1,706,755.41 3,391.203 16.0676 55 ......... 3,570.826 43,365.69 1,116.164 11.1444

1 ......... 93,526.415 1,606,755.41 2,577.995 16.1797 56 ......... 3,337.933 39,794.86 1,085.394 10.9220

2 ......... 88,173.727 1,513,229.00 2,519.256 16.1619 57 ......... 3,117.402 36,456.93 1,053.802 10.6947

3 ......... 83,142.460 1,425,055.27 2,478.954 16.1399 58 ......... 2,908.349 33,339.53 1,021.206 10.4634

4 ......... 78,406.975 1,341,912.81 2,449.646 16.1147 59 ......... 2,709.921 30,431.18 987.402 10.2295

5 ......... 73,945.680 1,263,505.84 2,426.481 16.0869 60 ......... 2,521.607 27,721.26 952.479 9.9935

6 ......... 69,741.041 1,189,560.16 2,407.448 16.0568 61 ......... 2,343.127 25,199.65 916.731 9.7547

7 ......... 65,776.144 1,119,819.12 2,390.156 16.0247 62 ......... 2,174.209 22,856.52 880.444 9.5126

8 ......... 62,037.908 1,054,042.97 2,375.098 15.9903 63 ......... 2,014.489 20,682.31 843.792 9.2668

9 ......... 58,513.306 992,005.06 2,362.076 15.9535 64 ......... 1,863.459 18,667.82 806.790 9.0178

10 ......... 55,191.181 933,491.76 2,352.025 15.9138 65 ......... 1,720.740 16,804.37 769.549 8.7658

11 ......... 52,058.724 878,300.58 2,343.597 15.8713 66 ......... 1,586.048 15,083.63 732.258 8.5102

12 ......... 49,103.555 826,241.85 2,335.148 15.8265 67 ......... 1,459.135 13,497.58 695.122 8.2504

13 ......... 46,313.325 777,138.30 2,324.365 15.7800 68 ......... 1,339.531 12,038.44 658.109 7.9871

14 ......... 43,675.009 730,824.97 2,307.557 15.7333 69 ......... 1,226.728 10,698.91 621.129 7.7215

15 ......... 41,178.220 687,149.96 2,282.939 15.6872 70 ......... 1,120.270 9,472.18 584.109 7.4553

16 ......... 38,815.885 645,971.74 2,251.447 15.6419 71 ......... 1,019.778 8,351.91 547.028 7.1899

17 ......... 36,581.623 607,155.86 2,214.311 15.5973 72 ......... 925.039 7,332.14 510.013 6.9263

18 ......... 34,470.326 570,574.24 2,173.671 15.5526 73 ......... 835.897 6,407.10 473.231 6.6649

19 ......... 32,477.530 536,103.91 2,132.026 15.5069 74 ......... 752.313 5,571.20 436.962 6.4054

20 ......... 30,598.645 503,626.38 2,091.492 15.4591 75 ......... 674.299 4,818.89 401.532 6.1465

21 ......... 28,827.524 473,027.73 2,052.369 15.4089 76 ......... 601.692 4,144.59 367.093 5.8882

22 ......... 27,157.204 444,200.21 2,013.796 15.3566 77 ......... 534.289 3,542.90 333.748 5.6311

23 ......... 25,582.828 417,043.01 1,976.620 15.3017 78 ......... 471.930 3,008.61 301.631 5.3751

24 ......... 24,099.179 391,460.18 1,941.056 15.2437 79 ......... 414.408 2,536.68 270.822 5.1212

25 ......... 22,701.057 367,361.00 1,907.038 15.1826 80 ......... 361.498 2,122.27 241.369 4.8708

26 ......... 21,383.779 344,659.94 1,874.726 15.1178 81 ......... 312.911 1,760.77 213.245 4.6271

27 ......... 20,142.479 323,276.16 1,843.828 15.0495 82 ......... 268.490 1,447.86 186.535 4.3926

28 ......... 18,972.798 303,133.69 1,814.288 14.9773 83 ......... 228.237 1,179.37 161.481 4.1673

29 ......... 17,869.891 284,160.89 1,785.312 14.9017 84 ......... 192.251 951.13 138.413 3.9474

30 ......... 16,829.833 266,291.00 1,756.758 14.8226 85 ......... 160.476 758.88 117.520 3.7290

31 ......... 15,848.950 249,461.16 1,728.506 14.7399 86 ......... 132.562 598.41 98.689 3.5142

32 ......... 14,924.102 233,612.21 1,700.769 14.6534 87 ......... 108.148 465.85 81.780 3.3075

33 ......... 14,052.151 218,688.11 1,673.578 14.5626 88 ......... 87.035 357.70 66.787 3.1098

34 ......... 13,230.129 204,635.96 1,646.961 14.4674 89 ......... 69.028 270.66 53.707 2.9211

35 ......... 12,455.103 191,405.83 1,620.810 14.3677 90 ......... 53.910 201.64 42.497 2.7402

36 ......... 11,724.321 178,950.73 1,595.035 14.2632 91 ......... 41.388 147.73 33.026 2.5693

37 ......... 11,035.206 167,226.41 1,569.560 14.1539 92 ......... 31.177 106.34 25.158 2.4108

38 ......... 10,385.665 156,191.20 1,544.654 14.0391 93 ......... 23.009 75.16 18.754 2.2667

39 ......... 9,773.270 145,805.54 1,520.127 13.9188 94 ......... 16.631 52.15 13.679 2.1359

40 ......... 9,196.052 136,032.27 1,496.113 13.7925 95 ......... 11.785 35.52 9.774 2.0142

41 ......... 8,651.949 126,836.21 1,472.541 13.6598 96 ......... 8.191 23.74 6.847 1.8981

42 ......... 8,139.113 118,184.26 1,449.438 13.5205 97 ......... 5.570 15.55 4.690 1.7910

43 ......... 7,655.471 110,045.15 1,426.500 13.3747 95 ......... 3.710 9.98 3.145 1.6891

44 ......... 7,199.271 102,389.68 1,403.628 13.2222 99 ......... 2.420 6.27 2.065 1.5899

45 ......... 6,768.589 95,190.41 1,380.453 13.0636 100 ......... 1.543 3.85 1.325 1.4935

46 ......... 6,361.816 88,421.82 1,356.808 12.8988 101 ......... 0.960 2.30 0.830 1.3998

47 ......... 5,977.402 82,060.00 1,332.496 12.7284 102 ......... 0.582 1.34 0.506 1.3089

48 ......... 5,614.232 76,082.60 1,307.670 12.5517 103 ......... 0.343 0.76 0.300 1.2207

49 ......... 5,271.068 70,468.37 1,282.292 12.3689 104 ......... 0.196 0.42 0.172 1.1352

50 ......... 4,946.973 65,197.30 1,256.559 12.1792 105 ......... 0.108 0.22 0.096 1.0523

51 ......... 4,640.579 60,250.33 1,230.183 11.9834 106 ......... 0.058 0.11 0.051 0.9720

52 ......... 4,350.800 55,609.75 1,203.078 11.7815 107 ......... 0.030 0.06 0.027 0.8943

53 ......... 4,076.495 51,258.95 1,175.045 11.5743 108 ......... 0.015 0.03 0.013 0.8191

54 ......... 3,816.767 47,182.46 1,146.062 11.3619 109 ......... 0.007 0.01 0.006 0.7464

x x x x x x x x

57
Table 5.G. -- Actuarial Functions at 7.0 Percent Interest for 1989-91 United States 

White Males

x D N M a x D N M a

0 ......... 100,000.000 1,490,237.01 2,507.859 13.9024 55 ......... 2,130.509 23,844.61 570.582 10.1920

1 ......... 92,652.336 1,390,237.01 1,702.252 14.0049 56 ......... 1,972.943 21,714.10 552.395 10.0059

2 ......... 86,533.322 1,297,584.67 1,644.605 13.9952 57 ......... 1,825.374 19,741.16 533.896 9.8149

3 ......... 80,833.081 1,211,051.35 1,605.423 13.9821 58 ......... 1,687.048 17,915.78 514.988 9.6196

4 ......... 75,516.708 1,130,218.27 1,577.195 13.9665 59 ......... 1,557.255 16,228.73 495.562 9.4214

5 ......... 70,554.260 1,054,701.56 1,555.093 13.9488 60 ......... 1,435.498 14,671.48 475.682 9.2205

6 ......... 65,920.570 984,147.30 1,537.102 13.9293 61 ......... 1,321.427 13,235.98 455.522 9.0164

7 ......... 61,591.818 918,226.73 1,520.910 13.9083 62 ......... 1,214.705 11,914.55 435.248 8.8086

8 ......... 57,548.478 856,634.91 1,506.942 13.8854 63 ......... 1,114.953 10,699.85 414.963 8.5967

9 ......... 53,771.658 799,086.43 1,494.975 13.8607 64 ......... 1,021.724 9,584.90 394.675 8.3811

10 ......... 50,244.736 745,314.78 1,485.825 13.8337 65 ......... 934.654 8,563.17 374.446 8.1619

11 ......... 46,950.095 695,070.04 1,478.224 13.8044 66 ......... 853.442 7,628.52 354.380 7.9385

12 ......... 43,871.046 648,119.94 1,470.675 13.7733 67 ......... 777.813 6,775.08 334.584 7.7104

13 ......... 40,991.433 604,248.90 1,461.131 13.7409 68 ......... 707.383 5,997.26 315.039 7.4781

14 ......... 38,295.013 563,257.47 1,446.394 13.7084 69 ......... 641.759 5,289.88 295.693 7.2428

15 ......... 35,768.348 524,962.45 1,425.010 13.6767 70 ......... 580.589 4,648.12 276.507 7.0059

16 ......... 33,401.264 489,194.10 1,397.911 13.6460 71 ......... 523.569 4,067.53 257.469 6.7689

17 ......... 31,184.477 455,792.84 1,366.254 13.6160 72 ......... 470.490 3,543.96 238.642 6.5325

18 ......... 29,110.051 424,608.36 1,331.933 13.5863 73 ......... 421.177 3,073.47 220.109 6.2973

19 ......... 27,170.815 395,498.31 1,297.093 13.5560 74 ......... 375.520 2,652.29 202.005 6.0630

20 ......... 25,359.690 368,327.50 1,263.499 13.5241 75 ......... 333.433 2,276.77 184.486 5.8283

21 ......... 23,668.524 342,967.81 1,231.378 13.4905 76 ......... 294.749 1,943.34 167.615 5.5932

22 ......... 22,088.742 319,299.28 1,200.004 13.4553 77 ......... 259.285 1,648.59 151.433 5.3582

23 ......... 20,613.729 297,210.54 1,170.049 13.4181 78 ......... 226.882 1,389.31 135.993 5.1235

24 ......... 19,236.779 276,596.81 1,141.660 13.3785 79 ......... 197.366 1,162.42 121.320 4.8897

25 ......... 17,951.397 257,360.03 1,114.760 13.3365 80 ......... 170.558 965.06 107.423 4.6582

26 ......... 16,751.694 239,408.64 1,089.447 13.2916 81 ......... 146.255 794.50 94.278 4.4323

27 ......... 15,631.810 222,656.94 1,065.468 13.2438 82 ......... 124.319 648.25 81.911 4.2144

28 ......... 14,586.458 207,025.13 1,042.758 13.1930 83 ......... 104.694 523.93 70.418 4.0044

29 ......... 13,610.135 192,438.67 1,020.689 13.1394 84 ......... 87.362 419.23 59.936 3.7988

30 ......... 12,698.208 178,828.54 999.145 13.0830 85 ......... 72.242 331.87 50.530 3.5939

31 ......... 11,846.367 166,130.33 978.028 13.0237 86 ......... 59.118 259.63 42.133 3.3917

32 ......... 11,050.833 154,283.96 957.489 12.9613 87 ......... 47.779 200.51 34.662 3.1966

33 ......... 10,307.935 143,233.13 937.544 12.8954 88 ......... 38.092 152.73 28.100 3.0095

34 ......... 9,614.242 132,925.20 918.201 12.8259 89 ......... 29.929 114.64 22.429 2.8304

35 ......... 8,966.447 123,310.95 899.375 12.7525 90 ......... 23.156 84.71 17.614 2.6583

36 ......... 8,361.474 114,344.51 880.993 12.6752 91 ......... 17.611 61.55 13.584 2.4953

37 ......... 7,796.464 105,983.03 862.995 12.5937 92 ......... 13.142 43.94 10.267 2.3438

38 ......... 7,268.983 98,186.57 845.563 12.5076 93 ......... 9.608 30.80 7.593 2.2058

39 ......... 6,776.436 90,917.59 828.556 12.4167 94 ......... 6.880 21.19 5.494 2.0805

40 ......... 6,316.623 84,141.15 812.061 12.3206 95 ......... 4.830 14.31 3.893 1.9637

41 ......... 5,887.346 77,824.53 796.022 12.2189 96 ......... 3.325 9.48 2.705 1.8520

42 ......... 5,486.619 71,937.18 780.448 12.1114 97 ......... 2.240 6.16 1.837 1.7491

43 ......... 5,112.363 66,450.56 765.130 11.9980 95 ......... 1.478 3.92 1.222 1.6508

44 ......... 4,762.778 61,338.20 749.999 11.8787 99 ......... 0.955 2.44 0.795 1.5551

45 ......... 4,436.006 56,575.42 734.810 11.7537 100 ......... 0.603 1.49 0.506 1.4619

46 ......... 4,130.448 52,139.42 719.458 11.6232 101 ......... 0.372 0.88 0.314 1.3713

47 ......... 3,844.595 48,008.97 703.821 11.4874 102 ......... 0.223 0.51 0.190 1.2832

48 ......... 3,577.260 44,164.37 688.002 11.3459 103 ......... 0.130 0.29 0.112 1.1976

49 ......... 3,327.215 40,587.11 671.984 11.1985 104 ......... 0.074 0.16 0.064 1.1144

50 ......... 3,093.456 37,259.90 655.892 11.0447 105 ......... 0.040 0.08 0.035 1.0337

51 ......... 2,874.741 34,166.44 639.553 10.8851 106 ......... 0.021 0.04 0.019 0.9555

52 ......... 2,670.039 31,291.70 622.919 10.7196 107 ......... 0.011 0.02 0.010 0.8797

53 ......... 2,478.321 28,621.66 605.876 10.5488 108 ......... 0.005 0.01 0.005 0.8062

54 ......... 2,298.732 26,143.34 588.420 10.3729 109 ......... 0.002 0.00 0.002 0.7351

x x x x x x x x

58
Table 5.H. -- Actuarial Functions at 8.0 Percent Interest for 1989-91 United States 

White Males

x D N M a x D N M a

0 ......... 100,000.000 1,323,131.64 1,990.249 12.2313 55 ......... 1,277.276 13,247.62 295.970 9.3718

1 ......... 91,794.444 1,223,131.64 1,192.101 12.3247 56 ......... 1,171.860 11,970.35 285.168 9.2148

2 ......... 84,938.272 1,131,337.20 1,135.516 12.3195 57 ......... 1,074.170 10,798.49 274.282 9.0529

3 ......... 78,608.444 1,046,398.92 1,097.412 12.3115 58 ......... 983.578 9,724.32 263.258 8.8867

4 ......... 72,758.400 967,790.48 1,070.216 12.3014 59 ......... 899.500 8,740.74 252.038 8.7173

5 ......... 67,347.791 895,032.08 1,049.118 12.2897 60 ......... 821.493 7,841.24 240.661 8.5451

6 ......... 62,342.051 827,684.29 1,032.104 12.2765 61 ......... 749.212 7,019.75 229.230 8.3695

7 ......... 57,708.951 765,342.24 1,016.933 12.2621 62 ......... 682.326 6,270.54 217.842 8.1899

8 ......... 53,421.247 707,633.29 1,003.966 12.2463 63 ......... 620.494 5,588.21 206.553 8.0061

9 ......... 49,453.112 654,212.04 992.961 12.2289 64 ......... 563.346 4,967.71 195.367 7.8182

10 ......... 45,781.581 604,758.93 984.623 12.2097 65 ......... 510.566 4,404.37 184.317 7.6264

11 ......... 42,383.491 558,977.35 977.761 12.1886 66 ......... 461.887 3,893.80 173.457 7.4302

12 ......... 39,237.222 516,593.86 971.010 12.1659 67 ......... 417.058 3,431.92 162.842 7.2289

13 ......... 36,322.304 477,356.64 962.553 12.1422 68 ......... 375.782 3,014.86 152.459 7.0229

14 ......... 33,618.826 441,034.33 949.616 12.1187 69 ......... 337.764 2,639.08 142.277 6.8134

15 ......... 31,109.943 407,415.51 931.017 12.0960 70 ......... 302.740 2,301.31 132.273 6.6016

16 ......... 28,782.151 376,305.56 907.665 12.0743 71 ......... 270.480 1,998.57 122.438 6.3890

17 ......... 26,623.113 347,523.41 880.638 12.0534 72 ......... 240.809 1,728.09 112.802 6.1762

18 ......... 24,622.002 320,900.30 851.610 12.0331 73 ......... 213.573 1,487.28 103.404 5.9638

19 ......... 22,768.954 296,278.30 822.414 12.0124 74 ......... 188.658 1,273.71 94.309 5.7514

20 ......... 21,054.474 273,509.34 794.523 11.9906 75 ......... 165.963 1,085.05 85.589 5.5379

21 ......... 19,468.462 252,454.87 768.101 11.9674 76 ......... 145.350 919.09 77.269 5.3233

22 ......... 18,000.786 232,986.41 742.534 11.9431 77 ......... 126.677 773.74 69.363 5.1080

23 ......... 16,643.210 214,985.62 718.349 11.9173 78 ......... 109.820 647.06 61.890 4.8920

24 ......... 15,387.671 198,342.41 695.640 11.8897 79 ......... 94.649 537.24 54.853 4.6762

25 ......... 14,226.524 182,954.74 674.321 11.8601 80 ......... 81.035 442.59 48.251 4.4617

26 ......... 13,152.833 168,728.22 654.447 11.8283 81 ......... 68.845 361.56 42.063 4.2518

27 ......... 12,159.896 155,575.38 635.794 11.7941 82 ......... 57.978 292.71 36.295 4.0487

28 ......... 11,241.660 143,415.49 618.291 11.7575 83 ......... 48.373 234.73 30.985 3.8526

29 ......... 10,392.094 132,173.83 601.441 11.7187 84 ......... 39.991 186.36 26.187 3.6600

30 ......... 9,606.012 121,781.73 585.143 11.6777 85 ......... 32.763 146.37 21.921 3.4675

31 ......... 8,878.629 112,175.72 569.316 11.6344 86 ......... 26.563 113.61 18.148 3.2769

32 ......... 8,205.702 103,297.09 554.065 11.5885 87 ......... 21.270 87.04 14.822 3.0924

33 ......... 7,583.198 95,091.39 539.392 11.5397 88 ......... 16.800 65.77 11.928 2.9150

34 ......... 7,007.382 87,508.19 525.294 11.4880 89 ......... 13.078 48.97 9.450 2.7448

35 ......... 6,474.722 80,500.81 511.700 11.4331 90 ......... 10.024 35.90 7.365 2.5809

36 ......... 5,981.962 74,026.09 498.548 11.3749 91 ......... 7.553 25.87 5.637 2.4251

37 ......... 5,526.097 68,044.12 485.792 11.3132 92 ......... 5.585 18.32 4.228 2.2802

38 ......... 5,104.515 62,518.03 473.550 11.2476 93 ......... 4.045 12.73 3.102 2.1479

39 ......... 4,714.571 57,413.51 461.718 11.1779 94 ......... 2.870 8.69 2.226 2.0277

40 ......... 4,353.974 52,698.94 450.349 11.1036 95 ......... 1.996 5.82 1.565 1.9155

41 ......... 4,020.504 48,344.97 439.395 11.0246 96 ......... 1.361 3.82 1.078 1.8081

42 ......... 3,712.152 44,324.46 428.858 10.9404 97 ......... 0.909 2.46 0.726 1.7089

43 ......... 3,426.909 40,612.31 418.590 10.8510 95 ......... 0.594 1.55 0.479 1.6142

44 ......... 3,163.016 37,185.40 408.541 10.7563 99 ......... 0.380 0.96 0.309 1.5217

45 ......... 2,918.725 34,022.39 398.548 10.6566 100 ......... 0.238 0.58 0.195 1.4316

46 ......... 2,692.515 31,103.66 388.540 10.5519 101 ......... 0.145 0.34 0.120 1.3438

47 ......... 2,482.971 28,411.15 378.441 10.4424 102 ......... 0.086 0.20 0.072 1.2584

48 ......... 2,288.925 25,928.18 368.320 10.3277 103 ......... 0.050 0.11 0.042 1.1752

49 ......... 2,109.220 23,639.25 358.165 10.2076 104 ......... 0.028 0.06 0.024 1.0944

50 ......... 1,942.876 21,530.03 348.059 10.0815 105 ......... 0.015 0.03 0.013 1.0158

51 ......... 1,788.792 19,587.15 337.891 9.9499 106 ......... 0.008 0.02 0.007 0.9395

52 ......... 1,646.034 17,798.36 327.637 9.8129 107 ......... 0.004 0.01 0.003 0.8655

53 ......... 1,513.696 16,152.33 317.228 9.6708 108 ......... 0.002 0.00 0.002 0.7937

54 ......... 1,391.008 14,638.63 306.665 9.5238 109 ......... 0.001 0.00 0.001 0.7241

x x x x x x x x

59
Table 5.I. -- Actuarial Functions at 9.0 Percent Interest for 1989-91 United States 

White Males

x D N M a x D N M a

0 ......... 100,000.000 1,190,867.42 1,671.498 10.9087 55 ......... 769.368 7,432.48 155.676 8.6605

1 ......... 90,952.294 1,090,867.42 880.672 10.9938 56 ......... 699.395 6,663.11 149.229 8.5270

2 ......... 83,386.920 999,915.12 825.121 10.9913 57 ......... 635.209 5,963.72 142.792 8.3886

3 ......... 76,464.697 916,528.20 788.056 10.9863 58 ......... 576.302 5,328.51 136.333 8.2460

4 ......... 70,124.886 840,063.50 761.845 10.9795 59 ......... 522.203 4,752.21 129.819 8.1003

5 ......... 64,314.610 769,938.62 741.697 10.9714 60 ......... 472.541 4,230.01 123.274 7.9516

6 ......... 58,988.130 705,624.01 725.598 10.9621 61 ......... 427.009 3,757.46 116.760 7.7995

7 ......... 54,103.328 646,635.88 711.375 10.9519 62 ......... 385.321 3,330.46 110.329 7.6433

8 ......... 49,624.036 592,532.55 699.330 10.9404 63 ......... 347.188 2,945.13 104.012 7.4828

9 ......... 45,516.509 542,908.51 689.201 10.9277 64 ......... 312.320 2,597.95 97.810 7.3182

10 ......... 41,750.662 497,392.00 681.597 10.9134 65 ......... 280.462 2,285.63 91.741 7.1495

11 ......... 38,297.159 455,641.34 675.397 10.8975 66 ......... 251.394 2,005.16 85.830 6.9762

12 ......... 35,128.964 417,344.18 669.353 10.8803 67 ......... 224.912 1,753.77 80.106 6.7976

13 ......... 32,220.905 382,215.22 661.850 10.8623 68 ......... 200.794 1,528.86 74.557 6.6141

14 ......... 29,549.092 349,994.31 650.479 10.8445 69 ......... 178.823 1,328.06 69.167 6.4267

15 ......... 27,093.061 320,445.22 634.281 10.8276 70 ......... 158.810 1,149.24 63.919 6.2366

16 ......... 24,835.870 293,352.16 614.132 10.8116 71 ......... 140.586 990.43 58.807 6.0450

17 ......... 22,762.094 268,516.29 591.024 10.7966 72 ......... 124.015 849.85 53.844 5.8528

18 ......... 20,858.064 245,754.20 566.433 10.7822 73 ......... 108.980 725.83 49.049 5.6602

19 ......... 19,111.333 224,896.13 541.927 10.7677 74 ......... 95.383 616.85 44.451 5.4671

20 ......... 17,510.137 205,784.80 518.731 10.7523 75 ......... 83.139 521.47 40.082 5.2722

21 ......... 16,042.574 188,274.66 496.960 10.7359 76 ......... 72.145 438.33 35.953 5.0757

22 ......... 14,697.083 172,232.09 476.084 10.7188 77 ......... 62.300 366.18 32.065 4.8778

23 ......... 13,463.997 157,535.01 456.519 10.7005 78 ......... 53.514 303.88 28.423 4.6786

24 ......... 12,334.088 144,071.01 438.317 10.6807 79 ......... 45.698 250.37 25.025 4.4788

25 ......... 11,298.746 131,736.92 421.386 10.6594 80 ......... 38.766 204.67 21.867 4.2796

26 ......... 10,350.183 120,438.18 405.746 10.6363 81 ......... 32.632 165.91 18.934 4.0841

27 ......... 9,481.037 110,087.99 391.202 10.6114 82 ......... 27.229 133.27 16.225 3.8945

28 ......... 8,684.677 100,606.96 377.681 10.5844 83 ......... 22.510 106.04 13.754 3.7110

29 ......... 7,954.695 91,922.28 364.782 10.5557 84 ......... 18.439 83.53 11.542 3.5303

30 ......... 7,285.525 83,967.58 352.422 10.5253 85 ......... 14.968 65.09 9.593 3.3490

31 ......... 6,672.074 76,682.06 340.528 10.4930 86 ......... 12.024 50.13 7.885 3.1690

32 ......... 6,109.814 70,009.98 329.173 10.4586 87 ......... 9.539 38.10 6.393 2.9942

33 ......... 5,594.508 63,900.17 318.347 10.4219 88 ......... 7.466 28.56 5.107 2.8259

34 ......... 5,122.271 58,305.66 308.042 10.3828 89 ......... 5.758 21.10 4.016 2.6639

35 ......... 4,689.485 53,183.39 298.196 10.3410 90 ......... 4.373 15.34 3.107 2.5075

36 ......... 4,292.842 48,493.91 288.758 10.2965 91 ......... 3.265 10.97 2.360 2.3586

37 ......... 3,929.317 44,201.06 279.688 10.2490 92 ......... 2.392 7.70 1.756 2.2197

38 ......... 3,596.253 40,271.75 271.063 10.1983 93 ......... 1.717 5.31 1.278 2.0929

39 ......... 3,291.056 36,675.49 262.804 10.1440 94 ......... 1.207 3.59 0.910 1.9774

40 ......... 3,011.453 33,384.44 254.940 10.0858 95 ......... 0.832 2.39 0.634 1.8696

41 ......... 2,755.294 30,372.98 247.433 10.0235 96 ......... 0.562 1.55 0.434 1.7661

42 ......... 2,520.638 27,617.69 240.279 9.9566 97 ......... 0.372 0.99 0.290 1.6705

43 ......... 2,305.604 25,097.05 233.370 9.8852 95 ......... 0.241 0.62 0.189 1.5790

44 ......... 2,108.534 22,791.45 226.672 9.8091 99 ......... 0.153 0.38 0.121 1.4897

45 ......... 1,927.834 20,682.91 220.071 9.7286 100 ......... 0.095 0.23 0.076 1.4025

46 ......... 1,762.106 18,755.08 213.521 9.6436 101 ......... 0.057 0.13 0.046 1.3174

47 ......... 1,610.062 16,992.97 206.973 9.5542 102 ......... 0.034 0.08 0.028 1.2345

48 ......... 1,470.618 15,382.91 200.470 9.4602 103 ......... 0.019 0.04 0.016 1.1537

49 ......... 1,342.727 13,912.29 194.005 9.3612 104 ......... 0.011 0.02 0.009 1.0750

50 ......... 1,225.485 12,569.57 187.631 9.2568 105 ......... 0.006 0.01 0.005 0.9984

51 ......... 1,117.944 11,344.08 181.276 9.1473 106 ......... 0.003 0.01 0.003 0.9240

52 ......... 1,019.286 10,226.14 174.926 9.0326 107 ......... 0.001 0.00 0.001 0.8517

53 ......... 928.738 9,206.85 168.540 8.9133 108 ......... 0.001 0.00 0.001 0.7815

54 ......... 845.632 8,278.11 162.118 8.7893 109 ......... 0.000 0.00 0.000 0.7134

x x x x x x x x

60
Table 5.J. -- Actuarial Functions at 10.0 Percent Interest for 1989-91 United States 

White Males

x D N M a x D N M a

0 ......... 100,000.000 1,083,885.02 1,464.998 9.8389 55 ......... 465.579 4,208.65 82.975 8.0396

1 ......... 90,125.455 983,885.02 681.362 9.9168 56 ......... 419.388 3,743.07 79.109 7.9251

2 ......... 81,877.686 893,759.56 626.817 9.9158 57 ......... 377.437 3,323.68 75.284 7.8059

3 ......... 74,398.197 811,881.88 590.753 9.9127 58 ......... 339.321 2,946.24 71.481 7.6828

4 ......... 67,609.453 737,483.68 565.482 9.9080 59 ......... 304.673 2,606.92 67.680 7.5565

5 ......... 61,443.890 669,874.23 546.233 9.9022 60 ......... 273.192 2,302.25 63.897 7.4272

6 ......... 55,842.841 608,430.34 530.993 9.8954 61 ......... 244.624 2,029.06 60.165 7.2946

7 ......... 50,752.877 552,587.50 517.650 9.8878 62 ......... 218.735 1,784.43 56.514 7.1580

8 ......... 46,127.783 501,834.62 506.454 9.8792 63 ......... 195.297 1,565.70 52.961 7.0170

9 ......... 41,925.018 455,706.83 497.124 9.8696 64 ......... 174.086 1,370.40 49.504 6.8720

10 ......... 38,106.713 413,781.82 490.184 9.8585 65 ......... 154.907 1,196.32 46.151 6.7228

11 ......... 34,636.859 375,675.10 484.576 9.8461 66 ......... 137.590 1,041.41 42.916 6.5689

12 ......... 31,482.637 341,038.24 479.160 9.8326 67 ......... 121.977 903.82 39.812 6.4097

13 ......... 28,613.916 309,555.61 472.497 9.8184 68 ......... 107.907 781.84 36.830 6.2455

14 ......... 26,002.645 280,941.69 462.491 9.8044 69 ......... 95.226 673.94 33.960 6.0772

15 ......... 23,624.644 254,939.05 448.367 9.7912 70 ......... 83.800 578.71 31.190 5.9058

16 ......... 21,459.539 231,314.40 430.956 9.7791 71 ......... 73.509 494.91 28.517 5.7326

17 ......... 19,488.887 209,854.86 411.172 9.7679 72 ......... 64.255 421.40 25.946 5.5582

18 ......... 17,696.306 190,365.98 390.308 9.7574 73 ......... 55.952 357.14 23.484 5.3831

19 ......... 16,066.949 172,669.67 369.706 9.7469 74 ......... 48.526 301.19 21.145 5.2068

20 ......... 14,586.994 156,602.72 350.383 9.7358 75 ......... 41.912 252.67 18.943 5.0285

21 ......... 13,242.931 142,015.73 332.410 9.7239 76 ......... 36.039 210.75 16.880 4.8479

22 ......... 12,021.953 128,772.80 315.335 9.7115 77 ......... 30.838 174.71 14.955 4.6655

23 ......... 10,913.190 116,750.84 299.476 9.6981 78 ......... 26.249 143.88 13.169 4.4813

24 ......... 9,906.462 105,837.66 284.857 9.6837 79 ......... 22.211 117.63 11.518 4.2959

25 ......... 8,992.399 95,931.19 271.382 9.6680 80 ......... 18.671 95.42 9.996 4.1105

26 ......... 8,162.574 86,938.79 259.047 9.6509 81 ......... 15.574 76.75 8.597 3.9280

27 ......... 7,409.157 78,776.22 247.682 9.6323 82 ......... 12.877 61.17 7.316 3.7506

28 ......... 6,725.126 71,367.06 237.211 9.6120 83 ......... 10.548 48.30 6.158 3.5785

29 ......... 6,103.854 64,641.94 227.314 9.5903 84 ......... 8.562 37.75 5.130 3.4087

30 ......... 5,539.559 58,538.08 217.915 9.5673 85 ......... 6.887 29.19 4.234 3.2377

31 ......... 5,027.002 52,998.52 208.954 9.5428 86 ......... 5.482 22.30 3.455 3.0674

32 ......... 4,561.524 47,971.52 200.477 9.5166 87 ......... 4.310 16.82 2.781 2.9017

33 ......... 4,138.831 43,410.00 192.468 9.4885 88 ......... 3.342 12.51 2.205 2.7417

34 ......... 3,755.020 39,271.17 184.913 9.4583 89 ......... 2.554 9.16 1.721 2.5874

35 ......... 3,406.502 35,516.15 177.761 9.4260 90 ......... 1.922 6.61 1.322 2.4380

36 ......... 3,090.026 32,109.65 170.968 9.3914 91 ......... 1.422 4.69 0.996 2.2955

37 ......... 2,802.645 29,019.62 164.498 9.3544 92 ......... 1.032 3.26 0.736 2.1623

38 ......... 2,541.764 26,216.97 158.402 9.3145 93 ......... 0.734 2.23 0.531 2.0405

39 ......... 2,304.910 23,675.21 152.618 9.2716 94 ......... 0.511 1.50 0.375 1.9295

40 ......... 2,089.915 21,370.30 147.160 9.2254 95 ......... 0.349 0.99 0.259 1.8257

41 ......... 1,894.761 19,280.39 141.998 9.1756 96 ......... 0.234 0.64 0.176 1.7259

42 ......... 1,717.634 17,385.62 137.123 9.1218 97 ......... 0.153 0.40 0.117 1.6337

43 ......... 1,556.821 15,667.99 132.458 9.0641 95 ......... 0.098 0.25 0.076 1.5454

44 ......... 1,410.810 14,111.17 127.976 9.0022 99 ......... 0.062 0.15 0.048 1.4590

45 ......... 1,278.178 12,700.36 123.600 8.9363 100 ......... 0.038 0.09 0.030 1.3745

46 ......... 1,157.677 11,422.18 119.297 8.8665 101 ......... 0.023 0.05 0.018 1.2920

47 ......... 1,048.170 10,264.51 115.034 8.7928 102 ......... 0.013 0.03 0.011 1.2114

48 ......... 948.687 9,216.33 110.838 8.7148 103 ......... 0.008 0.02 0.006 1.1329

49 ......... 858.310 8,267.65 106.706 8.6325 104 ......... 0.004 0.01 0.003 1.0563

50 ......... 776.244 7,409.34 102.668 8.5451 105 ......... 0.002 0.00 0.002 0.9817

51 ......... 701.689 6,633.09 98.680 8.4530 106 ......... 0.001 0.00 0.001 0.9090

52 ......... 633.949 5,931.40 94.731 8.3563 107 ......... 0.001 0.00 0.000 0.8384

53 ......... 572.381 5,297.46 90.795 8.2551 108 ......... 0.000 0.00 0.000 0.7697

54 ......... 516.425 4,725.07 86.873 8.1496 109 ......... 0.000 0.00 0.000 0.7030

x x x x x x x x

61
Table 5.K. -- Actuarial Functions at 11.0 Percent Interest for 1989-91 United States 

White Males

x D N M a x D N M a

0 ......... 100,000.000 995,726.41 1,324.410 8.9573 55 ......... 283.027 2,404.08 44.784 7.4942

1 ......... 89,313.514 895,726.41 547.834 9.0290 56 ......... 252.650 2,121.06 42.455 7.3952

2 ......... 80,409.058 806,412.89 494.266 9.0289 57 ......... 225.329 1,868.41 40.172 7.2919

3 ......... 72,405.495 726,003.84 459.169 9.0269 58 ......... 200.749 1,643.08 37.922 7.1847

4 ......... 65,205.803 653,598.34 434.796 9.0236 59 ......... 178.627 1,442.33 35.694 7.0745

5 ......... 58,725.570 588,392.54 416.399 9.0194 60 ......... 158.727 1,263.70 33.495 6.9615

6 ......... 52,891.483 529,666.97 401.964 9.0142 61 ......... 140.848 1,104.97 31.346 6.8451

7 ......... 47,637.462 476,775.48 389.441 9.0084 62 ......... 124.807 964.13 29.263 6.7249

8 ......... 42,906.218 429,138.02 379.027 9.0018 63 ......... 110.430 839.32 27.254 6.6005

9 ......... 38,645.650 386,231.80 370.426 8.9942 64 ......... 97.549 728.89 25.317 6.4720

10 ......... 34,809.562 347,586.15 364.087 8.9854 65 ......... 86.021 631.34 23.456 6.3394

11 ......... 31,354.889 312,776.59 359.010 8.9754 66 ......... 75.716 545.32 21.675 6.2022

12 ......... 28,242.788 281,421.70 354.151 8.9644 67 ......... 66.520 469.60 19.982 6.0596

13 ......... 25,438.031 253,178.92 348.228 8.9528 68 ......... 58.316 403.08 18.371 5.9120

14 ......... 22,908.329 227,740.88 339.412 8.9414 69 ......... 51.000 344.77 16.834 5.7602

15 ......... 20,625.803 204,832.56 327.081 8.9309 70 ......... 44.476 293.77 15.364 5.6051

16 ......... 18,566.741 184,206.75 312.018 8.9213 71 ......... 38.663 249.29 13.958 5.4479

17 ......... 16,709.831 165,640.01 295.055 8.9127 72 ......... 33.491 210.63 12.618 5.2891

18 ......... 15,036.174 148,930.18 277.327 8.9048 73 ......... 28.900 177.14 11.346 5.1293

19 ......... 13,528.755 133,894.01 259.980 8.8970 74 ......... 24.839 148.24 10.149 4.9680

20 ......... 12,171.943 120,365.25 243.855 8.8887 75 ......... 21.260 123.40 9.032 4.8042

21 ......... 10,950.853 108,193.31 228.994 8.8799 76 ......... 18.116 102.14 7.995 4.6379

22 ......... 9,851.640 97,242.46 215.001 8.8707 77 ......... 15.362 84.02 7.036 4.4693

23 ......... 8,862.473 87,390.81 202.122 8.8608 78 ......... 12.958 68.66 6.154 4.2985

24 ......... 7,972.445 78,528.34 190.357 8.8500 79 ......... 10.866 55.70 5.346 4.1261

25 ......... 7,171.636 70,555.90 179.610 8.8382 80 ......... 9.052 44.83 4.609 3.9531

26 ......... 6,451.185 63,384.26 169.862 8.8252 81 ......... 7.482 35.78 3.936 3.7824

27 ......... 5,802.977 56,933.08 160.960 8.8110 82 ......... 6.131 28.30 3.326 3.6161

28 ......... 5,219.780 51,130.10 152.833 8.7955 83 ......... 4.977 22.17 2.780 3.4545

29 ......... 4,694.892 45,910.32 145.221 8.7788 84 ......... 4.003 17.19 2.300 3.2946

30 ......... 4,222.468 41,215.43 138.057 8.7610 85 ......... 3.191 13.19 1.884 3.1331

31 ......... 3,797.257 36,992.96 131.288 8.7420 86 ......... 2.517 10.00 1.527 2.9717

32 ......... 3,414.606 33,195.70 124.942 8.7217 87 ......... 1.961 7.48 1.220 2.8144

33 ......... 3,070.280 29,781.10 119.001 8.6998 88 ......... 1.507 5.52 0.960 2.6621

34 ......... 2,760.465 26,710.81 113.447 8.6762 89 ......... 1.142 4.01 0.744 2.5149

35 ......... 2,481.695 23,950.35 108.236 8.6508 90 ......... 0.851 2.87 0.567 2.3720

36 ......... 2,230.856 21,468.66 103.332 8.6235 91 ......... 0.624 2.02 0.424 2.2354

37 ......... 2,005.152 19,237.80 98.703 8.5942 92 ......... 0.449 1.40 0.311 2.1076

38 ......... 1,802.121 17,232.65 94.381 8.5624 93 ......... 0.316 0.95 0.223 1.9905

39 ......... 1,619.468 15,430.53 90.317 8.5281 94 ......... 0.218 0.63 0.156 1.8837

40 ......... 1,455.181 13,811.06 86.517 8.4910 95 ......... 0.148 0.41 0.107 1.7837

41 ......... 1,307.412 12,355.88 82.955 8.4506 96 ......... 0.098 0.26 0.072 1.6875

42 ......... 1,174.514 11,048.47 79.621 8.4068 97 ......... 0.064 0.17 0.047 1.5984

43 ......... 1,054.960 9,873.95 76.460 8.3595 95 ......... 0.041 0.10 0.030 1.5130

44 ......... 947.405 8,818.99 73.451 8.3086 99 ......... 0.025 0.06 0.019 1.4294

45 ......... 850.605 7,871.59 70.538 8.2541 100 ......... 0.015 0.04 0.012 1.3476

46 ......... 763.473 7,020.98 67.700 8.1961 101 ......... 0.009 0.02 0.007 1.2675

47 ......... 685.028 6,257.51 64.914 8.1347 102 ......... 0.005 0.01 0.004 1.1892

48 ......... 614.425 5,572.48 62.197 8.0694 103 ......... 0.003 0.01 0.002 1.1128

49 ......... 550.884 4,958.06 59.545 8.0002 104 ......... 0.002 0.00 0.001 1.0382

50 ......... 493.724 4,407.17 56.977 7.9264 105 ......... 0.001 0.00 0.001 0.9654

51 ......... 442.282 3,913.45 54.463 7.8483 106 ......... 0.000 0.00 0.000 0.8945

52 ......... 395.985 3,471.17 51.996 7.7659 107 ......... 0.000 0.00 0.000 0.8255

53 ......... 354.307 3,075.18 49.560 7.6794 108 ......... 0.000 0.00 0.000 0.7583

54 ......... 316.790 2,720.87 47.154 7.5889 109 ......... 0.000 0.00 0.000 0.6929

x x x x x x x x

62
Table 5.L. -- Actuarial Functions at 12.0 Percent Interest for 1989-91 United States 

White Males

x D N M a x D N M a

0 ......... 100,000.000 921,908.18 1,224.124 8.2191 55 ......... 172.822 1,384.71 24.461 7.0123

1 ......... 88,516.071 821,908.18 454.481 8.2854 56 ......... 152.896 1,211.88 23.052 6.9262

2 ......... 78,979.592 733,392.11 401.866 8.2858 57 ......... 135.145 1,058.99 21.682 6.8359

3 ......... 70,483.327 654,412.52 367.701 8.2846 58 ......... 119.328 923.84 20.345 6.7421

4 ......... 62,908.028 583,929.19 344.186 8.2823 59 ......... 105.230 804.51 19.032 6.6453

5 ......... 56,150.292 521,021.16 326.596 8.2790 60 ......... 92.672 699.28 17.749 6.5458

6 ......... 50,120.510 464,870.87 312.917 8.2751 61 ......... 81.499 606.61 16.505 6.4432

7 ......... 44,738.694 414,750.36 301.156 8.2705 62 ......... 71.573 525.11 15.311 6.3368

8 ......... 39,935.570 370,011.66 291.463 8.2652 63 ......... 62.762 453.54 14.169 6.2263

9 ......... 35,648.825 330,076.09 283.529 8.2591 64 ......... 54.947 390.78 13.078 6.1119

10 ......... 31,823.513 294,427.27 277.734 8.2519 65 ......... 48.020 335.83 12.038 5.9935

11 ......... 28,409.251 262,603.76 273.134 8.2436 66 ......... 41.890 287.81 11.053 5.8706

12 ......... 25,361.039 234,194.51 268.771 8.2344 67 ......... 36.474 245.92 10.125 5.7424

13 ......... 22,638.514 208,833.47 263.500 8.2247 68 ......... 31.690 209.45 9.250 5.6092

14 ......... 20,205.183 186,194.95 255.724 8.2152 69 ......... 27.467 177.76 8.422 5.4717

15 ......... 18,029.563 165,989.77 244.945 8.2065 70 ......... 23.740 150.29 7.637 5.3308

16 ......... 16,084.775 147,960.21 231.895 8.1988 71 ......... 20.452 126.55 6.893 5.1876

17 ......... 14,346.841 131,875.43 217.331 8.1919 72 ......... 17.558 106.10 6.191 5.0426

18 ......... 12,794.595 117,528.59 202.246 8.1858 73 ......... 15.016 88.54 5.530 4.8962

19 ......... 11,409.116 104,733.99 187.617 8.1799 74 ......... 12.791 73.52 4.913 4.7481

20 ......... 10,173.234 93,324.88 174.140 8.1736 75 ......... 10.850 60.73 4.343 4.5973

21 ......... 9,070.935 83,151.64 161.830 8.1668 76 ......... 9.163 49.88 3.819 4.4437

22 ......... 8,087.561 74,080.71 150.342 8.1598 77 ......... 7.701 40.72 3.338 4.2876

23 ......... 7,210.559 65,993.15 139.865 8.1523 78 ......... 6.438 33.02 2.900 4.1289

24 ......... 6,428.512 58,782.59 130.378 8.1440 79 ......... 5.350 26.58 2.502 3.9681

25 ......... 5,731.155 52,354.08 121.789 8.1350 80 ......... 4.417 21.23 2.142 3.8064

26 ......... 5,109.382 46,622.92 114.069 8.1250 81 ......... 3.619 16.81 1.817 3.6464

27 ......... 4,554.961 41,513.54 107.082 8.1139 82 ......... 2.939 13.19 1.525 3.4902

28 ......... 4,060.607 36,958.58 100.759 8.1017 83 ......... 2.364 10.26 1.265 3.3381

29 ......... 3,619.673 32,897.97 94.890 8.0887 84 ......... 1.885 7.89 1.039 3.1873

30 ......... 3,226.377 29,278.30 89.416 8.0747 85 ......... 1.489 6.01 0.845 3.0345

31 ......... 2,875.568 26,051.92 84.290 8.0597 86 ......... 1.164 4.52 0.680 2.8815

32 ......... 2,562.708 23,176.35 79.527 8.0437 87 ......... 0.899 3.35 0.539 2.7318

33 ......... 2,283.713 20,613.65 75.108 8.0264 88 ......... 0.685 2.46 0.422 2.5867

34 ......... 2,034.936 18,329.93 71.015 8.0076 89 ......... 0.514 1.77 0.324 2.4461

35 ......... 1,813.100 16,295.00 67.208 7.9874 90 ......... 0.380 1.26 0.245 2.3093

36 ......... 1,615.288 14,481.90 63.656 7.9655 91 ......... 0.276 0.88 0.182 2.1783

37 ......... 1,438.900 12,866.61 60.335 7.9420 92 ......... 0.197 0.60 0.132 2.0554

38 ......... 1,281.659 11,427.71 57.261 7.9163 93 ......... 0.137 0.40 0.094 1.9428

39 ......... 1,141.473 10,146.05 54.397 7.8886 94 ......... 0.094 0.27 0.065 1.8399

40 ......... 1,016.518 9,004.58 51.742 7.8583 95 ......... 0.063 0.17 0.045 1.7435

41 ......... 905.139 7,988.06 49.276 7.8252 96 ......... 0.041 0.11 0.030 1.6506

42 ......... 805.873 7,082.92 46.989 7.7891 97 ......... 0.027 0.07 0.019 1.5646

43 ......... 717.380 6,277.05 44.839 7.7500 95 ......... 0.017 0.04 0.012 1.4820

44 ......... 638.489 5,559.67 42.811 7.7075 99 ......... 0.010 0.02 0.008 1.4010

45 ......... 568.134 4,921.18 40.865 7.6620 100 ......... 0.006 0.01 0.005 1.3216

46 ......... 505.384 4,353.04 38.987 7.6133 101 ......... 0.004 0.01 0.003 1.2438

47 ......... 449.408 3,847.66 37.159 7.5616 102 ......... 0.002 0.00 0.002 1.1678

48 ......... 399.491 3,398.25 35.393 7.5065 103 ......... 0.001 0.00 0.001 1.0934

49 ......... 354.979 2,998.76 33.684 7.4477 104 ......... 0.001 0.00 0.001 1.0207

50 ......... 315.306 2,643.78 32.043 7.3848 105 ......... 0.000 0.00 0.000 0.9497

51 ......... 279.932 2,328.47 30.452 7.3180 106 ......... 0.000 0.00 0.000 0.8804

52 ......... 248.392 2,048.54 28.905 7.2472 107 ......... 0.000 0.00 0.000 0.8129

53 ......... 220.264 1,800.15 27.390 7.1727 108 ......... 0.000 0.00 0.000 0.7471

54 ......... 195.182 1,579.89 25.908 7.0944 109 ......... 0.000 0.00 0.000 0.6831

x x x x x x x x

63
Table 6.A. -- Actuarial Functions at 1.0 Percent Interest for 1989-91 United States 

White Females

x D N M a x D N M a

0 ......... 100,000.000 5,479,540.37 45,747.125 53.7954 55 ......... 54,225.437 1,299,445.28 41,359.642 22.9638

1 ......... 98,349.505 5,379,540.37 45,086.729 53.6982 56 ......... 53,409.025 1,245,219.84 41,080.116 22.3148

2 ......... 97,317.910 5,281,190.87 45,028.891 53.2674 57 ......... 52,578.510 1,191,810.82 40,778.403 21.6673

3 ......... 96,319.425 5,183,872.96 44,993.950 52.8196 58 ......... 51,730.568 1,139,232.31 40,451.041 21.0224

4 ......... 95,337.899 5,087,553.53 44,966.082 52.3634 59 ......... 50,863.686 1,087,501.74 40,096.342 20.3807

5 ......... 94,373.027 4,992,215.64 44,945.150 51.8988 60 ......... 49,974.770 1,036,638.05 39,711.027 19.7432

6 ......... 93,418.858 4,897,842.61 44,925.367 51.4288 61 ......... 49,065.771 986,663.28 39,296.827 19.1090

7 ......... 92,476.197 4,804,423.75 44,907.645 50.9531 62 ......... 48,136.957 937,597.51 38,853.813 18.4777

8 ......... 91,544.892 4,711,947.55 44,891.946 50.4714 63 ......... 47,186.998 889,460.55 38,380.458 17.8497

9 ......... 90,623.877 4,620,402.66 44,877.316 49.9844 64 ......... 46,215.161 842,273.56 37,875.819 17.2250

10 ......... 89,713.032 4,529,778.78 44,863.737 49.4919 65 ......... 45,218.663 796,058.40 37,336.897 16.6046

11 ......... 88,813.132 4,440,065.75 44,852.085 48.9933 66 ......... 44,198.995 750,839.73 36,764.938 15.9877

12 ......... 87,920.482 4,351,252.62 44,838.773 48.4908 67 ......... 43,156.065 706,640.74 36,159.622 15.3741

13 ......... 87,035.924 4,263,332.14 44,824.714 47.9836 68 ......... 42,087.772 663,484.67 35,518.617 14.7643

14 ......... 86,155.913 4,176,296.21 44,806.445 47.4737 69 ......... 40,990.099 621,396.90 34,837.655 14.1597

15 ......... 85,279.627 4,090,140.30 44,783.189 46.9615 70 ......... 39,857.215 580,406.80 34,110.613 13.5622

16 ......... 84,407.132 4,004,860.67 44,755.046 46.4469 71 ......... 38,685.514 540,549.59 33,333.538 12.9729

17 ......... 83,537.642 3,920,453.54 44,721.271 45.9304 72 ......... 37,472.046 501,864.07 32,503.095 12.3930

18 ......... 82,673.752 3,836,915.90 44,684.486 45.4103 73 ......... 36,215.939 464,392.03 31,617.998 11.8229

19 ......... 81,816.296 3,754,242.15 44,645.582 44.8862 74 ......... 34,918.779 428,176.09 30,679.411 11.2621

20 ......... 80,966.896 3,672,425.85 44,606.244 44.3571 75 ......... 33,584.488 393,257.31 29,690.851 10.7095

21 ......... 80,126.295 3,591,458.96 44,567.295 43.8225 76 ......... 32,217.333 359,672.82 28,656.216 10.1640

22 ......... 79,292.795 3,511,332.66 44,527.125 43.2831 77 ......... 30,817.720 327,455.49 27,575.586 9.6256

23 ......... 78,467.946 3,432,039.87 44,487.353 42.7381 78 ......... 29,381.458 296,637.77 26,444.450 9.0961

24 ......... 77,651.657 3,353,571.92 44,447.975 42.1874 79 ......... 27,900.905 267,256.31 25,254.803 8.5788

25 ......... 76,843.841 3,275,920.26 44,408.987 41.6309 80 ......... 26,369.648 239,355.40 23,999.793 8.0769

26 ......... 76,043.636 3,199,076.42 44,369.612 41.0690 81 ......... 24,789.601 212,985.76 22,680.831 7.5917

27 ......... 75,252.509 3,123,032.78 44,331.392 40.5007 82 ......... 23,167.942 188,196.16 21,304.614 7.1231

28 ......... 74,468.079 3,047,780.28 44,292.037 39.9273 83 ......... 21,512.915 165,028.21 19,878.972 6.6711

29 ......... 73,690.307 2,973,312.20 44,251.572 39.3488 84 ......... 19,835.067 143,515.30 18,414.123 6.2354

30 ......... 72,918.410 2,899,621.89 44,209.282 38.7653 85 ......... 18,144.983 123,680.23 16,920.427 5.8162

31 ......... 72,151.636 2,826,703.48 44,164.473 38.1773 86 ......... 16,448.175 105,535.25 15,403.271 5.4162

32 ......... 71,389.989 2,754,551.84 44,117.199 37.5846 87 ......... 14,754.154 89,087.07 13,872.104 5.0381

33 ......... 70,633.470 2,683,161.85 44,067.511 36.9871 88 ......... 13,084.151 74,332.92 12,348.182 4.6811

34 ......... 69,882.795 2,612,528.38 44,016.177 36.3844 89 ......... 11,463.508 61,248.77 10,857.084 4.3429

35 ......... 69,136.531 2,542,645.59 43,961.822 35.7772 90 ......... 9,911.654 49,785.26 9,418.731 4.0229

36 ......... 68,396.097 2,473,509.06 43,905.908 35.1645 91 ......... 8,437.928 39,873.61 8,043.140 3.7255

37 ......... 67,659.395 2,405,112.96 43,846.396 34.5474 92 ......... 7,056.468 31,435.68 6,745.224 3.4549

38 ......... 66,925.781 2,337,453.57 43,782.676 33.9261 93 ......... 5,791.911 24,379.21 5,550.533 3.2092

39 ......... 66,195.312 2,270,527.79 43,714.839 33.3004 94 ......... 4,666.301 18,587.30 4,482.268 2.9833

40 ......... 65,467.375 2,204,332.47 43,642.301 32.6707 95 ......... 3,689.474 13,921.00 3,551.642 2.7732

41 ......... 64,741.378 2,138,865.10 43,564.495 32.0371 96 ......... 2,858.904 10,231.52 2,757.602 2.5788

42 ......... 64,016.096 2,074,123.72 43,480.218 31.4000 97 ......... 2,167.276 7,372.62 2,094.279 2.4018

43 ......... 63,291.659 2,010,107.63 43,389.604 30.7594 95 ......... 1,607.410 5,205.34 1,555.872 2.2383

44 ......... 62,566.902 1,946,815.97 43,291.496 30.1157 99 ......... 1,166.327 3,597.93 1,130.704 2.0848

45 ......... 61,840.066 1,884,249.06 43,184.135 29.4697 100 ......... 827.769 2,431.61 803.694 1.9375

46 ......... 61,109.468 1,822,409.00 43,065.815 28.8220 101 ......... 573.562 1,603.84 557.683 1.7963

47 ......... 60,374.120 1,761,299.53 42,935.510 28.1731 102 ......... 387.194 1,030.27 376.993 1.6609

48 ......... 59,633.076 1,700,925.41 42,792.230 27.5232 103 ......... 254.065 643.08 247.697 1.5312

49 ......... 58,886.049 1,641,292.33 42,635.630 26.8723 104 ......... 161.620 389.02 157.769 1.4070

50 ......... 58,133.376 1,582,406.29 42,465.987 26.2203 105 ......... 99.380 227.40 97.129 1.2881

51 ......... 57,373.580 1,524,272.91 42,281.769 25.5675 106 ......... 58.872 128.02 57.604 1.1745

52 ......... 56,602.865 1,466,899.33 42,079.110 24.9156 107 ......... 33.470 69.14 32.785 1.0658

53 ......... 55,821.722 1,410,296.46 41,858.391 24.2643 108 ......... 18.182 35.67 17.829 0.9621

54 ......... 55,029.464 1,354,474.74 41,618.823 23.6136 109 ......... 9.389 17.49 9.216 0.8630

x x x x x x x x

64
Table 6.B. -- Actuarial Functions at 2.0 Percent Interest for 1989-91 United States 

White Females

x D N M a x D N M a

0 ......... 100,000.000 3,987,916.58 21,805.557 38.8792 55 ......... 31,540.543 659,365.41 18,611.810 19.9053

1 ......... 97,385.294 3,887,916.58 21,151.636 38.9230 56 ......... 30,761.107 627,824.87 18,450.816 19.4097

2 ......... 95,419.070 3,790,531.29 21,094.927 38.7251 57 ......... 29,985.879 597,063.76 18,278.747 18.9115

3 ......... 93,514.184 3,695,112.22 21,061.003 38.5139 58 ......... 29,213.054 567,077.88 18,093.880 18.4118

4 ......... 91,653.781 3,601,598.04 21,034.212 38.2957 59 ......... 28,441.909 537,864.83 17,895.540 17.9110

5 ......... 89,836.722 3,509,944.26 21,014.285 38.0703 60 ......... 27,670.877 509,422.92 17,682.192 17.4101

6 ......... 88,056.570 3,420,107.53 20,995.638 37.8399 61 ......... 26,901.218 481,752.04 17,455.100 16.9082

7 ......... 86,313.430 3,332,050.96 20,979.097 37.6041 62 ......... 26,133.234 454,850.82 17,214.590 16.4051

8 ......... 84,606.500 3,245,737.53 20,964.588 37.3627 63 ......... 25,366.355 428,717.59 16,960.128 15.9010

9 ......... 82,934.161 3,161,131.03 20,951.200 37.1162 64 ......... 24,600.357 403,351.23 16,691.509 15.3962

10 ......... 81,295.696 3,078,196.87 20,938.895 36.8642 65 ......... 23,833.940 378,750.88 16,407.453 14.8912

11 ......... 79,691.207 2,996,901.18 20,928.439 36.6064 66 ......... 23,068.095 354,916.94 16,108.939 14.3856

12 ......... 78,116.807 2,917,209.97 20,916.612 36.3442 67 ......... 22,302.953 331,848.84 15,796.113 13.8791

13 ......... 76,572.737 2,839,093.16 20,904.243 36.0771 68 ......... 21,537.618 309,545.89 15,468.091 13.3723

14 ......... 75,055.395 2,762,520.42 20,888.328 35.8064 69 ......... 20,770.259 288,008.27 15,123.038 12.8664

15 ......... 73,563.659 2,687,465.03 20,868.267 35.5325 70 ......... 19,998.209 267,238.01 14,758.248 12.3631

16 ......... 72,097.196 2,613,901.37 20,844.228 35.2552 71 ......... 19,220.015 247,239.80 14,372.176 11.8637

17 ......... 70,654.959 2,541,804.17 20,815.661 34.9749 72 ......... 18,434.610 228,019.79 13,963.634 11.3691

18 ......... 69,238.761 2,471,149.21 20,784.854 34.6903 73 ......... 17,641.987 209,585.18 13,532.474 10.8799

19 ......... 67,848.876 2,401,910.45 20,752.592 34.4009 74 ......... 16,843.331 191,943.19 13,079.739 10.3958

20 ......... 66,486.203 2,334,061.58 20,720.290 34.1060 75 ......... 16,040.906 175,099.86 12,607.575 9.9158

21 ......... 65,150.883 2,267,575.37 20,688.620 33.8050 76 ......... 15,237.052 159,058.95 12,118.249 9.4390

22 ......... 63,841.072 2,202,424.49 20,656.278 33.4986 77 ......... 14,432.217 143,821.90 11,612.180 8.9653

23 ......... 62,557.579 2,138,583.42 20,624.571 33.1858 78 ......... 13,624.705 129,389.69 11,087.652 8.4967

24 ......... 61,299.874 2,076,025.84 20,593.485 32.8667 79 ......... 12,811.301 115,764.98 10,541.400 8.0362

25 ......... 60,067.439 2,014,725.97 20,563.008 32.5411 80 ......... 11,989.484 102,953.68 9,970.784 7.5870

26 ......... 58,859.169 1,954,658.53 20,532.531 32.2091 81 ......... 11,160.583 90,964.20 9,376.972 7.1505

27 ......... 57,675.775 1,895,799.36 20,503.238 31.8699 82 ......... 10,328.233 79,803.61 8,763.456 6.7267

28 ......... 56,515.010 1,838,123.58 20,473.371 31.5245 83 ......... 9,496.401 69,475.38 8,134.138 6.3160

29 ......... 55,376.464 1,781,608.58 20,442.963 31.1727 84 ......... 8,669.911 59,978.98 7,493.853 5.9181

30 ......... 54,259.183 1,726,232.11 20,411.495 30.8146 85 ......... 7,853.419 51,309.07 6,847.358 5.5333

31 ......... 53,162.262 1,671,972.93 20,378.479 30.4504 86 ......... 7,049.220 43,455.65 6,197.149 5.1646

32 ......... 52,085.373 1,618,810.67 20,343.988 30.0799 87 ......... 6,261.219 36,406.43 5,547.368 4.8146

33 ......... 51,028.196 1,566,725.29 20,308.092 29.7031 88 ......... 5,498.084 30,145.21 4,907.001 4.4829

34 ......... 49,990.921 1,515,697.10 20,271.370 29.3194 89 ......... 4,769.848 24,647.13 4,286.571 4.1673

35 ......... 48,972.204 1,465,706.18 20,232.868 28.9293 90 ......... 4,083.705 19,877.28 3,693.954 3.8675

36 ......... 47,972.747 1,416,733.97 20,193.650 28.5321 91 ......... 3,442.431 15,793.57 3,132.753 3.5879

37 ......... 46,990.773 1,368,761.23 20,152.317 28.1283 92 ......... 2,850.611 12,351.14 2,608.432 3.3328

38 ......... 46,025.565 1,321,770.45 20,108.497 27.7182 93 ......... 2,316.827 9,500.53 2,130.543 3.1007

39 ......... 45,076.908 1,275,744.89 20,062.302 27.3015 94 ......... 1,848.271 7,183.70 1,707.414 2.8867

40 ......... 44,144.135 1,230,667.98 20,013.390 26.8784 95 ......... 1,447.034 5,335.43 1,342.417 2.6872

41 ......... 43,226.614 1,186,523.85 19,961.441 26.4489 96 ......... 1,110.286 3,888.40 1,034.043 2.5022

42 ......... 42,323.314 1,143,297.23 19,905.722 26.0134 97 ......... 833.433 2,778.11 778.960 2.3333

43 ......... 41,434.125 1,100,973.92 19,846.401 25.5717 95 ......... 612.075 1,944.68 573.944 2.1772

44 ......... 40,558.094 1,059,539.79 19,782.804 25.1240 99 ......... 439.764 1,332.61 413.634 2.0303

45 ......... 39,693.924 1,018,981.70 19,713.891 24.6710 100 ......... 309.050 892.84 291.544 1.8890

46 ......... 38,840.409 979,287.77 19,638.688 24.2131 101 ......... 212.042 583.79 200.595 1.7532

47 ......... 37,996.825 940,447.36 19,556.680 23.7507 102 ......... 141.740 371.75 134.450 1.6228

48 ......... 37,162.499 902,450.54 19,467.390 23.2839 103 ......... 92.093 230.01 87.583 1.4976

49 ......... 36,337.188 865,288.04 19,370.756 22.8127 104 ......... 58.010 137.92 55.305 1.3775

50 ......... 35,521.038 828,950.85 19,267.099 22.3369 105 ......... 35.321 79.91 33.754 1.2623

51 ......... 34,713.088 793,429.82 19,155.641 21.8568 106 ......... 20.718 44.59 19.844 1.1520

52 ......... 33,911.025 758,716.73 19,034.227 21.3737 107 ......... 11.663 23.87 11.195 1.0464

53 ......... 33,115.166 724,805.70 18,903.290 20.8874 108 ......... 6.274 12.20 6.034 0.9453

54 ......... 32,325.123 691,690.54 18,762.564 20.3979 109 ......... 3.208 5.93 3.092 0.8486

x x x x x x x x

65
Table 6.C. -- Actuarial Functions at 3.0 Percent Interest for 1989-91 United States 

White Females

x D N M a x D N M a

0 ......... 100,000.000 3,056,878.98 10,964.690 29.5688 55 ......... 18,442.987 339,999.75 8,540.082 17.4352

1 ......... 96,439.806 2,956,878.98 10,317.117 29.6604 56 ......... 17,812.587 321,556.76 8,446.856 17.0522

2 ......... 93,575.266 2,860,439.17 10,261.504 29.5683 57 ......... 17,195.103 303,744.18 8,348.185 16.6646

3 ......... 90,816.828 2,766,863.91 10,228.559 29.4664 58 ......... 16,589.294 286,549.07 8,243.204 16.2731

4 ......... 88,145.912 2,676,047.08 10,202.793 29.3593 59 ......... 15,994.572 269,959.78 8,131.666 15.8782

5 ......... 85,559.577 2,587,901.17 10,183.815 29.2468 60 ......... 15,409.898 253,965.21 8,012.853 15.4807

6 ......... 83,049.964 2,502,341.59 10,166.228 29.1306 61 ......... 14,835.826 238,555.31 7,887.613 15.0797

7 ......... 80,615.584 2,419,291.63 10,150.779 29.0102 62 ......... 14,272.363 223,719.48 7,756.261 14.6750

8 ......... 78,254.137 2,338,676.04 10,137.359 28.8857 63 ......... 13,719.041 209,447.12 7,618.639 14.2669

9 ......... 75,962.628 2,260,421.90 10,125.097 28.7570 64 ......... 13,175.588 195,728.08 7,474.770 13.8554

10 ......... 73,738.963 2,184,459.28 10,113.935 28.6242 65 ......... 12,641.174 182,552.49 7,324.111 13.4411

11 ......... 71,581.835 2,110,720.31 10,104.544 28.4868 66 ......... 12,116.194 169,911.32 7,167.321 13.0235

12 ......... 69,486.406 2,039,138.48 10,094.023 28.3459 67 ......... 11,600.583 157,795.12 7,004.609 12.6023

13 ......... 67,451.635 1,969,652.07 10,083.128 28.2010 68 ......... 11,093.742 146,194.54 6,835.649 12.1781

14 ......... 65,473.141 1,902,200.44 10,069.245 28.0531 69 ......... 10,594.617 135,100.80 6,659.642 11.7518

15 ......... 63,548.826 1,836,727.30 10,051.914 27.9026 70 ......... 10,101.768 124,506.18 6,475.374 11.3252

16 ......... 61,677.325 1,773,178.47 10,031.350 27.7493 71 ......... 9,614.417 114,404.41 6,282.250 10.8993

17 ......... 59,856.697 1,711,501.15 10,007.149 27.5933 72 ......... 9,132.005 104,790.00 6,079.869 10.4750

18 ......... 58,087.453 1,651,644.45 9,981.304 27.4338 73 ......... 8,654.513 95,657.99 5,868.358 10.0530

19 ......... 56,368.782 1,593,557.00 9,954.500 27.2702 74 ......... 8,182.501 87,003.48 5,648.419 9.6329

20 ......... 54,700.396 1,537,188.21 9,927.924 27.1020 75 ......... 7,717.025 78,820.98 5,421.268 9.2139

21 ......... 53,081.378 1,482,487.82 9,902.121 26.9286 76 ......... 7,259.136 71,103.95 5,188.147 8.7951

22 ......... 51,509.224 1,429,406.44 9,876.027 26.7505 77 ......... 6,808.947 63,844.82 4,949.390 8.3766

23 ......... 49,983.621 1,377,897.22 9,850.692 26.5670 78 ......... 6,365.565 57,035.87 4,704.326 7.9601

24 ......... 48,503.191 1,327,913.60 9,826.096 26.3779 79 ......... 5,927.425 50,670.30 4,451.591 7.5485

25 ......... 47,066.596 1,279,410.40 9,802.215 26.1830 80 ......... 5,493.337 44,742.88 4,190.147 7.1449

26 ......... 45,672.076 1,232,343.81 9,778.567 25.9824 81 ......... 5,063.906 39,249.54 3,920.715 6.7508

27 ......... 44,319.312 1,186,671.73 9,756.057 25.7755 82 ......... 4,640.745 34,185.64 3,645.047 6.3664

28 ......... 43,005.730 1,142,352.42 9,733.329 25.5628 83 ......... 4,225.554 29,544.89 3,365.023 5.9920

29 ......... 41,730.221 1,099,346.69 9,710.415 25.3441 84 ......... 3,820.342 25,319.34 3,082.885 5.6275

30 ......... 40,491.295 1,057,616.47 9,686.931 25.1196 85 ......... 3,426.962 21,499.00 2,800.777 5.2735

31 ......... 39,287.537 1,017,125.17 9,662.532 24.8893 86 ......... 3,046.173 18,072.03 2,519.803 4.9327

32 ......... 38,117.998 977,837.64 9,637.290 24.6529 87 ......... 2,679.386 15,025.86 2,241.740 4.6079

33 ......... 36,981.750 939,719.64 9,611.276 24.4104 88 ......... 2,329.972 12,346.48 1,970.366 4.2990

34 ......... 35,878.257 902,737.89 9,584.920 24.1611 89 ......... 2,001.736 10,016.50 1,709.993 4.0039

35 ......... 34,805.895 866,859.63 9,557.556 23.9055 90 ......... 1,697.147 8,014.77 1,463.708 3.7225

36 ......... 33,764.528 832,053.74 9,529.953 23.6428 91 ......... 1,416.751 6,317.62 1,232.742 3.4592

37 ......... 32,752.287 798,289.21 9,501.145 23.3735 92 ......... 1,161.794 4,900.87 1,019.050 3.2184

38 ......... 31,768.091 765,536.92 9,470.899 23.0977 93 ......... 935.078 3,739.08 826.173 2.9987

39 ......... 30,811.231 733,768.83 9,439.323 22.8150 94 ......... 738.725 2,804.00 657.055 2.7957

40 ......... 29,880.708 702,957.60 9,406.215 22.5255 95 ......... 572.741 2,065.27 512.588 2.6059

41 ......... 28,975.574 673,076.89 9,371.393 22.2291 96 ......... 435.189 1,492.53 391.717 2.4296

42 ......... 28,094.638 644,101.32 9,334.406 21.9261 97 ......... 323.502 1,057.34 292.705 2.2684

43 ......... 27,237.353 616,006.68 9,295.410 21.6162 95 ......... 235.274 733.84 213.900 2.1191

44 ......... 26,402.631 588,769.33 9,254.010 21.2996 99 ......... 167.398 498.57 152.877 1.9783

45 ......... 25,589.197 562,366.70 9,209.584 20.9767 100 ......... 116.500 331.17 106.854 1.8427

46 ......... 24,795.871 536,777.50 9,161.574 20.6479 101 ......... 79.155 214.67 72.903 1.7120

47 ......... 24,021.815 511,981.63 9,109.729 20.3132 102 ......... 52.398 135.51 48.451 1.5863

48 ......... 23,266.249 487,959.81 9,053.827 19.9729 103 ......... 33.714 83.12 31.293 1.4653

49 ......... 22,528.679 464,693.57 8,993.915 19.6268 104 ......... 21.030 49.40 19.591 1.3491

50 ......... 21,808.862 442,164.89 8,930.273 19.2746 105 ......... 12.681 28.37 11.854 1.2375

51 ......... 21,105.884 420,356.02 8,862.505 18.9165 106 ......... 7.366 15.69 6.909 1.1303

52 ......... 20,418.046 399,250.14 8,789.401 18.5538 107 ......... 4.106 8.33 3.864 1.0276

53 ......... 19,745.273 378,832.10 8,711.328 18.1860 108 ......... 2.187 4.22 2.064 0.9291

54 ......... 19,087.073 359,086.82 8,628.233 17.8131 109 ......... 1.108 2.03 1.048 0.8347

x x x x x x x x

66
Table 6.D. -- Actuarial Functions at 4.0 Percent Interest for 1989-91 United States 

White Females

x D N M a x D N M a

0 ......... 100,000.000 2,446,205.17 5,915.186 23.4621 55 ......... 10,840.391 177,983.31 3,994.879 15.4185

1 ......... 95,512.500 2,346,205.17 5,273.840 23.5644 56 ......... 10,369.184 167,142.92 3,940.610 15.1192

2 ......... 91,784.393 2,250,692.67 5,219.291 23.5215 57 ......... 9,913.482 156,773.73 3,883.723 14.8142

3 ......... 88,222.221 2,158,908.28 5,187.287 23.4713 58 ......... 9,472.252 146,860.25 3,823.781 14.5043

4 ......... 84,804.269 2,070,686.06 5,162.498 23.4172 59 ......... 9,044.860 137,388.00 3,760.706 14.1896

5 ......... 81,524.484 1,985,881.79 5,144.415 23.3593 60 ......... 8,630.439 128,343.14 3,694.164 13.8710

6 ......... 78,372.330 1,904,357.30 5,127.819 23.2988 61 ......... 8,229.032 119,712.70 3,624.697 13.5476

7 ......... 75,343.571 1,825,984.97 5,113.380 23.2354 62 ......... 7,840.374 111,483.67 3,552.540 13.2192

8 ......... 72,433.320 1,750,641.40 5,100.958 23.1690 63 ......... 7,463.947 103,643.29 3,477.666 12.8859

9 ......... 69,636.182 1,678,208.08 5,089.717 23.0997 64 ......... 7,099.351 96,179.35 3,400.146 12.5476

10 ......... 66,947.734 1,608,571.90 5,079.584 23.0273 65 ......... 6,745.901 89,080.00 3,319.747 12.2051

11 ......... 64,364.376 1,541,624.17 5,071.139 22.9515 66 ......... 6,403.577 82,334.10 3,236.881 11.8575

12 ......... 61,879.454 1,477,259.79 5,061.770 22.8732 67 ......... 6,072.117 75,930.52 3,151.713 11.5048

13 ......... 59,489.866 1,415,380.34 5,052.161 22.7920 68 ......... 5,750.986 69,858.40 3,064.124 11.1472

14 ......... 57,189.667 1,355,890.47 5,040.034 22.7087 69 ......... 5,439.429 64,107.42 2,973.760 10.7857

15 ......... 54,975.073 1,298,700.80 5,025.042 22.6234 70 ......... 5,136.525 58,667.99 2,880.064 10.4217

16 ......... 52,843.028 1,243,725.73 5,007.423 22.5362 71 ......... 4,841.711 53,531.46 2,782.808 10.0563

17 ......... 50,790.069 1,190,882.70 4,986.888 22.4472 72 ......... 4,554.554 48,689.75 2,681.872 9.6903

18 ......... 48,814.885 1,140,092.63 4,965.168 22.3554 73 ......... 4,274.903 44,135.20 2,577.395 9.3243

19 ......... 46,915.081 1,091,277.75 4,942.860 22.2607 74 ......... 4,002.889 39,860.29 2,469.801 8.9579

20 ......... 45,088.748 1,044,362.67 4,920.953 22.1624 75 ......... 3,738.878 35,857.40 2,359.747 8.5904

21 ......... 43,333.502 999,273.92 4,899.889 22.0601 76 ......... 3,483.214 32,118.53 2,247.887 8.2209

22 ......... 41,645.731 955,940.42 4,878.792 21.9541 77 ......... 3,235.781 28,635.31 2,134.423 7.8496

23 ......... 40,023.686 914,294.69 4,858.505 21.8438 78 ......... 2,995.988 25,399.53 2,019.083 7.4778

24 ......... 38,464.807 874,271.00 4,838.999 21.7291 79 ......... 2,762.950 22,403.54 1,901.275 7.1086

25 ......... 36,966.636 835,806.19 4,820.243 21.6097 80 ......... 2,535.987 19,640.59 1,780.580 6.7448

26 ......... 35,526.447 798,839.56 4,801.848 21.4858 81 ......... 2,315.263 17,104.60 1,657.394 6.3878

27 ......... 34,142.704 763,313.11 4,784.507 21.3566 82 ......... 2,101.388 14,789.34 1,532.567 6.0379

28 ......... 32,812.182 729,170.41 4,767.167 21.2226 83 ......... 1,894.987 12,687.95 1,406.988 5.6955

29 ......... 31,532.860 696,358.22 4,749.851 21.0836 84 ......... 1,696.792 10,792.97 1,281.678 5.3608

30 ......... 30,302.484 664,825.36 4,732.277 20.9396 85 ......... 1,507.438 9,096.18 1,157.585 5.0342

31 ......... 29,118.919 634,522.88 4,714.193 20.7907 86 ......... 1,327.054 7,588.74 1,035.180 4.7185

32 ......... 27,980.432 605,403.96 4,695.664 20.6367 87 ......... 1,156.041 6,261.68 915.207 4.4165

33 ......... 26,885.349 577,423.53 4,676.752 20.4773 88 ......... 995.618 5,105.64 799.247 4.1281

34 ......... 25,832.322 550,538.18 4,657.776 20.3120 89 ......... 847.135 4,110.02 689.057 3.8517

35 ......... 24,819.258 524,705.86 4,638.263 20.1411 90 ......... 711.327 3,262.89 585.831 3.5870

36 ......... 23,845.177 499,886.60 4,618.770 19.9638 91 ......... 588.094 2,551.56 489.957 3.3387

37 ......... 22,907.906 476,041.42 4,598.620 19.7807 92 ......... 477.624 1,963.47 402.106 3.1109

38 ......... 22,005.881 453,133.52 4,577.669 19.5915 93 ......... 380.723 1,485.84 323.575 2.9027

39 ......... 21,137.839 431,127.64 4,556.007 19.3960 94 ......... 297.885 1,105.12 255.380 2.7099

40 ......... 20,302.350 409,989.80 4,533.511 19.1942 95 ......... 228.732 807.24 197.685 2.5292

41 ......... 19,498.058 389,687.45 4,510.079 18.9860 96 ......... 172.128 578.50 149.878 2.3609

42 ......... 18,723.483 370,189.39 4,485.429 18.7714 97 ......... 126.722 406.38 111.093 2.2068

43 ......... 17,977.610 351,465.91 4,459.691 18.5502 95 ......... 91.275 279.65 80.520 2.0638

44 ......... 17,259.101 333,488.30 4,432.628 18.3225 99 ......... 64.319 188.38 57.073 1.9288

45 ......... 16,566.528 316,229.20 4,403.867 18.0884 100 ......... 44.332 124.06 39.560 1.7984

46 ......... 15,898.571 299,662.67 4,373.084 17.8484 101 ......... 29.831 79.73 26.765 1.6726

47 ......... 15,254.165 283,764.10 4,340.161 17.6024 102 ......... 19.557 49.90 17.638 1.5513

48 ......... 14,632.309 268,509.93 4,305.004 17.3505 103 ......... 12.463 30.34 11.296 1.4344

49 ......... 14,032.211 253,877.62 4,267.687 17.0925 104 ......... 7.699 17.88 7.012 1.3219

50 ......... 13,453.252 239,845.41 4,228.428 16.8281 105 ......... 4.598 10.18 4.206 1.2136

51 ......... 12,894.417 226,392.16 4,187.026 16.5574 106 ......... 2.645 5.58 2.430 1.1095

52 ......... 12,354.245 213,497.74 4,142.793 16.2813 107 ......... 1.460 2.93 1.348 1.0094

53 ......... 11,832.297 201,143.50 4,096.009 15.9995 108 ......... 0.770 1.47 0.714 0.9134

54 ......... 11,327.893 189,311.20 4,046.693 15.7120 109 ......... 0.386 0.70 0.359 0.8213

x x x x x x x x

67
Table 6.E. -- Actuarial Functions at 5.0 Percent Interest for 1989-91 United States 

White Females

x D N M a x D N M a

0 ......... 100,000.000 2,026,757.53 3,487.737 19.2676 55 ......... 6,404.234 94,494.93 1,904.475 13.7551

1 ......... 94,602.857 1,926,757.53 2,852.499 19.3668 56 ......... 6,067.515 88,090.70 1,872.720 13.5184

2 ......... 90,044.444 1,832,154.67 2,798.984 19.3472 57 ......... 5,745.615 82,023.18 1,839.749 13.2758

3 ......... 85,725.516 1,742,110.23 2,767.886 19.3220 58 ......... 5,437.604 76,277.57 1,805.339 13.0278

4 ......... 81,619.490 1,656,384.71 2,744.027 19.2940 59 ......... 5,142.807 70,839.96 1,769.476 12.7746

5 ......... 77,715.610 1,574,765.22 2,726.790 19.2632 60 ......... 4,860.437 65,697.15 1,732.001 12.5167

6 ......... 73,999.196 1,497,049.61 2,711.119 19.2306 61 ......... 4,590.238 60,836.72 1,693.251 12.2535

7 ......... 70,461.922 1,423,050.42 2,697.616 19.1960 62 ......... 4,331.789 56,246.48 1,653.385 11.9846

8 ......... 67,095.086 1,352,588.50 2,686.110 19.1593 63 ......... 4,084.539 51,914.69 1,612.411 11.7100

9 ......... 63,889.768 1,285,493.41 2,675.796 19.1205 64 ......... 3,848.019 47,830.15 1,570.393 11.4298

10 ......... 60,838.190 1,221,603.64 2,666.587 19.0796 65 ......... 3,621.617 43,982.13 1,527.230 11.1443

11 ......... 57,933.532 1,160,765.45 2,658.987 19.0362 66 ......... 3,405.096 40,360.52 1,483.166 10.8530

12 ......... 55,166.440 1,102,831.92 2,650.634 18.9910 67 ......... 3,198.091 36,955.42 1,438.309 10.5555

13 ......... 52,530.981 1,047,665.48 2,642.149 18.9438 68 ......... 3,000.109 33,757.33 1,392.617 10.2520

14 ......... 50,018.900 995,134.50 2,631.543 18.8952 69 ......... 2,810.555 30,757.22 1,345.926 9.9435

15 ......... 47,624.060 945,115.60 2,618.555 18.8453 70 ......... 2,628.768 27,946.66 1,297.974 9.6311

16 ......... 45,341.130 897,491.54 2,603.437 18.7942 71 ......... 2,454.289 25,317.90 1,248.675 9.3158

17 ......... 43,164.576 852,150.41 2,585.986 18.7419 72 ......... 2,286.740 22,863.61 1,197.997 8.9983

18 ......... 41,090.838 808,985.83 2,567.703 18.6877 73 ......... 2,125.892 20,576.87 1,146.041 8.6792

19 ......... 39,115.532 767,895.00 2,549.103 18.6315 74 ......... 1,971.662 18,450.98 1,093.045 8.3581

20 ......... 37,234.796 728,779.47 2,531.012 18.5725 75 ......... 1,824.082 16,479.31 1,039.353 8.0343

21 ......... 35,444.482 691,544.67 2,513.783 18.5106 76 ......... 1,683.167 14,655.23 985.299 7.7069

22 ......... 33,739.557 656,100.19 2,496.691 18.4460 77 ......... 1,548.711 12,972.06 930.993 7.3760

23 ......... 32,116.633 622,360.63 2,480.412 18.3781 78 ......... 1,420.284 11,423.35 876.315 7.0430

24 ......... 30,571.766 590,244.00 2,464.909 18.3068 79 ......... 1,297.335 10,003.07 820.998 6.7105

25 ......... 29,101.202 559,672.23 2,450.144 18.2319 80 ......... 1,179.425 8,705.73 764.866 6.3813

26 ......... 27,701.087 530,571.03 2,435.800 18.1534 81 ......... 1,066.517 7,526.31 708.121 6.0569

27 ......... 26,368.596 502,869.94 2,422.408 18.0708 82 ......... 958.777 6,459.79 651.168 5.7375

28 ......... 25,099.683 476,501.35 2,409.143 17.9844 83 ......... 856.370 5,501.02 594.417 5.4236

29 ......... 23,891.341 451,401.66 2,396.024 17.8939 84 ......... 759.500 4,644.65 538.327 5.1154

30 ......... 22,740.470 427,510.32 2,382.835 17.7995 85 ......... 668.318 3,885.15 483.311 4.8133

31 ......... 21,644.148 404,769.85 2,369.393 17.7011 86 ......... 582.742 3,216.83 429.559 4.5202

32 ......... 20,599.833 383,125.70 2,355.752 17.5985 87 ......... 502.811 2,634.09 377.378 4.2387

33 ......... 19,605.098 362,525.87 2,341.961 17.4914 88 ......... 428.912 2,131.28 327.423 3.9690

34 ......... 18,657.816 342,920.77 2,328.255 17.3795 89 ......... 361.470 1,702.36 280.405 3.7096

35 ......... 17,755.389 324,262.96 2,314.296 17.2628 90 ......... 300.630 1,340.89 236.778 3.4603

36 ......... 16,896.082 306,507.57 2,300.483 17.1407 91 ......... 246.181 1,040.26 196.645 3.2256

37 ......... 16,077.365 289,611.49 2,286.342 17.0136 92 ......... 198.033 794.08 160.220 3.0098

38 ......... 15,297.212 273,534.12 2,271.778 16.8813 93 ......... 156.353 596.05 127.969 2.8122

39 ......... 14,553.859 258,236.91 2,256.863 16.7435 94 ......... 121.168 439.70 100.230 2.6288

40 ......... 13,845.477 243,683.05 2,241.522 16.6002 95 ......... 92.153 318.53 76.985 2.4565

41 ......... 13,170.340 229,837.57 2,225.694 16.4511 96 ......... 68.688 226.38 57.908 2.2957

42 ......... 12,526.690 216,667.23 2,209.203 16.2964 97 ......... 50.087 157.69 42.578 2.1483

43 ......... 11,913.125 204,140.54 2,192.147 16.1358 95 ......... 35.733 107.60 30.609 2.0112

44 ......... 11,328.070 192,227.42 2,174.384 15.9691 99 ......... 24.940 71.87 21.518 1.8816

45 ......... 10,769.941 180,899.35 2,155.686 15.7967 100 ......... 17.026 46.93 14.792 1.7562

46 ......... 10,237.265 170,129.41 2,135.865 15.6186 101 ......... 11.348 29.90 9.924 1.6349

47 ......... 9,728.779 159,892.14 2,114.867 15.4350 102 ......... 7.369 18.55 6.485 1.5178

48 ......... 9,243.295 150,163.36 2,092.658 15.2457 103 ......... 4.651 11.18 4.118 1.4047

49 ......... 8,779.789 140,920.07 2,069.309 15.0505 104 ......... 2.846 6.53 2.535 1.2956

50 ......... 8,337.374 132,140.28 2,044.980 14.8491 105 ......... 1.683 3.69 1.508 1.1905

51 ......... 7,914.942 123,802.91 2,019.566 14.6417 106 ......... 0.959 2.00 0.864 1.0893

52 ......... 7,511.148 115,887.96 1,992.673 14.4288 107 ......... 0.525 1.04 0.475 0.9919

53 ......... 7,125.301 108,376.82 1,964.500 14.2101 108 ......... 0.274 0.52 0.249 0.8982

54 ......... 6,756.586 101,251.52 1,935.085 13.9856 109 ......... 0.136 0.25 0.124 0.8082

x x x x x x x x

68
Table 6.F. -- Actuarial Functions at 6.0 Percent Interest for 1989-91 United States 

White Females

x D N M a x D N M a

0 ......... 100,000.000 1,726,419.43 2,278.146 16.2642 55 ......... 3,802.384 50,835.63 924.896 12.3694

1 ......... 93,710.377 1,626,419.43 1,648.900 16.3558 56 ......... 3,568.479 47,033.25 906.219 12.1802

2 ......... 88,353.507 1,532,709.05 1,596.391 16.3475 57 ......... 3,347.282 43,464.77 887.012 11.9851

3 ......... 83,322.138 1,444,355.54 1,566.164 16.3346 58 ......... 3,137.955 40,117.49 867.154 11.7846

4 ......... 78,582.820 1,361,033.40 1,543.194 16.3197 59 ......... 2,939.834 36,979.53 846.653 11.5788

5 ......... 74,118.296 1,282,450.58 1,526.754 16.3028 60 ......... 2,752.208 34,039.70 825.433 11.3681

6 ......... 69,908.117 1,208,332.29 1,511.950 16.2846 61 ......... 2,574.688 31,287.49 803.698 11.1520

7 ......... 65,938.418 1,138,424.17 1,499.314 16.2650 62 ......... 2,406.801 28,712.80 781.548 10.9299

8 ......... 62,195.388 1,072,485.75 1,488.648 16.2438 63 ......... 2,248.016 26,306.00 758.997 10.7019

9 ......... 58,665.424 1,010,290.36 1,479.177 16.2212 64 ......... 2,097.862 24,057.99 736.090 10.4679

10 ......... 55,336.364 951,624.94 1,470.801 16.1971 65 ......... 1,955.806 21,960.12 712.780 10.2282

11 ......... 52,197.269 896,288.58 1,463.953 16.1712 66 ......... 1,821.528 20,004.32 689.209 9.9822

12 ......... 49,235.252 844,091.31 1,456.499 16.1440 67 ......... 1,694.654 18,182.79 665.439 9.7295

13 ......... 46,440.849 794,856.06 1,448.997 16.1155 68 ......... 1,574.746 16,488.14 641.455 9.4703

14 ......... 43,802.834 748,415.21 1,439.709 16.0860 69 ......... 1,461.333 14,913.39 617.178 9.2053

15 ......... 41,312.162 704,612.37 1,428.443 16.0558 70 ......... 1,353.919 13,452.06 592.481 8.9356

16 ......... 38,960.747 663,300.21 1,415.452 16.0248 71 ......... 1,252.130 12,098.14 567.330 8.6620

17 ......... 36,740.567 624,339.46 1,400.598 15.9932 72 ......... 1,155.644 10,846.01 541.719 8.3853

18 ......... 34,645.498 587,598.90 1,385.183 15.9603 73 ......... 1,064.221 9,690.36 515.710 8.1056

19 ......... 32,668.897 552,953.40 1,369.649 15.9260 74 ......... 977.702 8,626.14 489.430 7.8229

20 ......... 30,804.748 520,284.50 1,354.682 15.8898 75 ......... 895.987 7,648.44 463.057 7.5363

21 ......... 29,046.964 489,479.75 1,340.562 15.8513 76 ......... 818.970 6,752.45 436.756 7.2451

22 ......... 27,388.921 460,432.79 1,326.687 15.8109 77 ......... 746.440 5,933.48 410.582 6.9490

23 ......... 25,825.514 433,043.87 1,313.597 15.7681 78 ......... 678.083 5,187.04 384.477 6.6496

24 ......... 24,351.344 407,218.35 1,301.248 15.7226 79 ......... 613.541 4,508.96 358.317 6.3491

25 ......... 22,961.316 382,867.01 1,289.598 15.6744 80 ......... 552.516 3,895.42 332.021 6.0503

26 ......... 21,650.409 359,905.69 1,278.388 15.6235 81 ......... 494.909 3,342.90 305.688 5.7546

27 ......... 20,414.545 338,255.29 1,268.020 15.5693 82 ......... 440.716 2,847.99 279.509 5.4622

28 ......... 19,248.832 317,840.74 1,257.847 15.5122 83 ......... 389.930 2,407.28 253.669 5.1736

29 ......... 18,149.310 298,591.91 1,247.881 15.4520 84 ......... 342.560 2,017.35 228.370 4.8890

30 ......... 17,112.066 280,442.60 1,237.957 15.3886 85 ......... 298.590 1,674.79 203.790 4.6090

31 ......... 16,133.439 263,330.53 1,227.937 15.3220 86 ......... 257.900 1,376.20 180.002 4.3362

32 ......... 15,210.153 247,197.09 1,217.865 15.2521 87 ......... 220.426 1,118.30 157.126 4.0733

33 ......... 14,339.114 231,986.94 1,207.778 15.1786 88 ......... 186.256 897.87 135.433 3.8206

34 ......... 13,517.537 217,647.83 1,197.848 15.1011 89 ......... 155.488 711.62 115.208 3.5766

35 ......... 12,742.375 204,130.29 1,187.830 15.0198 90 ......... 128.098 556.13 96.619 3.3414

36 ......... 12,011.289 191,387.91 1,178.011 14.9340 91 ......... 103.908 428.03 79.679 3.1193

37 ......... 11,321.447 179,376.62 1,168.053 14.8440 92 ......... 82.797 324.12 64.450 2.9147

38 ......... 10,670.451 168,055.18 1,157.894 14.7496 93 ......... 64.754 241.32 51.094 2.7268

39 ......... 10,056.158 157,384.73 1,147.588 14.6506 94 ......... 49.708 176.57 39.714 2.5521

40 ......... 9,476.441 147,328.57 1,137.088 14.5468 95 ......... 37.449 126.86 30.268 2.3876

41 ......... 8,929.308 137,852.13 1,126.357 14.4382 96 ......... 27.650 89.41 22.588 2.2338

42 ......... 8,412.800 128,922.82 1,115.281 14.3246 97 ......... 19.972 61.76 16.476 2.0926

43 ......... 7,925.257 120,510.02 1,103.935 14.2058 95 ......... 14.114 41.79 11.748 1.9611

44 ......... 7,464.952 112,584.76 1,092.230 14.0818 99 ......... 9.758 27.68 8.191 1.8365

45 ......... 7,030.202 105,119.81 1,080.024 13.9526 100 ......... 6.599 17.92 5.584 1.7158

46 ......... 6,619.450 98,089.61 1,067.208 13.8184 101 ......... 4.357 11.32 3.716 1.5988

47 ......... 6,231.315 91,470.16 1,053.759 13.6791 102 ......... 2.802 6.97 2.408 1.4856

48 ......... 5,864.508 85,238.85 1,039.668 13.5347 103 ......... 1.752 4.16 1.516 1.3762

49 ......... 5,517.881 79,374.34 1,024.994 13.3849 104 ......... 1.062 2.41 0.925 1.2704

50 ......... 5,190.402 73,856.46 1,009.848 13.2294 105 ......... 0.622 1.35 0.546 1.1683

51 ......... 4,880.933 68,666.05 994.176 13.0682 106 ......... 0.351 0.73 0.310 1.0698

52 ......... 4,588.227 63,785.12 977.748 12.9019 107 ......... 0.190 0.38 0.169 0.9749

53 ......... 4,311.468 59,196.89 960.701 12.7301 108 ......... 0.098 0.19 0.088 0.8835

54 ......... 4,049.792 54,885.43 943.070 12.5527 109 ......... 0.048 0.09 0.044 0.7956

x x x x x x x x

69
Table 6.G. -- Actuarial Functions at 7.0 Percent Interest for 1989-91 United States 

White Females

x D N M a x D N M a

0 ......... 100,000.000 1,503,349.59 1,650.027 14.0335 55 ......... 2,268.667 27,687.62 457.328 11.2044

1 ......... 92,834.579 1,403,349.59 1,026.663 14.1167 56 ......... 2,109.211 25,418.95 446.289 11.0514

2 ......... 86,709.756 1,310,515.01 975.130 14.1138 57 ......... 1,959.978 23,309.74 435.042 10.8929

3 ......... 81,007.769 1,223,805.25 945.743 14.1073 58 ......... 1,820.237 21,349.76 423.523 10.7291

4 ......... 75,686.071 1,142,797.48 923.619 14.0992 59 ......... 1,689.375 19,529.52 411.742 10.5602

5 ......... 70,718.960 1,067,111.41 907.933 14.0895 60 ......... 1,566.775 17,840.15 399.662 10.3865

6 ......... 66,078.493 996,392.45 893.940 14.0789 61 ......... 1,452.018 16,273.37 387.405 10.2074

7 ......... 61,743.769 930,313.96 882.108 14.0673 62 ......... 1,344.651 14,821.35 375.030 10.0225

8 ......... 57,694.563 868,570.19 872.214 14.0546 63 ......... 1,244.202 13,476.70 362.549 9.8316

9 ......... 53,911.449 810,875.63 863.511 14.0409 64 ......... 1,150.246 12,232.50 349.989 9.6347

10 ......... 50,376.907 756,964.18 855.886 14.0260 65 ......... 1,062.335 11,082.26 337.328 9.4320

11 ......... 47,075.045 706,587.27 849.709 14.0098 66 ......... 980.153 10,019.92 324.644 9.2228

12 ......... 43,988.709 659,512.23 843.049 13.9928 67 ......... 903.360 9,039.77 311.973 9.0068

13 ......... 41,104.303 615,523.52 836.410 13.9747 68 ......... 831.596 8,136.41 299.308 8.7841

14 ......... 38,407.093 574,419.21 828.266 13.9561 69 ......... 764.492 7,304.81 286.607 8.5551

15 ......... 35,884.693 536,012.12 818.480 13.9371 70 ......... 701.679 6,540.32 273.808 8.3210

16 ......... 33,525.918 500,127.43 807.301 13.9176 71 ......... 642.862 5,838.64 260.895 8.0823

17 ......... 31,319.971 466,601.51 794.638 13.8979 72 ......... 587.779 5,195.78 247.869 7.8397

18 ......... 29,257.983 435,281.54 781.620 13.8774 73 ......... 536.222 4,608.00 234.764 7.5935

19 ......... 27,330.913 406,023.56 768.624 13.8558 74 ......... 488.024 4,071.78 221.646 7.3434

20 ......... 25,530.505 378,692.64 756.220 13.8329 75 ......... 443.056 3,583.75 208.605 7.0887

21 ......... 23,848.693 353,162.14 744.628 13.8084 76 ......... 401.187 3,140.70 195.721 6.8285

22 ......... 22,277.212 329,313.44 733.342 13.7825 77 ......... 362.239 2,739.51 183.019 6.5627

23 ......... 20,809.277 307,036.23 722.795 13.7548 78 ......... 325.991 2,377.27 170.469 6.2924

24 ......... 19,438.065 286,226.96 712.937 13.7251 79 ......... 292.205 2,051.28 158.010 6.0200

25 ......... 18,157.204 266,788.89 703.725 13.6933 80 ......... 260.683 1,759.08 145.603 5.7480

26 ......... 16,960.567 248,631.69 694.943 13.6594 81 ......... 231.321 1,498.39 133.295 5.4776

27 ......... 15,842.951 231,671.12 686.896 13.6230 82 ......... 204.066 1,267.07 121.173 5.2091

28 ......... 14,798.675 215,828.17 679.076 13.5843 83 ......... 178.863 1,063.01 109.320 4.9431

29 ......... 13,822.947 201,029.49 671.485 13.5432 84 ......... 155.665 884.14 97.824 4.6798

30 ......... 12,911.154 187,206.55 663.997 13.4996 85 ......... 134.416 728.48 86.759 4.4196

31 ......... 12,059.010 174,295.39 656.508 13.4535 86 ......... 115.014 594.06 76.150 4.1651

32 ......... 11,262.645 162,236.38 649.050 13.4048 87 ......... 97.383 479.05 66.044 3.9192

33 ......... 10,518.437 150,973.74 641.651 13.3532 88 ......... 81.518 381.66 56.549 3.6820

34 ......... 9,823.099 140,455.30 634.435 13.2985 89 ......... 67.416 300.15 47.780 3.4521

35 ......... 9,173.255 130,632.20 627.223 13.2406 90 ......... 55.021 232.73 39.796 3.2298

36 ......... 8,566.132 121,458.94 620.220 13.1790 91 ......... 44.214 177.71 32.588 3.0193

37 ......... 7,998.696 112,892.81 613.184 13.1139 92 ......... 34.902 133.49 26.168 2.8249

38 ......... 7,468.306 104,894.12 606.074 13.0452 93 ......... 27.041 98.59 20.591 2.6461

39 ......... 6,972.580 97,425.81 598.928 12.9727 94 ......... 20.564 71.55 15.883 2.4795

40 ......... 6,509.217 90,453.23 591.716 12.8962 95 ......... 15.347 50.99 12.012 2.3223

41 ......... 6,076.078 83,944.01 584.414 12.8155 96 ......... 11.226 35.64 8.894 2.1750

42 ......... 5,671.112 77,867.94 576.948 12.7306 97 ......... 8.033 24.42 6.435 2.0395

43 ......... 5,292.527 72,196.82 569.371 12.6413 95 ......... 5.624 16.38 4.552 1.9133

44 ......... 4,938.543 66,904.30 561.627 12.5474 99 ......... 3.852 10.76 3.148 1.7935

45 ......... 4,607.462 61,965.75 553.628 12.4490 100 ......... 2.580 6.91 2.128 1.6771

46 ......... 4,297.718 57,358.29 545.307 12.3462 101 ......... 1.688 4.33 1.405 1.5642

47 ......... 4,007.909 53,060.57 536.656 12.2390 102 ......... 1.075 2.64 0.903 1.4547

48 ......... 3,736.731 49,052.66 527.678 12.1272 103 ......... 0.666 1.56 0.564 1.3487

49 ......... 3,483.009 45,315.93 518.415 12.0106 104 ......... 0.400 0.90 0.341 1.2461

50 ......... 3,245.677 41,832.92 508.944 11.8888 105 ......... 0.232 0.50 0.200 1.1469

51 ......... 3,023.635 38,587.25 499.236 11.7619 106 ......... 0.130 0.27 0.112 1.0510

52 ......... 2,815.746 35,563.61 489.154 11.6303 107 ......... 0.070 0.14 0.061 0.9585

53 ......... 2,621.174 32,747.87 478.790 11.4936 108 ......... 0.036 0.07 0.031 0.8693

54 ......... 2,439.077 30,126.69 468.172 11.3517 109 ......... 0.017 0.03 0.015 0.7833

x x x x x x x x

70
Table 6.H. -- Actuarial Functions at 8.0 Percent Interest for 1989-91 United States 

White Females

x D N M a x D N M a

0 ......... 100,000.000 1,332,342.02 1,307.998 12.3234 55 ......... 1,360.104 15,255.08 230.098 10.2161

1 ......... 91,975.000 1,232,342.02 690.406 12.3987 56 ......... 1,252.799 13,894.98 223.541 10.0911

2 ......... 85,111.454 1,140,367.02 639.823 12.3985 57 ......... 1,153.380 12,642.18 216.923 9.9610

3 ......... 78,778.324 1,055,255.57 611.245 12.3953 58 ......... 1,061.229 11,488.80 210.207 9.8259

4 ......... 72,921.577 976,477.24 589.929 12.3908 59 ......... 975.815 10,427.57 203.402 9.6860

5 ......... 67,505.006 903,555.67 574.956 12.3850 60 ......... 896.619 9,451.75 196.489 9.5415

6 ......... 62,491.401 836,050.66 561.723 12.3787 61 ......... 823.253 8,555.13 189.539 9.3919

7 ......... 57,851.322 773,559.26 550.636 12.3715 62 ......... 755.320 7,731.88 182.588 9.2366

8 ......... 53,556.855 715,707.94 541.452 12.3635 63 ......... 692.424 6,976.56 175.642 9.0756

9 ......... 49,581.676 662,151.08 533.448 12.3548 64 ......... 634.208 6,284.14 168.717 8.9086

10 ......... 45,902.011 612,569.41 526.500 12.3452 65 ......... 580.314 5,649.93 161.801 8.7360

11 ......... 42,496.287 566,667.40 520.924 12.3345 66 ......... 530.463 5,069.61 154.936 8.5570

12 ......... 39,342.457 524,171.11 514.968 12.3233 67 ......... 484.376 4,539.15 148.142 8.3711

13 ......... 36,422.318 484,828.65 509.084 12.3113 68 ......... 441.768 4,054.78 141.414 8.1785

14 ......... 33,717.219 448,406.33 501.935 12.2990 69 ......... 402.360 3,613.01 134.730 7.9795

15 ......... 31,211.135 414,689.12 493.423 12.2866 70 ......... 365.881 3,210.65 128.056 7.7751

16 ......... 28,889.567 383,477.98 483.791 12.2739 71 ......... 332.108 2,844.77 121.384 7.5658

17 ......... 26,738.788 354,588.41 472.980 12.2612 72 ......... 300.840 2,512.66 114.717 7.3521

18 ......... 24,747.126 327,849.62 461.969 12.2480 73 ......... 271.910 2,211.82 108.072 7.1344

19 ......... 22,903.116 303,102.50 451.079 12.2341 74 ......... 245.179 1,939.91 101.482 6.9122

20 ......... 21,196.290 280,199.38 440.780 12.2193 75 ......... 220.526 1,694.73 94.991 6.6849

21 ......... 19,616.659 259,003.09 431.245 12.2032 76 ......... 197.837 1,474.20 88.637 6.4516

22 ......... 18,154.376 239,386.43 422.048 12.1862 77 ......... 176.977 1,276.37 82.432 6.2120

23 ......... 16,801.092 221,232.06 413.532 12.1677 78 ......... 157.793 1,099.39 76.357 5.9673

24 ......... 15,548.682 204,430.97 405.647 12.1478 79 ......... 140.130 941.60 70.382 5.7195

25 ......... 14,389.626 188,882.28 398.346 12.1263 80 ......... 123.855 801.47 64.487 5.4710

26 ......... 13,316.833 174,492.66 391.451 12.1032 81 ......... 108.887 677.61 58.694 5.2231

27 ......... 12,324.142 161,175.82 385.192 12.0781 82 ......... 95.168 568.72 53.041 4.9760

28 ......... 11,405.215 148,851.68 379.164 12.0512 83 ......... 82.642 473.56 47.564 4.7302

29 ......... 10,554.588 137,446.47 373.368 12.0224 84 ......... 71.258 390.91 42.301 4.4859

30 ......... 9,767.102 126,891.88 367.704 11.9918 85 ......... 60.961 319.66 37.283 4.2436

31 ......... 9,038.000 117,124.78 362.091 11.9591 86 ......... 51.679 258.69 32.516 4.0058

32 ......... 8,362.981 108,086.78 356.553 11.9244 87 ......... 43.352 207.02 28.017 3.7752

33 ......... 7,738.057 99,723.80 351.110 11.8874 88 ......... 35.953 163.66 23.830 3.5521

34 ......... 7,159.609 91,985.74 345.850 11.8479 89 ......... 29.458 127.71 19.998 3.3353

35 ......... 6,624.059 84,826.13 340.642 11.8058 90 ......... 23.819 98.25 16.542 3.1249

36 ......... 6,128.378 78,202.07 335.632 11.7606 91 ......... 18.964 74.43 13.450 2.9250

37 ......... 5,669.438 72,073.69 330.646 11.7127 92 ......... 14.831 55.47 10.722 2.7401

38 ......... 5,244.486 66,404.25 325.652 11.6617 93 ......... 11.384 40.64 8.374 2.5697

39 ......... 4,851.034 61,159.77 320.681 11.6076 94 ......... 8.577 29.25 6.410 2.4107

40 ......... 4,486.727 56,308.73 315.710 11.5501 95 ......... 6.342 20.68 4.811 2.2602

41 ......... 4,149.390 51,822.01 310.723 11.4891 96 ......... 4.596 14.33 3.534 2.1190

42 ......... 3,836.977 47,672.62 305.672 11.4245 97 ......... 3.258 9.74 2.537 1.9890

43 ......... 3,547.677 43,835.64 300.593 11.3562 95 ......... 2.260 6.48 1.780 1.8676

44 ......... 3,279.743 40,287.96 295.450 11.2839 99 ......... 1.534 4.22 1.221 1.7523

45 ......... 3,031.536 37,008.22 290.187 11.2077 100 ......... 1.018 2.69 0.819 1.6400

46 ......... 2,801.554 33,976.68 284.762 11.1278 101 ......... 0.660 1.67 0.536 1.5310

47 ......... 2,588.445 31,175.13 279.176 11.0440 102 ......... 0.416 1.01 0.342 1.4250

48 ......... 2,390.963 28,586.69 273.431 10.9561 103 ......... 0.256 0.59 0.212 1.3223

49 ......... 2,207.983 26,195.72 267.559 10.8641 104 ......... 0.152 0.34 0.127 1.2227

50 ......... 2,038.480 23,987.74 261.610 10.7675 105 ......... 0.087 0.19 0.074 1.1262

51 ......... 1,881.440 21,949.26 255.569 10.6662 106 ......... 0.048 0.10 0.041 1.0328

52 ......... 1,735.859 20,067.82 249.354 10.5607 107 ......... 0.026 0.05 0.022 0.9426

53 ......... 1,600.947 18,331.96 243.024 10.4507 108 ......... 0.013 0.02 0.011 0.8555

54 ......... 1,475.933 16,731.01 236.599 10.3359 109 ......... 0.006 0.01 0.005 0.7714

x x x x x x x x

71
Table 6.I. -- Actuarial Functions at 9.0 Percent Interest for 1989-91 United States 

White Females

x D N M a x D N M a

0 ......... 100,000.000 1,197,650.40 1,111.435 10.9765 55 ......... 819.259 8,496.43 117.719 9.3709

1 ......... 91,131.193 1,097,650.40 499.508 11.0447 56 ......... 747.701 7,677.17 113.806 9.2677

2 ......... 83,556.940 1,006,519.21 449.849 11.0459 57 ......... 682.050 6,929.47 109.892 9.1598

3 ......... 76,629.944 922,962.27 422.050 11.0444 58 ......... 621.799 6,247.42 105.957 9.0473

4 ......... 70,282.157 846,332.33 401.506 11.0419 59 ......... 566.507 5,625.62 102.006 8.9304

5 ......... 64,464.744 776,050.17 387.208 11.0384 60 ......... 515.755 5,059.11 98.030 8.8091

6 ......... 59,129.446 711,585.42 374.686 11.0344 61 ......... 469.209 4,543.36 94.069 8.6830

7 ......... 54,236.804 652,455.98 364.292 11.0298 62 ......... 426.541 4,074.15 90.143 8.5516

8 ......... 49,750.004 598,219.17 355.761 11.0245 63 ......... 387.436 3,647.61 86.257 8.4148

9 ......... 45,634.839 548,469.17 348.394 11.0187 64 ......... 351.606 3,260.17 82.418 8.2722

10 ......... 41,860.489 502,834.33 342.058 11.0121 65 ......... 318.775 2,908.57 78.618 8.1242

11 ......... 38,399.080 460,973.84 337.020 11.0048 66 ......... 288.718 2,589.79 74.882 7.9700

12 ......... 35,223.181 422,574.76 331.687 10.9971 67 ......... 261.215 2,301.07 71.218 7.8091

13 ......... 32,309.626 387,351.58 326.468 10.9887 68 ......... 236.052 2,039.86 67.623 7.6416

14 ......... 29,635.574 355,041.96 320.184 10.9803 69 ......... 213.022 1,803.81 64.084 7.4677

15 ......... 27,181.188 325,406.38 312.771 10.9717 70 ......... 191.932 1,590.78 60.583 7.2883

16 ......... 24,928.558 298,225.19 304.459 10.9632 71 ......... 172.617 1,398.85 57.116 7.1038

17 ......... 22,860.994 273,296.64 295.216 10.9547 72 ......... 154.931 1,226.23 53.682 6.9147

18 ......... 20,964.061 250,435.64 285.889 10.9460 73 ......... 138.748 1,071.30 50.291 6.7212

19 ......... 19,223.942 229,471.58 276.748 10.9368 74 ......... 123.960 932.56 46.959 6.5231

20 ......... 17,628.080 210,247.64 268.183 10.9269 75 ......... 110.473 808.60 43.708 6.3194

21 ......... 16,164.693 192,619.56 260.325 10.9161 76 ......... 98.197 698.12 40.554 6.1094

22 ......... 14,822.484 176,454.87 252.816 10.9045 77 ......... 87.037 599.93 37.502 5.8927

23 ......... 13,591.720 161,632.38 245.927 10.8920 78 ......... 76.891 512.89 34.542 5.6704

24 ......... 12,463.148 148,040.66 239.607 10.8783 79 ......... 67.657 436.00 31.657 5.4442

25 ......... 11,428.282 135,577.51 233.809 10.8633 80 ......... 59.251 368.34 28.837 5.2166

26 ......... 10,479.237 124,149.23 228.383 10.8472 81 ......... 51.612 309.09 26.091 4.9887

27 ......... 9,609.098 113,670.00 223.502 10.8294 82 ......... 44.696 257.48 23.436 4.7607

28 ......... 8,811.030 104,060.90 218.846 10.8103 83 ......... 38.457 212.78 20.888 4.5330

29 ......... 8,079.077 95,249.87 214.409 10.7897 84 ......... 32.855 174.33 18.461 4.3059

30 ......... 7,407.701 87,170.79 210.113 10.7676 85 ......... 27.850 141.47 16.169 4.0798

31 ......... 6,791.838 79,763.09 205.895 10.7440 86 ......... 23.393 113.62 14.011 3.8571

32 ......... 6,226.921 72,971.25 201.772 10.7187 87 ......... 19.443 90.23 11.993 3.6406

33 ......... 5,708.756 66,744.33 197.756 10.6916 88 ......... 15.977 70.78 10.132 3.4304

34 ......... 5,233.546 61,035.57 193.911 10.6624 89 ......... 12.971 54.81 8.445 3.2255

35 ......... 4,797.646 55,802.03 190.140 10.6311 90 ......... 10.392 41.84 6.937 3.0260

36 ......... 4,397.915 51,004.38 186.544 10.5974 91 ......... 8.197 31.45 5.601 2.8361

37 ......... 4,031.239 46,606.47 182.998 10.5613 92 ......... 6.352 23.25 4.433 2.6599

38 ......... 3,694.866 42,575.23 179.481 10.5228 93 ......... 4.831 16.90 3.436 2.4974

39 ......... 3,386.315 38,880.36 176.010 10.4816 94 ......... 3.607 12.06 2.610 2.3453

40 ......... 3,103.273 35,494.05 172.572 10.4376 95 ......... 2.642 8.46 1.944 2.2012

41 ......... 2,843.622 32,390.77 169.154 10.3907 96 ......... 1.897 5.82 1.417 2.0657

42 ......... 2,605.397 29,547.15 165.724 10.3407 97 ......... 1.333 3.92 1.009 1.9407

43 ......... 2,386.856 26,941.75 162.307 10.2876 95 ......... 0.916 2.59 0.702 1.8239

44 ......... 2,186.347 24,554.90 158.879 10.2310 99 ......... 0.616 1.67 0.478 1.7128

45 ......... 2,002.347 22,368.55 155.403 10.1712 100 ......... 0.405 1.05 0.318 1.6045

46 ......... 1,833.466 20,366.20 151.853 10.1080 101 ......... 0.260 0.65 0.206 1.4991

47 ......... 1,678.456 18,532.74 148.230 10.0415 102 ......... 0.163 0.39 0.130 1.3965

48 ......... 1,536.177 16,854.28 144.539 9.9716 103 ......... 0.099 0.23 0.080 1.2968

49 ......... 1,405.599 15,318.10 140.801 9.8979 104 ......... 0.058 0.13 0.048 1.2001

50 ......... 1,285.788 13,912.51 137.049 9.8202 105 ......... 0.033 0.07 0.027 1.1062

51 ......... 1,175.846 12,626.72 133.273 9.7384 106 ......... 0.018 0.04 0.015 1.0153

52 ......... 1,074.910 11,450.87 129.425 9.6529 107 ......... 0.010 0.02 0.008 0.9272

53 ......... 982.272 10,375.96 125.541 9.5632 108 ......... 0.005 0.01 0.004 0.8421

54 ......... 897.261 9,393.69 121.635 9.4693 109 ......... 0.002 0.00 0.002 0.7599

x x x x x x x x

72
Table 6.J. -- Actuarial Functions at 10.0 Percent Interest for 1989-91 United States 

White Females

x D N M a x D N M a

0 ......... 100,000.000 1,089,092.94 991.551 9.8909 55 ......... 495.771 4,780.36 61.193 8.6423

1 ......... 90,302.727 989,092.94 385.187 9.9531 56 ......... 448.354 4,284.58 58.847 8.5562

2 ......... 82,044.628 898,790.21 336.427 9.9549 57 ......... 405.269 3,836.23 56.521 8.4659

3 ......... 74,558.978 816,745.59 309.380 9.9544 58 ......... 366.110 3,430.96 54.204 8.3714

4 ......... 67,761.082 742,186.61 289.572 9.9530 59 ......... 330.522 3,064.85 51.899 8.2728

5 ......... 61,587.323 674,425.52 275.912 9.9507 60 ......... 298.176 2,734.33 49.600 8.1702

6 ......... 55,976.622 612,838.20 264.058 9.9481 61 ......... 268.800 2,436.15 47.331 8.0631

7 ......... 50,878.088 556,861.58 254.308 9.9450 62 ......... 242.135 2,167.35 45.103 7.9510

8 ......... 46,244.877 505,983.49 246.377 9.9414 63 ......... 217.936 1,925.22 42.916 7.8339

9 ......... 42,034.011 459,738.62 239.592 9.9373 64 ......... 195.984 1,707.28 40.776 7.7113

10 ......... 38,206.954 417,704.60 233.809 9.9327 65 ......... 176.069 1,511.30 38.678 7.5836

11 ......... 34,729.039 379,497.65 229.252 9.9274 66 ......... 158.018 1,335.23 36.633 7.4499

12 ......... 31,567.074 344,768.61 224.473 9.9218 67 ......... 141.665 1,177.21 34.646 7.3098

13 ......... 28,692.705 313,201.54 219.838 9.9157 68 ......... 126.855 1,035.55 32.714 7.1632

14 ......... 26,078.747 284,508.83 214.308 9.9096 69 ......... 113.438 908.69 30.830 7.0105

15 ......... 23,701.489 258,430.08 207.845 9.9035 70 ......... 101.278 795.25 28.982 6.8522

16 ......... 21,539.626 234,728.60 200.663 9.8975 71 ......... 90.258 693.98 27.169 6.6888

17 ......... 19,573.564 213,188.97 192.749 9.8917 72 ......... 80.274 603.72 25.390 6.5208

18 ......... 17,786.236 193,615.41 184.835 9.8857 73 ......... 71.235 523.44 23.649 6.3481

19 ......... 16,161.620 175,829.17 177.150 9.8794 74 ......... 63.064 452.21 21.954 6.1706

20 ......... 14,685.247 159,667.55 170.015 9.8726 75 ......... 55.692 389.15 20.315 5.9875

21 ......... 13,343.738 144,982.30 163.529 9.8652 76 ......... 49.053 333.45 18.740 5.7978

22 ......... 12,124.529 131,638.56 157.387 9.8572 77 ......... 43.083 284.40 17.229 5.6012

23 ......... 11,016.715 119,514.03 151.803 9.8484 78 ......... 37.715 241.32 15.777 5.3985

24 ......... 10,010.119 108,497.32 146.727 9.8388 79 ......... 32.884 203.60 14.375 5.1915

25 ......... 9,095.494 98,487.20 142.112 9.8281 80 ......... 28.536 170.72 13.017 4.9825

26 ......... 8,264.351 89,391.71 137.833 9.8165 81 ......... 24.632 142.18 11.706 4.7723

27 ......... 7,509.233 81,127.35 134.019 9.8037 82 ......... 21.137 117.55 10.450 4.5614

28 ......... 6,822.970 73,618.12 130.413 9.7897 83 ......... 18.021 96.41 9.256 4.3500

29 ......... 6,199.295 66,795.15 127.009 9.7746 84 ......... 15.256 78.39 8.130 4.1384

30 ......... 5,632.457 60,595.86 123.742 9.7583 85 ......... 12.814 63.14 7.075 3.9270

31 ......... 5,117.237 54,963.40 120.564 9.7408 86 ......... 10.666 50.32 6.091 3.7181

32 ......... 4,648.955 49,846.16 117.486 9.7220 87 ......... 8.784 39.66 5.179 3.5144

33 ......... 4,223.352 45,197.21 114.515 9.7017 88 ......... 7.153 30.87 4.346 3.3161

34 ......... 3,836.593 40,973.86 111.697 9.6798 89 ......... 5.754 23.72 3.598 3.1222

35 ......... 3,485.071 37,137.26 108.957 9.6561 90 ......... 4.568 17.97 2.935 2.9328

36 ......... 3,165.659 33,652.19 106.369 9.6304 91 ......... 3.571 13.40 2.353 2.7520

37 ......... 2,875.343 30,486.53 103.839 9.6027 92 ......... 2.742 9.83 1.848 2.5840

38 ......... 2,611.461 27,611.19 101.353 9.5731 93 ......... 2.066 7.08 1.422 2.4287

39 ......... 2,371.625 24,999.73 98.923 9.5412 94 ......... 1.529 5.02 1.072 2.2832

40 ......... 2,153.637 22,628.10 96.536 9.5069 95 ......... 1.110 3.49 0.792 2.1450

41 ......... 1,955.502 20,474.47 94.186 9.4702 96 ......... 0.790 2.38 0.573 2.0148

42 ......... 1,775.391 18,518.97 91.849 9.4309 97 ......... 0.550 1.59 0.405 1.8946

43 ......... 1,611.685 16,743.57 89.542 9.3889 95 ......... 0.374 1.04 0.280 1.7822

44 ......... 1,462.874 15,131.89 87.248 9.3439 99 ......... 0.249 0.67 0.189 1.6750

45 ......... 1,327.581 13,669.02 84.943 9.2962 100 ......... 0.162 0.42 0.125 1.5704

46 ......... 1,204.559 12,341.43 82.611 9.2456 101 ......... 0.103 0.26 0.080 1.4684

47 ......... 1,092.696 11,136.88 80.252 9.1921 102 ......... 0.064 0.15 0.050 1.3690

48 ......... 990.979 10,044.18 77.871 9.1356 103 ......... 0.039 0.09 0.031 1.2723

49 ......... 898.500 9,053.20 75.482 9.0759 104 ......... 0.023 0.05 0.018 1.1782

50 ......... 814.442 8,154.70 73.105 9.0126 105 ......... 0.013 0.03 0.010 1.0869

51 ......... 738.032 7,340.26 70.735 8.9457 106 ......... 0.007 0.01 0.006 0.9983

52 ......... 668.544 6,602.23 68.342 8.8755 107 ......... 0.004 0.01 0.003 0.9123

53 ......... 605.374 5,933.68 65.948 8.8017 108 ......... 0.002 0.00 0.002 0.8292

54 ......... 547.954 5,328.31 63.563 8.7240 109 ......... 0.001 0.00 0.001 0.7487

x x x x x x x x

73
Table 6.K. -- Actuarial Functions at 11.0 Percent Interest for 1989-91 United States 

White Females

x D N M a x D N M a

0 ......... 100,000.000 999,870.73 913.711 8.9987 55 ......... 301.380 2,715.31 32.295 8.0096

1 ......... 89,489.189 899,870.73 312.810 9.0556 56 ......... 270.100 2,413.93 30.882 7.9372

2 ......... 80,573.005 810,381.54 264.925 9.0577 57 ......... 241.945 2,143.83 29.493 7.8608

3 ......... 72,561.970 729,808.54 238.602 9.0577 58 ......... 216.598 1,901.89 28.122 7.7807

4 ......... 65,352.041 657,246.57 219.498 9.0570 59 ......... 193.782 1,685.29 26.771 7.6968

5 ......... 58,862.657 591,894.53 206.442 9.0555 60 ......... 173.243 1,491.51 25.435 7.6094

6 ......... 53,018.193 533,031.87 195.215 9.0538 61 ......... 154.768 1,318.27 24.129 7.5177

7 ......... 47,754.986 480,013.68 186.064 9.0516 62 ......... 138.159 1,163.50 22.857 7.4214

8 ......... 43,015.134 432,258.69 178.687 9.0490 63 ......... 123.231 1,025.34 21.621 7.3204

9 ......... 38,746.118 389,243.56 172.432 9.0460 64 ......... 109.820 902.11 20.422 7.2144

10 ......... 34,901.130 350,497.44 167.149 9.0426 65 ......... 97.772 792.29 19.257 7.1034

11 ......... 31,438.334 315,596.31 163.025 9.0386 66 ......... 86.957 694.52 18.132 6.9868

12 ......... 28,318.536 284,157.98 158.737 9.0343 67 ......... 77.256 607.56 17.048 6.8642

13 ......... 25,508.075 255,839.44 154.617 9.0297 68 ......... 68.556 530.30 16.004 6.7353

14 ......... 22,975.375 230,331.36 149.745 9.0251 69 ......... 60.753 461.75 14.994 6.6004

15 ......... 20,692.893 207,355.99 144.102 9.0206 70 ......... 53.752 400.99 14.014 6.4600

16 ......... 18,636.033 186,663.10 137.888 9.0162 71 ......... 47.472 347.24 13.060 6.3147

17 ......... 16,782.433 168,027.06 131.103 9.0121 72 ......... 41.840 299.77 12.133 6.1646

18 ......... 15,112.585 151,244.63 124.379 9.0079 73 ......... 36.794 257.93 11.234 6.0100

19 ......... 13,608.471 136,132.04 117.908 9.0035 74 ......... 32.281 221.13 10.366 5.8504

20 ......... 12,253.930 122,523.57 111.954 8.9987 75 ......... 28.250 188.85 9.535 5.6851

21 ......... 11,034.213 110,269.64 106.590 8.9934 76 ......... 24.659 160.60 8.743 5.5131

22 ......... 9,935.699 99,235.43 101.557 8.9878 77 ......... 21.462 135.95 7.990 5.3341

23 ......... 8,946.545 89,299.73 97.022 8.9815 78 ......... 18.619 114.48 7.273 5.1488

24 ......... 8,055.866 80,353.19 92.937 8.9745 79 ......... 16.088 95.86 6.588 4.9589

25 ......... 7,253.856 72,297.32 89.257 8.9667 80 ......... 13.835 79.78 5.929 4.7663

26 ......... 6,531.624 65,043.47 85.875 8.9582 81 ......... 11.834 65.94 5.299 4.5721

27 ......... 5,881.358 58,511.84 82.888 8.9487 82 ......... 10.064 54.11 4.702 4.3765

28 ......... 5,295.722 52,630.48 80.089 8.9383 83 ......... 8.503 44.04 4.138 4.1799

29 ......... 4,768.303 47,334.76 77.471 8.9270 84 ......... 7.133 35.54 3.611 3.9823

30 ......... 4,293.278 42,566.46 74.981 8.9147 85 ......... 5.938 28.41 3.123 3.7843

31 ......... 3,865.418 38,273.18 72.580 8.9014 86 ......... 4.898 22.47 2.671 3.5880

32 ......... 3,480.054 34,407.76 70.276 8.8871 87 ......... 3.997 17.57 2.256 3.3960

33 ......... 3,132.980 30,927.71 68.072 8.8717 88 ......... 3.226 13.58 1.880 3.2086

34 ......... 2,820.432 27,794.73 66.000 8.8548 89 ......... 2.571 10.35 1.546 3.0248

35 ......... 2,538.934 24,974.30 64.004 8.8365 90 ......... 2.023 7.78 1.252 2.8447

36 ......... 2,285.460 22,435.36 62.135 8.8166 91 ......... 1.567 5.75 0.997 2.6724

37 ......... 2,057.163 20,149.90 60.326 8.7950 92 ......... 1.192 4.19 0.777 2.5120

38 ......... 1,851.537 18,092.74 58.563 8.7717 93 ......... 0.891 3.00 0.594 2.3635

39 ......... 1,666.344 16,241.20 56.855 8.7466 94 ......... 0.653 2.10 0.444 2.2241

40 ......... 1,499.549 14,574.86 55.194 8.7195 95 ......... 0.470 1.45 0.326 2.0914

41 ......... 1,349.324 13,075.31 53.572 8.6903 96 ......... 0.331 0.98 0.234 1.9663

42 ......... 1,214.009 11,725.99 51.974 8.6589 97 ......... 0.228 0.65 0.164 1.8506

43 ......... 1,092.138 10,511.98 50.410 8.6251 95 ......... 0.154 0.42 0.112 1.7422

44 ......... 982.368 9,419.84 48.870 8.5889 99 ......... 0.102 0.27 0.075 1.6388

45 ......... 883.482 8,437.47 47.336 8.5502 100 ......... 0.066 0.17 0.049 1.5377

46 ......... 794.392 7,553.99 45.798 8.5092 101 ......... 0.041 0.10 0.031 1.4389

47 ......... 714.127 6,759.60 44.257 8.4655 102 ......... 0.025 0.06 0.020 1.3426

48 ......... 641.815 6,045.47 42.715 8.4193 103 ......... 0.015 0.03 0.012 1.2486

49 ......... 576.679 5,403.66 41.181 8.3703 104 ......... 0.009 0.02 0.007 1.1572

50 ......... 518.019 4,826.98 39.669 8.3182 105 ......... 0.005 0.01 0.004 1.0682

51 ......... 465.190 4,308.96 38.176 8.2628 106 ......... 0.003 0.01 0.002 0.9818

52 ......... 417.595 3,843.77 36.681 8.2045 107 ......... 0.001 0.00 0.001 0.8979

53 ......... 374.730 3,426.17 35.199 8.1431 108 ......... 0.001 0.00 0.001 0.8166

54 ......... 336.131 3,051.44 33.736 8.0781 109 ......... 0.000 0.00 0.000 0.7378

x x x x x x x x

74
Table 6.L. -- Actuarial Functions at 12.0 Percent Interest for 1989-91 United States 

White Females

x D N M a x D N M a

0 ......... 100,000.000 925,307.38 859.924 8.2531 55 ......... 184.029 1,556.23 17.290 7.4564

1 ......... 88,690.179 825,307.38 264.388 8.3055 56 ......... 163.457 1,372.20 16.435 7.3949

2 ......... 79,140.625 736,617.20 217.354 8.3077 57 ......... 145.111 1,208.75 15.602 7.3298

3 ......... 70,635.648 657,476.57 191.730 8.3080 58 ......... 128.748 1,063.64 14.787 7.2614

4 ......... 63,049.113 586,840.93 173.300 8.3077 59 ......... 114.158 934.89 13.991 7.1894

5 ......... 56,281.368 523,791.81 160.816 8.3067 60 ......... 101.147 820.73 13.211 7.1143

6 ......... 50,240.582 467,510.44 150.177 8.3054 61 ......... 89.554 719.58 12.455 7.0352

7 ......... 44,849.068 417,269.86 141.582 8.3039 62 ......... 79.229 630.03 11.726 6.9520

8 ......... 40,036.944 372,420.80 134.716 8.3019 63 ......... 70.038 550.80 11.024 6.8643

9 ......... 35,741.502 332,383.85 128.947 8.2997 64 ......... 61.858 480.76 10.348 6.7720

10 ......... 31,907.226 296,642.35 124.117 8.2970 65 ......... 54.580 418.90 9.698 6.6750

11 ......... 28,484.857 264,735.12 120.380 8.2939 66 ......... 48.110 364.32 9.075 6.5728

12 ......... 25,429.058 236,250.27 116.530 8.2906 67 ......... 42.361 316.21 8.481 6.4647

13 ......... 22,700.849 210,821.21 112.863 8.2869 68 ......... 37.255 273.85 7.914 6.3508

14 ......... 20,264.319 188,120.36 108.566 8.2833 69 ......... 32.720 236.60 7.370 6.2310

15 ......... 18,088.209 167,856.04 103.633 8.2799 70 ......... 28.691 203.88 6.847 6.1061

16 ......... 16,144.803 149,767.83 98.250 8.2765 71 ......... 25.112 175.19 6.342 5.9762

17 ......... 14,409.177 133,623.03 92.424 8.2735 72 ......... 21.936 150.08 5.856 5.8416

18 ......... 12,859.615 119,213.85 86.703 8.2704 73 ......... 19.118 128.14 5.389 5.7025

19 ......... 11,476.342 106,354.24 81.245 8.2673 74 ......... 16.623 109.02 4.942 5.5585

20 ......... 10,241.758 94,877.89 76.269 8.2638 75 ......... 14.418 92.40 4.518 5.4088

21 ......... 9,139.984 84,636.14 71.827 8.2600 76 ......... 12.472 77.98 4.117 5.2524

22 ......... 8,156.568 75,496.15 67.695 8.2559 77 ......... 10.759 65.51 3.740 5.0889

23 ......... 7,278.960 67,339.58 64.005 8.2513 78 ......... 9.250 54.75 3.384 4.9190

24 ......... 6,495.778 60,060.62 60.711 8.2461 79 ......... 7.921 45.50 3.046 4.7442

25 ......... 5,796.860 53,564.85 57.770 8.2403 80 ......... 6.751 37.58 2.725 4.5664

26 ......... 5,173.090 47,767.98 55.091 8.2339 81 ......... 5.723 30.83 2.420 4.3865

27 ......... 4,616.485 42,594.90 52.747 8.2267 82 ......... 4.823 25.11 2.134 4.2047

28 ......... 4,119.685 37,978.41 50.569 8.2188 83 ......... 4.039 20.28 1.866 4.0214

29 ......... 3,676.271 33,858.73 48.551 8.2101 84 ......... 3.358 16.24 1.618 3.8366

30 ......... 3,280.482 30,182.45 46.648 8.2006 85 ......... 2.770 12.88 1.390 3.6507

31 ......... 2,927.184 26,901.97 44.830 8.1904 86 ......... 2.265 10.11 1.181 3.4659

32 ......... 2,611.828 23,974.79 43.101 8.1793 87 ......... 1.832 7.85 0.991 3.2847

33 ......... 2,330.350 21,362.96 41.461 8.1673 88 ......... 1.465 6.02 0.820 3.1073

34 ......... 2,079.142 19,032.61 39.934 8.1541 89 ......... 1.157 4.55 0.670 2.9329

35 ......... 1,854.919 16,953.47 38.476 8.1397 90 ......... 0.903 3.39 0.539 2.7615

36 ......... 1,654.825 15,098.55 37.123 8.1240 91 ......... 0.693 2.49 0.426 2.5971

37 ......... 1,476.223 13,443.72 35.824 8.1068 92 ......... 0.523 1.80 0.330 2.4437

38 ......... 1,316.803 11,967.50 34.571 8.0883 93 ......... 0.387 1.28 0.250 2.3015

39 ......... 1,174.513 10,650.70 33.367 8.0682 94 ......... 0.281 0.89 0.186 2.1678

40 ......... 1,047.512 9,476.18 32.206 8.0464 95 ......... 0.200 0.61 0.135 2.0404

41 ......... 934.156 8,428.67 31.084 8.0228 96 ......... 0.140 0.41 0.096 1.9199

42 ......... 832.971 7,494.52 29.987 7.9973 97 ......... 0.096 0.27 0.067 1.8084

43 ......... 742.661 6,661.55 28.924 7.9698 95 ......... 0.064 0.17 0.045 1.7039

44 ......... 662.052 5,918.88 27.886 7.9402 99 ......... 0.042 0.11 0.030 1.6040

45 ......... 590.093 5,256.83 26.861 7.9085 100 ......... 0.027 0.07 0.020 1.5062

46 ......... 525.851 4,666.74 25.843 7.8746 101 ......... 0.017 0.04 0.012 1.4106

47 ......... 468.499 4,140.89 24.832 7.8386 102 ......... 0.010 0.02 0.008 1.3171

48 ......... 417.300 3,672.39 23.829 7.8004 103 ......... 0.006 0.01 0.005 1.2258

49 ......... 371.601 3,255.09 22.841 7.7596 104 ......... 0.003 0.01 0.003 1.1368

50 ......... 330.821 2,883.49 21.876 7.7162 105 ......... 0.002 0.00 0.001 1.0502

51 ......... 294.431 2,552.67 20.930 7.6698 106 ......... 0.001 0.00 0.001 0.9659

52 ......... 261.947 2,258.24 19.993 7.6210 107 ......... 0.001 0.00 0.000 0.8839

53 ......... 232.960 1,996.29 19.071 7.5693 108 ......... 0.000 0.00 0.000 0.8043

54 ......... 207.098 1,763.33 18.170 7.5145 109 ......... 0.000 0.00 0.000 0.7272

x x x x x x x x

75
Table 7.A. -- Actuarial Functions at 1.0 Percent Interest for 1989-91 United States 

Total Other than White Population

x D N M a x D N M a

0 ......... 100,000.000 5,048,998.26 50,009.918 49.4900 55 ......... 48,399.659 995,043.59 38,547.742 19.5589

1 ......... 97,453.465 4,948,998.26 48,453.483 49.7832 56 ......... 47,359.683 946,643.93 37,986.971 18.9884

2 ......... 96,379.767 4,851,544.79 48,344.670 49.3378 57 ......... 46,298.126 899,284.25 37,394.321 18.4238

3 ......... 95,359.511 4,755,165.02 48,278.670 48.8657 58 ......... 45,213.079 852,986.13 36,767.672 17.8659

4 ......... 94,363.465 4,659,805.51 48,226.777 48.3815 59 ......... 44,103.840 807,773.05 36,106.087 17.3153

5 ......... 93,390.163 4,565,442.05 48,187.767 47.8857 60 ......... 42,969.198 763,669.21 35,408.117 16.7725

6 ......... 92,429.710 4,472,051.89 48,151.969 47.3833 61 ......... 41,812.916 720,700.01 34,677.272 16.2363

7 ......... 91,483.785 4,379,622.17 48,121.189 46.8732 62 ......... 40,636.467 678,887.09 33,914.812 15.7064

8 ......... 90,551.224 4,288,138.39 48,094.408 46.3559 63 ......... 39,439.145 638,250.63 33,119.832 15.1832

9 ......... 89,631.819 4,197,587.17 48,071.550 45.8314 64 ......... 38,217.645 598,811.48 32,288.818 14.6685

10 ......... 88,724.459 4,107,955.35 48,051.633 45.3001 65 ......... 36,971.949 560,593.84 31,421.515 14.1627

11 ......... 87,828.968 4,019,230.89 48,034.603 44.7620 66 ......... 35,702.579 523,621.89 30,518.203 13.6662

12 ......... 86,941.626 3,931,401.92 48,016.854 44.2189 67 ......... 34,414.160 487,919.31 29,583.276 13.1779

13 ......... 86,057.972 3,844,460.29 47,994.009 43.6729 68 ......... 33,111.664 453,505.15 28,621.514 12.6962

14 ......... 85,171.115 3,758,402.32 47,959.210 43.1277 69 ......... 31,797.361 420,393.48 27,635.050 12.2210

15 ......... 84,278.739 3,673,231.21 47,910.114 42.5843 70 ......... 30,472.452 388,596.12 26,624.965 11.7524

16 ......... 83,376.924 3,588,952.47 47,842.741 42.0449 71 ......... 29,135.631 358,123.67 25,589.852 11.2916

17 ......... 82,470.349 3,505,575.54 47,761.680 41.5071 72 ......... 27,785.169 328,988.04 24,527.861 10.8404

18 ......... 81,559.341 3,423,105.20 47,667.210 40.9707 73 ......... 26,422.802 301,202.87 23,440.595 10.3994

19 ......... 80,647.528 3,341,545.85 47,562.915 40.4340 74 ......... 25,054.998 274,780.07 22,334.403 9.9671

20 ......... 79,737.579 3,260,898.33 47,451.457 39.8954 75 ......... 23,690.354 249,725.07 21,217.829 9.5412

21 ......... 78,830.441 3,181,160.75 47,333.800 39.3545 76 ......... 22,335.724 226,034.72 20,097.756 9.1199

22 ......... 77,923.808 3,102,330.31 47,207.667 38.8124 77 ......... 20,994.441 203,698.99 18,977.619 8.7025

23 ......... 77,020.242 3,024,406.50 47,075.623 38.2677 78 ......... 19,667.864 182,704.55 17,858.908 8.2895

24 ......... 76,122.204 2,947,386.26 46,940.162 37.7191 79 ......... 18,350.918 163,036.69 16,736.694 7.8844

25 ......... 75,229.720 2,871,264.05 46,801.363 37.1666 80 ......... 17,039.176 144,685.77 15,606.643 7.4914

26 ......... 74,345.131 2,796,034.33 46,661.622 36.6088 81 ......... 15,729.277 127,646.60 14,465.449 7.1152

27 ......... 73,466.861 2,721,689.20 46,519.443 36.0465 82 ......... 14,425.072 111,917.32 13,316.980 6.7585

28 ......... 72,593.397 2,648,222.34 46,373.374 35.4802 83 ......... 13,139.022 97,492.25 12,173.752 6.4201

29 ......... 71,723.284 2,575,628.94 46,222.007 34.9106 84 ......... 11,892.630 84,353.23 11,057.450 6.0929

30 ......... 70,853.639 2,503,905.66 46,062.494 34.3391 85 ......... 10,705.257 72,460.60 9,987.825 5.7687

31 ......... 69,984.634 2,433,052.02 45,895.010 33.7655 86 ......... 9,579.753 61,755.34 8,968.314 5.4464

32 ......... 69,117.164 2,363,067.39 45,720.457 33.1893 87 ......... 8,512.093 52,175.59 7,995.503 5.1296

33 ......... 68,250.649 2,293,950.22 45,538.271 32.6107 88 ......... 7,501.713 43,663.49 7,069.402 4.8205

34 ......... 67,383.823 2,225,699.57 45,347.194 32.0302 89 ......... 6,545.980 36,161.78 6,187.942 4.5243

35 ......... 66,517.589 2,158,315.75 45,148.126 31.4473 90 ......... 5,645.600 29,615.80 5,352.374 4.2458

36 ......... 65,650.719 2,091,798.16 44,939.847 30.8625 91 ......... 4,802.842 23,970.20 4,565.513 3.9908

37 ......... 64,782.731 2,026,147.44 44,721.865 30.2760 92 ......... 4,025.862 19,167.36 3,836.086 3.7611

38 ......... 63,913.847 1,961,364.71 44,494.394 29.6876 93 ......... 3,324.839 15,141.50 3,174.924 3.5541

39 ......... 63,046.320 1,897,450.86 44,259.678 29.0961 94 ......... 2,710.693 11,816.66 2,593.696 3.3593

40 ......... 62,179.633 1,834,404.54 44,017.211 28.5017 95 ......... 2,185.319 9,105.96 2,095.161 3.1669

41 ......... 61,314.617 1,772,224.91 43,767.835 27.9038 96 ......... 1,739.903 6,920.64 1,671.382 2.9776

42 ......... 60,449.441 1,710,910.29 43,509.735 27.3032 97 ......... 1,363.843 5,180.74 1,312.548 2.7986

43 ......... 59,583.001 1,650,460.85 43,241.804 26.7002 95 ......... 1,052.063 3,816.90 1,014.272 2.6280

44 ......... 58,712.947 1,590,877.85 42,961.681 26.0959 99 ......... 798.214 2,764.84 770.839 2.4638

45 ......... 57,837.026 1,532,164.91 42,667.077 25.4911 100 ......... 594.898 1,966.62 575.427 2.3058

46 ......... 56,953.080 1,474,327.88 42,355.775 24.8867 101 ......... 434.924 1,371.72 421.342 2.1539

47 ......... 56,059.042 1,417,374.80 42,025.629 24.2836 102 ......... 311.436 936.80 302.160 2.0080

48 ......... 55,152.935 1,361,315.76 41,674.561 23.6826 103 ......... 218.060 625.36 211.869 1.8678

49 ......... 54,233.482 1,306,162.82 41,301.177 23.0841 104 ......... 149.013 407.30 144.980 1.7333

50 ......... 53,301.291 1,251,929.34 40,905.951 22.4878 105 ......... 99.178 258.29 96.620 1.6043

51 ......... 52,355.755 1,198,628.05 40,488.150 21.8939 106 ......... 64.142 159.11 62.567 1.4806

52 ......... 51,394.510 1,146,272.29 40,045.279 21.3034 107 ......... 40.207 94.97 39.266 1.3621

53 ......... 50,415.889 1,094,877.78 39,575.515 20.7169 108 ......... 24.356 54.76 23.813 1.2485

54 ......... 49,418.302 1,044,461.90 39,077.095 20.1351 109 ......... 14.211 30.41 13.910 1.1398

x x x x x x x x

76
Table 7.B. -- Actuarial Functions at 2.0 Percent Interest for 1989-91 United States 

Total Other than White Population

x D N M a x D N M a

0 ......... 100,000.000 3,750,920.74 26,452.534 36.5092 55 ......... 28,151.946 511,239.68 18,127.638 17.1600

1 ......... 96,498.039 3,650,920.74 24,911.358 36.8341 56 ......... 27,276.968 483,087.73 17,804.660 16.7105

2 ......... 94,499.231 3,554,422.71 24,804.668 36.6132 57 ......... 26,404.134 455,810.76 17,466.668 16.2629

3 ......... 92,582.227 3,459,923.47 24,740.590 36.3714 58 ......... 25,532.527 429,406.63 17,112.789 15.8180

4 ......... 90,717.002 3,367,341.25 24,690.703 36.1192 59 ......... 24,661.945 403,874.10 16,742.845 15.3764

5 ......... 88,901.102 3,276,624.25 24,653.568 35.8570 60 ......... 23,791.913 379,212.16 16,356.381 14.9387

6 ......... 87,124.200 3,187,723.14 24,619.825 35.5883 61 ......... 22,924.706 355,420.24 15,955.682 14.5038

7 ......... 85,387.154 3,100,598.94 24,591.096 35.3122 62 ......... 22,061.268 332,495.54 15,541.747 14.0715

8 ......... 83,688.145 3,015,211.79 24,566.345 35.0291 63 ......... 21,201.336 310,434.27 15,114.389 13.6422

9 ......... 82,026.282 2,931,523.64 24,545.426 34.7388 64 ......... 20,343.274 289,232.94 14,672.040 13.2176

10 ......... 80,399.876 2,849,497.36 24,527.379 34.4416 65 ......... 19,487.246 268,889.66 14,214.900 12.7982

11 ......... 78,808.127 2,769,097.49 24,512.098 34.1372 66 ......... 18,633.692 249,402.41 13,743.449 12.3845

12 ......... 77,247.099 2,690,289.36 24,496.328 33.8271 67 ......... 17,785.157 230,768.72 13,260.280 11.9754

13 ......... 75,712.352 2,613,042.26 24,476.229 33.5128 68 ......... 16,944.265 212,983.57 12,768.117 11.5697

14 ......... 74,197.481 2,537,329.91 24,445.914 33.1970 69 ......... 16,112.169 196,039.30 12,268.262 11.1672

15 ......... 72,700.276 2,463,132.43 24,403.562 32.8806 70 ......... 15,289.439 179,927.13 11,761.456 10.7681

16 ......... 71,217.233 2,390,432.15 24,346.015 32.5654 71 ......... 14,475.373 164,637.69 11,247.183 10.3736

17 ......... 69,752.257 2,319,214.92 24,277.455 32.2493 72 ......... 13,669.089 150,162.32 10,724.730 9.9855

18 ......... 68,305.448 2,249,462.66 24,198.337 31.9324 73 ......... 12,871.424 136,493.23 10,195.087 9.6044

19 ......... 66,879.635 2,181,157.21 24,111.847 31.6132 74 ......... 12,085.464 123,621.81 9,661.507 9.2290

20 ......... 65,476.746 2,114,277.58 24,020.323 31.2905 75 ......... 11,315.186 111,536.34 9,128.199 8.8572

21 ......... 64,097.221 2,048,800.83 23,924.655 30.9640 76 ......... 10,563.586 100,221.16 8,598.466 8.4874

22 ......... 62,738.859 1,984,703.61 23,823.102 30.6344 77 ......... 9,831.887 89,657.57 8,073.895 8.1191

23 ......... 61,403.415 1,921,964.75 23,717.832 30.3006 78 ......... 9,120.339 79,825.68 7,555.129 7.7525

24 ......... 60,092.490 1,860,561.34 23,610.896 29.9616 79 ......... 8,426.219 70,705.34 7,039.840 7.3911

25 ......... 58,805.710 1,800,468.85 23,502.399 29.6172 80 ......... 7,747.200 62,279.12 6,526.040 7.0389

26 ......... 57,544.495 1,741,663.14 23,394.237 29.2664 81 ......... 7,081.514 54,531.92 6,012.260 6.7006

27 ......... 56,307.201 1,684,118.64 23,285.267 28.9095 82 ......... 6,430.675 47,450.41 5,500.275 6.3788

28 ......... 55,092.284 1,627,811.44 23,174.413 28.5470 83 ......... 5,799.931 41,019.74 4,995.622 6.0725

29 ......... 53,898.294 1,572,719.16 23,060.664 28.1794 84 ......... 5,198.271 35,219.81 4,507.686 5.7753

30 ......... 52,722.770 1,518,820.86 22,941.969 27.8077 85 ......... 4,633.394 30,021.53 4,044.737 5.4794

31 ......... 51,565.586 1,466,098.09 22,818.565 27.4317 86 ......... 4,105.610 25,388.14 3,607.803 5.1838

32 ......... 50,427.144 1,414,532.51 22,691.213 27.0510 87 ......... 3,612.276 21,282.53 3,194.972 4.8917

33 ......... 49,306.759 1,364,105.36 22,559.595 26.6657 88 ......... 3,152.291 17,670.25 2,805.815 4.6055

34 ......... 48,203.272 1,314,798.60 22,422.907 26.2761 89 ......... 2,723.715 14,517.96 2,439.049 4.3302

35 ......... 47,117.102 1,266,595.33 22,281.899 25.8819 90 ......... 2,326.046 11,794.25 2,094.786 4.0705

36 ......... 46,047.151 1,219,478.23 22,135.813 25.4833 91 ......... 1,959.421 9,468.20 1,773.770 3.8321

37 ......... 44,992.873 1,173,431.08 21,984.420 25.0804 92 ......... 1,626.333 7,508.78 1,479.102 3.6170

38 ......... 43,954.226 1,128,438.21 21,827.986 24.6730 93 ......... 1,329.972 5,882.45 1,214.630 3.4230

39 ......... 42,932.544 1,084,483.98 21,668.152 24.2602 94 ......... 1,073.676 4,552.48 984.412 3.2401

40 ......... 41,927.236 1,041,551.44 21,504.659 23.8419 95 ......... 857.095 3,478.80 788.883 3.0588

41 ......... 40,938.629 999,624.20 21,338.155 23.4176 96 ......... 675.710 2,621.71 624.304 2.8799

42 ......... 39,965.272 958,685.57 21,167.516 22.9880 97 ......... 524.470 1,946.00 486.314 2.7104

43 ......... 39,006.237 918,720.30 20,992.114 22.5532 95 ......... 400.608 1,421.53 372.735 2.5484

44 ......... 38,059.823 879,714.06 20,810.528 22.1140 99 ......... 300.967 1,020.92 280.949 2.3921

45 ......... 37,124.451 841,654.24 20,621.427 21.6712 100 ......... 222.107 719.95 207.991 2.2415

46 ......... 36,198.661 804,529.79 20,423.567 21.2254 101 ......... 160.788 497.84 151.027 2.0963

47 ......... 35,281.104 768,331.13 20,215.788 20.7774 102 ......... 114.007 337.06 107.398 1.9565

48 ......... 34,370.538 733,050.02 19,997.008 20.3279 103 ......... 79.042 223.05 74.669 1.8219

49 ......... 33,466.199 698,679.48 19,766.601 19.8772 104 ......... 53.485 144.01 50.661 1.6925

50 ......... 32,568.506 665,213.29 19,525.108 19.4250 105 ......... 35.248 90.52 33.474 1.5681

51 ......... 31,677.123 632,644.78 19,272.323 18.9717 106 ......... 22.573 55.27 21.489 1.4486

52 ......... 30,790.677 600,967.66 19,006.997 18.5178 107 ......... 14.011 32.70 13.370 1.3339

53 ......... 29,908.259 570,176.98 18,728.318 18.0642 108 ......... 8.404 18.69 8.038 1.2238

54 ......... 29,029.044 540,268.72 18,435.539 17.6113 109 ......... 4.855 10.28 4.654 1.1183

x x x x x x x x

77
Table 7.C. -- Actuarial Functions at 3.0 Percent Interest for 1989-91 United States 

Total Other than White Population

x D N M a x D N M a

0 ......... 100,000.000 2,919,360.79 14,970.074 28.1936 55 ......... 16,461.542 266,672.72 8,694.375 15.1997

1 ......... 95,561.165 2,819,360.79 13,443.860 28.5032 56 ......... 15,795.055 250,211.18 8,507.351 14.8411

2 ......... 92,673.202 2,723,799.63 13,339.232 28.3914 57 ......... 15,141.186 234,416.13 8,313.532 14.4820

3 ......... 89,911.753 2,631,126.43 13,277.003 28.2634 58 ......... 14,499.223 219,274.94 8,112.574 14.1232

4 ......... 87,244.986 2,541,214.68 13,229.024 28.1273 59 ......... 13,868.874 204,775.72 7,904.533 13.7651

5 ......... 84,668.503 2,453,969.69 13,193.657 27.9833 60 ......... 13,249.704 190,906.84 7,689.311 13.4084

6 ......... 82,170.605 2,369,301.19 13,161.833 27.8339 61 ......... 12,642.808 177,657.14 7,468.328 13.0520

7 ......... 79,750.455 2,287,130.58 13,135.001 27.6786 62 ......... 12,048.506 165,014.33 7,242.263 12.6958

8 ......... 77,404.733 2,207,380.13 13,112.108 27.5174 63 ......... 11,466.447 152,965.82 7,011.132 12.3403

9 ......... 75,131.066 2,129,975.39 13,092.948 27.3501 64 ......... 10,895.558 141,499.38 6,774.217 11.9869

10 ......... 72,926.412 2,054,844.33 13,076.578 27.1770 65 ......... 10,335.751 130,603.82 6,531.756 11.6361

11 ......... 70,788.616 1,981,917.92 13,062.852 26.9977 66 ......... 9,787.086 120,268.07 6,284.133 11.2884

12 ......... 68,712.784 1,911,129.30 13,048.824 26.8133 67 ......... 9,250.712 110,480.98 6,032.819 10.9430

13 ......... 66,693.736 1,842,416.52 13,031.119 26.6250 68 ......... 8,727.767 101,230.27 5,779.312 10.5986

14 ......... 64,724.755 1,775,722.78 13,004.674 26.4350 69 ......... 8,218.591 92,502.50 5,524.343 10.2553

15 ......... 62,802.982 1,710,998.02 12,968.088 26.2439 70 ......... 7,723.210 84,283.91 5,268.339 9.9131

16 ......... 60,924.539 1,648,195.04 12,918.858 26.0531 71 ......... 7,241.008 76,560.70 5,011.084 9.5732

17 ......... 59,091.956 1,587,270.50 12,860.777 25.8610 72 ......... 6,771.296 69,319.69 4,752.275 9.2373

18 ......... 57,304.456 1,528,178.55 12,794.401 25.6677 73 ......... 6,314.250 62,548.40 4,492.452 8.9059

19 ......... 55,563.538 1,470,874.09 12,722.545 25.4719 74 ......... 5,871.126 56,234.15 4,233.238 8.5781

20 ......... 53,869.883 1,415,310.55 12,647.245 25.2728 75 ......... 5,443.556 50,363.02 3,976.672 8.2519

21 ......... 52,222.912 1,361,440.67 12,569.300 25.0698 76 ......... 5,032.634 44,919.47 3,724.300 7.9256

22 ......... 50,619.919 1,309,217.76 12,487.363 24.8637 77 ......... 4,638.567 39,886.83 3,476.814 7.5990

23 ......... 49,061.442 1,258,597.84 12,403.252 24.6535 78 ......... 4,261.091 35,248.27 3,234.443 7.2721

24 ......... 47,547.855 1,209,536.40 12,318.640 24.4383 79 ......... 3,898.572 30,987.17 2,996.033 6.9483

25 ......... 46,077.953 1,161,988.54 12,233.626 24.2179 80 ......... 3,549.609 27,088.60 2,760.621 6.6314

26 ......... 44,651.947 1,115,910.59 12,149.697 23.9913 81 ......... 3,213.104 23,538.99 2,527.503 6.3259

27 ......... 43,267.670 1,071,258.64 12,065.962 23.7589 82 ......... 2,889.470 20,325.89 2,297.454 6.0345

28 ......... 41,923.091 1,027,990.97 11,981.606 23.5209 83 ......... 2,580.759 17,436.42 2,072.902 5.7563

29 ......... 40,616.312 986,067.88 11,895.888 23.2776 84 ......... 2,290.585 14,855.66 1,857.896 5.4855

30 ......... 39,344.736 945,451.57 11,807.311 23.0299 85 ......... 2,021.854 12,565.07 1,655.881 5.2146

31 ......... 38,107.575 906,106.83 11,716.114 22.7776 86 ......... 1,774.153 10,543.22 1,467.069 4.9427

32 ......... 36,904.445 867,999.26 11,622.913 22.5202 87 ......... 1,545.814 8,769.07 1,290.405 4.6728

33 ......... 35,734.171 831,094.81 11,527.526 22.2577 88 ......... 1,335.874 7,223.25 1,125.488 4.4071

34 ......... 34,595.270 795,360.64 11,429.426 21.9904 89 ......... 1,143.047 5,887.38 971.570 4.1506

35 ......... 33,487.422 760,765.37 11,329.207 21.7179 90 ......... 966.682 4,744.33 828.497 3.9079

36 ......... 32,409.241 727,277.95 11,226.388 21.4405 91 ......... 806.410 3,777.65 696.381 3.6845

37 ......... 31,359.763 694,868.71 11,120.868 21.1580 92 ......... 662.828 2,971.24 576.287 3.4827

38 ......... 30,338.396 663,508.95 11,012.893 20.8703 93 ......... 536.780 2,308.41 469.545 3.3005

39 ......... 29,345.503 633,170.55 10,903.642 20.5764 94 ......... 429.131 1,771.63 377.530 3.1284

40 ......... 28,380.113 603,825.05 10,792.975 20.2763 95 ......... 339.241 1,342.50 300.140 2.9574

41 ......... 27,441.897 575,444.93 10,681.365 19.9696 96 ......... 264.852 1,003.26 235.631 2.7880

42 ......... 26,529.346 548,003.04 10,568.093 19.6565 97 ......... 203.576 738.41 182.069 2.6272

43 ......... 25,641.344 521,473.69 10,452.790 19.3372 95 ......... 153.989 534.83 138.411 2.4732

44 ......... 24,776.299 495,832.35 10,334.580 19.0124 99 ......... 114.564 380.84 103.472 2.3243

45 ......... 23,932.753 471,056.05 10,212.674 18.6825 100 ......... 83.726 266.28 75.970 2.1804

46 ......... 23,109.368 447,123.30 10,086.360 18.3481 101 ......... 60.022 182.55 54.705 2.0414

47 ......... 22,304.921 424,013.93 9,955.000 18.0099 102 ......... 42.146 122.53 38.577 1.9073

48 ......... 21,518.291 401,709.01 9,818.029 17.6683 103 ......... 28.936 80.39 26.595 1.7780

49 ......... 20,748.695 380,190.71 9,675.179 17.3236 104 ......... 19.390 51.45 17.891 1.6534

50 ......... 19,996.095 359,442.02 9,526.910 16.9756 105 ......... 12.655 32.06 11.721 1.5334

51 ......... 19,259.989 339,445.92 9,373.214 16.6244 106 ......... 8.025 19.40 7.460 1.4179

52 ......... 18,539.264 320,185.94 9,213.460 16.2707 107 ......... 4.933 11.38 4.601 1.3068

53 ......... 17,833.120 301,646.67 9,047.294 15.9150 108 ......... 2.930 6.45 2.742 1.2000

54 ......... 17,140.831 283,813.55 8,874.417 15.5577 109 ......... 1.676 3.52 1.574 1.0975

x x x x x x x x

78
Table 7.D. -- Actuarial Functions at 4.0 Percent Interest for 1989-91 United States 

Total Other than White Population

x D N M a x D N M a

0 ......... 100,000.000 2,361,718.95 9,164.656 22.6172 55 ......... 9,675.740 141,079.99 4,249.587 13.5808

1 ......... 94,642.308 2,261,718.95 7,653.117 22.8975 56 ......... 9,194.724 131,404.25 4,140.715 13.2913

2 ......... 90,899.593 2,167,076.64 7,550.492 22.8403 57 ......... 8,729.339 122,209.52 4,028.973 12.9999

3 ......... 87,343.003 2,076,177.05 7,490.040 22.7704 58 ......... 8,278.851 113,480.18 3,914.229 12.7072

4 ......... 83,937.498 1,988,834.05 7,443.880 22.6942 59 ......... 7,842.787 105,201.33 3,796.582 12.4138

5 ......... 80,675.433 1,904,896.55 7,410.181 22.6119 60 ......... 7,420.605 97,358.55 3,676.046 12.1200

6 ......... 77,542.500 1,824,221.12 7,380.149 22.5254 61 ......... 7,012.624 89,937.94 3,553.472 11.8251

7 ......... 74,535.019 1,746,678.62 7,355.072 22.4343 62 ......... 6,618.721 82,925.32 3,429.286 11.5289

8 ......... 71,647.097 1,672,143.60 7,333.882 22.3386 63 ......... 6,238.406 76,306.60 3,303.537 11.2317

9 ......... 68,873.875 1,600,496.50 7,316.317 22.2381 64 ......... 5,870.811 70,068.19 3,175.881 10.9350

10 ......... 66,210.017 1,531,622.62 7,301.455 22.1328 65 ......... 5,515.623 64,197.38 3,046.493 10.6392

11 ......... 63,651.136 1,465,412.61 7,289.113 22.0226 66 ......... 5,172.611 58,681.76 2,915.621 10.3447

12 ......... 61,190.524 1,401,761.47 7,276.621 21.9081 67 ......... 4,842.119 53,509.14 2,784.075 10.0508

13 ......... 58,821.427 1,340,570.95 7,261.006 21.7905 68 ......... 4,524.466 48,667.02 2,652.658 9.7564

14 ......... 56,535.966 1,281,749.52 7,237.907 21.6714 69 ......... 4,219.543 44,142.56 2,521.753 9.4615

15 ......... 54,329.855 1,225,213.55 7,206.257 21.5514 70 ......... 3,927.081 39,923.01 2,391.580 9.1661

16 ......... 52,198.067 1,170,883.70 7,164.078 21.4316 71 ......... 3,646.489 35,995.93 2,262.030 8.8714

17 ......... 50,141.165 1,118,685.63 7,114.794 21.3107 72 ......... 3,377.159 32,349.45 2,132.950 8.5789

18 ......... 48,156.879 1,068,544.47 7,059.014 21.1888 73 ......... 3,118.928 28,972.29 2,004.610 8.2892

19 ......... 46,244.886 1,020,387.59 6,999.210 21.0649 74 ......... 2,872.162 25,853.36 1,877.802 8.0014

20 ......... 44,404.168 974,142.70 6,937.141 20.9381 75 ......... 2,637.389 22,981.20 1,753.497 7.7136

21 ......... 42,632.684 929,738.53 6,873.510 20.8081 76 ......... 2,414.853 20,343.81 1,632.399 7.4245

22 ......... 40,926.719 887,105.85 6,807.263 20.6755 77 ......... 2,204.362 17,928.95 1,514.787 7.1334

23 ......... 39,285.264 846,179.13 6,739.912 20.5394 78 ......... 2,005.506 15,724.59 1,400.714 6.8407

24 ......... 37,707.191 806,893.87 6,672.812 20.3989 79 ......... 1,817.241 13,719.09 1,289.584 6.5494

25 ......... 36,190.144 769,186.68 6,606.041 20.2540 80 ......... 1,638.669 11,901.85 1,180.906 6.2631

26 ......... 34,732.930 732,996.53 6,540.756 20.1038 81 ......... 1,469.060 10,263.18 1,074.322 5.9862

27 ......... 33,332.541 698,263.60 6,476.248 19.9484 82 ......... 1,308.389 8,794.12 970.154 5.7213

28 ......... 31,986.159 664,931.06 6,411.887 19.7881 83 ......... 1,157.364 7,485.73 869.451 5.4679

29 ......... 30,691.150 632,944.90 6,347.115 19.6230 84 ......... 1,017.356 6,328.36 773.957 5.2204

30 ......... 29,444.433 602,253.75 6,280.827 19.4539 85 ......... 889.365 5,311.01 685.095 4.9717

31 ......... 28,244.362 572,809.32 6,213.234 19.2805 86 ......... 772.903 4,421.64 602.840 4.7208

32 ......... 27,089.626 544,564.96 6,144.820 19.1023 87 ......... 666.953 3,648.74 526.617 4.4708

33 ......... 25,978.372 517,475.33 6,075.474 18.9195 88 ......... 570.831 2,981.79 456.147 4.2236

34 ......... 24,908.572 491,496.96 6,004.842 18.7320 89 ......... 483.737 2,410.96 391.008 3.9840

35 ......... 23,879.086 466,588.39 5,933.379 18.5396 90 ......... 405.166 1,927.22 331.042 3.7566

36 ......... 22,888.047 442,709.30 5,860.766 18.3424 91 ......... 334.741 1,522.05 276.201 3.5469

37 ......... 21,933.934 419,821.26 5,786.962 18.1403 92 ......... 272.495 1,187.31 226.829 3.3572

38 ......... 21,015.526 397,887.32 5,712.168 17.9330 93 ......... 218.554 914.82 183.368 3.1858

39 ......... 20,132.286 376,871.80 5,637.217 17.7198 94 ......... 173.044 696.26 146.264 3.0236

40 ......... 19,282.775 356,739.51 5,562.024 17.5004 95 ......... 135.481 523.22 115.357 2.8619

41 ......... 18,466.025 337,456.74 5,486.920 17.2745 96 ......... 104.755 387.74 89.842 2.7014

42 ......... 17,680.304 318,990.71 5,411.431 17.0422 97 ......... 79.745 282.98 68.861 2.5486

43 ......... 16,924.189 301,310.41 5,335.327 16.8035 95 ......... 59.741 203.24 51.924 2.4020

44 ......... 16,195.986 284,386.22 5,258.055 16.5591 99 ......... 44.018 143.50 38.499 2.2599

45 ......... 15,494.141 268,190.23 5,179.132 16.3091 100 ......... 31.860 99.48 28.034 2.1223

46 ......... 14,817.223 252,696.09 5,098.142 16.0542 101 ......... 22.621 67.62 20.020 1.9892

47 ......... 14,163.914 237,878.87 5,014.727 15.7947 102 ......... 15.731 45.00 14.000 1.8605

48 ......... 13,533.006 223,714.95 4,928.585 15.5311 103 ......... 10.697 29.27 9.571 1.7361

49 ......... 12,923.531 210,181.95 4,839.610 15.2635 104 ......... 7.099 18.57 6.384 1.6160

50 ......... 12,335.009 197,258.42 4,748.146 14.9918 105 ......... 4.588 11.47 4.147 1.5001

51 ......... 11,766.687 184,923.41 4,654.248 14.7158 106 ......... 2.882 6.88 2.617 1.3884

52 ......... 11,217.460 173,156.72 4,557.586 14.4364 107 ......... 1.754 4.00 1.600 1.2808

53 ......... 10,686.445 161,939.26 4,458.012 14.1537 108 ......... 1.032 2.25 0.946 1.1771

54 ......... 10,172.828 151,252.82 4,355.412 13.8683 109 ......... 0.585 1.21 0.538 1.0774

x x x x x x x x

79
Table 7.E. -- Actuarial Functions at 5.0 Percent Interest for 1989-91 United States 

Total Other than White Population

x D N M a x D N M a

0 ......... 100,000.000 1,971,675.91 6,110.671 18.7168 55 ......... 5,716.187 75,626.62 2,114.919 12.2303

1 ......... 93,740.952 1,871,675.91 4,613.528 18.9665 56 ......... 5,380.281 69,910.43 2,051.213 11.9938

2 ......... 89,176.417 1,777,934.96 4,512.848 18.9373 57 ......... 5,059.314 64,530.15 1,986.450 11.7547

3 ......... 84,871.180 1,688,758.54 4,454.107 18.8979 58 ......... 4,752.525 59,470.84 1,920.581 11.5135

4 ......... 80,785.270 1,603,887.36 4,409.681 18.8537 59 ......... 4,459.322 54,718.31 1,853.688 11.2705

5 ......... 76,906.227 1,523,102.09 4,377.556 18.8047 60 ......... 4,179.090 50,258.99 1,785.805 11.0263

6 ......... 73,215.670 1,446,195.86 4,349.200 18.7525 61 ......... 3,911.713 46,079.90 1,717.432 10.7800

7 ......... 69,705.757 1,372,980.19 4,325.748 18.6968 62 ......... 3,656.828 42,168.19 1,648.819 10.5314

8 ......... 66,366.807 1,303,274.44 4,306.119 18.6374 63 ......... 3,413.880 38,511.36 1,580.005 10.2808

9 ......... 63,190.367 1,236,907.63 4,290.004 18.5743 64 ......... 3,182.121 35,097.48 1,510.813 10.0296

10 ......... 60,167.796 1,173,717.26 4,276.498 18.5074 65 ......... 2,961.128 31,915.36 1,441.349 9.7781

11 ......... 57,291.554 1,113,549.47 4,265.389 18.4365 66 ......... 2,750.531 28,954.23 1,371.758 9.5268

12 ......... 54,552.248 1,056,257.91 4,254.252 18.3623 67 ......... 2,550.270 26,203.70 1,302.475 9.2749

13 ......... 51,940.734 1,001,705.66 4,240.464 18.2856 68 ......... 2,360.272 23,653.43 1,233.918 9.0215

14 ......... 49,447.163 949,764.93 4,220.261 18.2077 69 ......... 2,180.240 21,293.16 1,166.280 8.7664

15 ......... 47,065.118 900,317.77 4,192.843 18.1292 70 ......... 2,009.799 19,112.92 1,099.660 8.5099

16 ......... 44,787.731 853,252.65 4,156.653 18.0510 71 ......... 1,848.425 17,103.12 1,033.990 8.2528

17 ......... 42,613.097 808,464.92 4,114.768 17.9722 72 ......... 1,695.596 15,254.69 969.182 7.9967

18 ......... 40,536.949 765,851.82 4,067.814 17.8927 73 ......... 1,551.030 13,559.10 905.359 7.7420

19 ......... 38,556.755 725,314.87 4,017.952 17.8116 74 ......... 1,414.712 12,008.07 842.899 7.4880

20 ......... 36,669.462 686,758.12 3,966.695 17.7283 75 ......... 1,286.700 10,593.35 782.254 7.2330

21 ......... 34,871.251 650,088.65 3,914.648 17.6425 76 ......... 1,166.911 9,306.65 723.737 6.9755

22 ......... 33,157.045 615,217.40 3,860.978 17.5547 77 ......... 1,055.052 8,139.74 667.446 6.7150

23 ......... 31,524.093 582,060.36 3,806.933 17.4640 78 ......... 950.734 7,084.69 613.368 6.4518

24 ......... 29,969.614 550,536.27 3,753.601 17.3698 79 ......... 853.280 6,133.96 561.187 6.1887

25 ......... 28,489.926 520,566.65 3,701.037 17.2720 80 ......... 762.105 5,280.68 510.644 5.9291

26 ......... 27,082.358 492,076.73 3,650.133 17.1696 81 ......... 676.717 4,518.57 461.546 5.6772

27 ......... 25,742.902 464,994.37 3,600.313 17.0630 82 ......... 596.964 3,841.86 414.018 5.4357

28 ......... 24,467.816 439,251.47 3,551.080 16.9522 83 ......... 523.028 3,244.89 368.510 5.2040

29 ......... 23,253.607 414,783.65 3,502.005 16.8374 84 ......... 455.378 2,721.86 325.766 4.9771

30 ......... 22,096.546 391,530.04 3,452.259 16.7191 85 ......... 394.297 2,266.48 286.369 4.7482

31 ......... 20,994.088 369,433.50 3,402.017 16.5970 86 ......... 339.401 1,872.19 250.249 4.5162

32 ......... 19,944.002 348,439.41 3,351.649 16.4709 87 ......... 290.086 1,532.79 217.096 4.2839

33 ......... 18,943.719 328,495.41 3,301.081 16.3406 88 ......... 245.914 1,242.70 186.738 4.0534

34 ......... 17,990.622 309,551.69 3,250.066 16.2063 89 ......... 206.409 996.79 158.943 3.8292

35 ......... 17,082.802 291,561.07 3,198.942 16.0675 90 ......... 171.237 790.38 133.600 3.6157

36 ......... 16,217.884 274,478.26 3,147.490 15.9244 91 ......... 140.125 619.14 110.643 3.4185

37 ......... 15,393.806 258,260.38 3,095.693 15.7769 92 ......... 112.982 479.02 90.172 3.2397

38 ......... 14,608.775 242,866.57 3,043.700 15.6247 93 ......... 89.754 366.03 72.324 3.0782

39 ......... 13,861.514 228,257.80 2,992.095 15.4670 94 ......... 70.387 276.28 57.231 2.9251

40 ......... 13,150.163 214,396.29 2,940.816 15.3037 95 ......... 54.584 205.89 44.779 2.7721

41 ......... 12,473.234 201,246.12 2,890.086 15.1342 96 ......... 41.803 151.31 34.598 2.6196

42 ......... 11,828.766 188,772.89 2,839.580 14.9588 97 ......... 31.519 109.51 26.305 2.4743

43 ......... 11,215.060 176,944.12 2,789.149 14.7774 95 ......... 23.388 77.99 19.674 2.3345

44 ......... 10,630.291 165,729.06 2,738.431 14.5903 99 ......... 17.068 54.60 14.469 2.1988

45 ......... 10,072.779 155,098.77 2,687.123 14.3978 100 ......... 12.236 37.53 10.449 2.0672

46 ......... 9,540.973 145,025.99 2,634.973 14.2003 101 ......... 8.605 25.29 7.401 1.9395

47 ......... 9,033.440 135,485.02 2,581.773 13.9982 102 ......... 5.927 16.69 5.132 1.8158

48 ......... 8,548.860 126,451.58 2,527.356 13.7916 103 ......... 3.992 10.76 3.479 1.6960

49 ......... 8,086.101 117,902.72 2,471.686 13.5809 104 ......... 2.624 6.77 2.302 1.5802

50 ......... 7,644.366 109,816.62 2,415.003 13.3657 105 ......... 1.680 4.15 1.482 1.4682

51 ......... 7,222.711 102,172.25 2,357.366 13.1460 106 ......... 1.045 2.47 0.928 1.3601

52 ......... 6,820.004 94,949.54 2,298.597 12.9222 107 ......... 0.630 1.42 0.562 1.2557

53 ......... 6,435.279 88,129.54 2,238.634 12.6947 108 ......... 0.367 0.79 0.329 1.1551

54 ......... 6,067.641 81,694.26 2,177.438 12.4639 109 ......... 0.206 0.42 0.186 1.0581

x x x x x x x x

80
Table 7.F. -- Actuarial Functions at 6.0 Percent Interest for 1989-91 United States 

Total Other than White Population

x D N M a x D N M a

0 ......... 100,000.000 1,688,336.49 4,433.783 15.8834 55 ......... 3,393.871 41,041.81 1,070.749 11.0929

1 ......... 92,856.604 1,588,336.49 2,950.765 16.1053 56 ......... 3,164.297 37,647.93 1,033.282 10.8977

2 ......... 87,501.780 1,495,479.89 2,851.975 16.0909 57 ......... 2,947.456 34,483.64 995.552 10.6995

3 ......... 82,491.755 1,407,978.11 2,794.881 16.0681 58 ......... 2,742.607 31,536.18 957.540 10.4986

4 ......... 77,779.637 1,325,486.35 2,752.108 16.0416 59 ......... 2,549.127 28,793.57 919.302 10.2955

5 ......... 73,346.379 1,247,706.72 2,721.470 16.0112 60 ......... 2,366.398 26,244.45 880.863 10.0905

6 ......... 69,167.908 1,174,360.34 2,694.682 15.9784 61 ......... 2,194.100 23,878.05 842.513 9.8828

7 ......... 65,230.797 1,105,192.43 2,672.735 15.9428 62 ......... 2,031.784 21,683.95 804.390 9.6724

8 ......... 61,520.293 1,039,961.63 2,654.540 15.9044 63 ......... 1,878.904 19,652.17 766.517 9.4594

9 ......... 58,023.214 978,441.34 2,639.742 15.8629 64 ......... 1,734.828 17,773.26 728.794 9.2450

10 ......... 54,726.597 920,418.13 2,627.458 15.8185 65 ......... 1,599.118 16,038.43 691.282 9.0296

11 ......... 51,618.856 865,691.53 2,617.449 15.7708 66 ......... 1,471.374 14,439.32 654.054 8.8135

12 ......... 48,687.095 814,072.67 2,607.509 15.7205 67 ......... 1,351.376 12,967.94 617.342 8.5961

13 ......... 45,919.032 765,385.58 2,595.320 15.6682 68 ......... 1,238.898 11,616.57 581.357 8.3765

14 ......... 43,302.149 719,466.55 2,577.627 15.6150 69 ......... 1,133.603 10,377.67 546.188 8.1546

15 ......... 40,827.300 676,164.40 2,553.843 15.5616 70 ......... 1,035.125 9,244.06 511.877 7.9304

16 ......... 38,485.223 635,337.10 2,522.745 15.5086 71 ......... 943.030 8,208.94 478.373 7.7049

17 ......... 36,271.163 596,851.88 2,487.094 15.4553 72 ......... 856.899 7,265.91 445.621 7.4793

18 ......... 34,178.489 560,580.71 2,447.506 15.4016 73 ......... 776.446 6,409.01 413.671 7.2543

19 ......... 32,202.213 526,402.22 2,405.861 15.3468 74 ......... 701.523 5,632.56 382.699 7.0290

20 ......... 30,337.041 494,200.01 2,363.455 15.2903 75 ......... 632.026 4,931.04 352.910 6.8020

21 ......... 28,577.197 463,862.97 2,320.803 15.2319 76 ......... 567.778 4,299.02 324.438 6.5716

22 ......... 26,916.052 435,285.77 2,277.235 15.1720 77 ......... 508.509 3,731.24 297.307 6.3376

23 ......... 25,349.043 408,369.72 2,233.776 15.1099 78 ......... 453.907 3,222.73 271.488 6.1000

24 ......... 23,871.712 383,020.68 2,191.296 15.0450 79 ......... 403.537 2,768.82 246.811 5.8614

25 ......... 22,479.009 359,148.97 2,149.822 14.9771 80 ......... 357.017 2,365.28 223.133 5.6251

26 ......... 21,166.827 336,669.96 2,110.037 14.9055 81 ......... 314.026 2,008.27 200.350 5.3952

27 ......... 19,930.134 315,503.13 2,071.466 14.8305 82 ......... 274.404 1,694.24 178.503 5.1743

28 ......... 18,764.256 295,573.00 2,033.710 14.7519 83 ......... 238.150 1,419.84 157.782 4.9620

29 ......... 17,664.848 276,808.74 1,996.429 14.6700 84 ......... 205.391 1,181.69 138.503 4.7534

30 ......... 16,627.518 259,143.89 1,958.995 14.5852 85 ......... 176.163 976.30 120.901 4.5420

31 ......... 15,648.887 242,516.37 1,921.545 14.4974 86 ......... 150.206 800.13 104.916 4.3269

32 ......... 14,725.911 226,867.49 1,884.355 14.4060 87 ......... 127.170 649.93 90.382 4.1107

33 ......... 13,855.384 212,141.58 1,847.370 14.3111 88 ......... 106.789 522.76 77.199 3.8953

34 ......... 13,034.157 198,286.19 1,810.410 14.2128 89 ......... 88.788 415.97 65.243 3.6850

35 ......... 12,259.685 185,252.03 1,773.720 14.1107 90 ......... 72.964 327.18 54.444 3.4842

36 ......... 11,529.163 172,992.35 1,737.144 14.0048 91 ......... 59.144 254.22 44.754 3.2983

37 ......... 10,840.094 161,463.19 1,700.669 13.8950 92 ......... 47.237 195.07 36.195 3.1297

38 ......... 10,190.237 150,623.09 1,664.402 13.7811 93 ......... 37.172 147.84 28.804 2.9771

39 ......... 9,577.774 140,432.85 1,628.744 13.6624 94 ......... 28.876 110.66 22.612 2.8324

40 ......... 9,000.538 130,855.08 1,593.647 13.5386 95 ......... 22.181 81.79 17.552 2.6873

41 ......... 8,456.679 121,854.54 1,559.252 13.4093 96 ......... 16.827 59.61 13.453 2.5423

42 ......... 7,944.081 113,397.86 1,525.334 13.2745 97 ......... 12.568 42.78 10.147 2.4039

43 ......... 7,460.866 105,453.78 1,491.784 13.1343 95 ......... 9.238 30.21 7.528 2.2705

44 ......... 7,005.131 97,992.92 1,458.362 12.9887 99 ......... 6.678 20.97 5.491 2.1408

45 ......... 6,575.122 90,987.79 1,424.870 12.8382 100 ......... 4.742 14.30 3.933 2.0146

46 ......... 6,169.225 84,412.66 1,391.150 12.6829 101 ......... 3.304 9.55 2.763 1.8920

47 ......... 5,785.949 78,243.44 1,357.075 12.5230 102 ......... 2.254 6.25 1.900 1.7731

48 ......... 5,423.917 72,457.49 1,322.550 12.3589 103 ......... 1.504 4.00 1.278 1.6577

49 ......... 5,081.915 67,033.57 1,287.562 12.1906 104 ......... 0.979 2.49 0.838 1.5458

50 ......... 4,758.972 61,951.66 1,252.274 12.0179 105 ......... 0.621 1.51 0.535 1.4376

51 ......... 4,454.053 57,192.69 1,216.731 11.8406 106 ......... 0.383 0.89 0.332 1.3329

52 ......... 4,166.037 52,738.63 1,180.832 11.6592 107 ......... 0.229 0.51 0.200 1.2316

53 ......... 3,893.941 48,572.60 1,144.549 11.4739 108 ......... 0.132 0.28 0.116 1.1338

54 ......... 3,636.849 44,678.65 1,107.869 11.2850 109 ......... 0.073 0.15 0.065 1.0394

x x x x x x x x

81
Table 7.G. -- Actuarial Functions at 7.0 Percent Interest for 1989-91 United States 

Total Other than White Population

x D N M a x D N M a

0 ......... 100,000.000 1,475,530.41 3,469.973 13.7553 55 ......... 2,024.930 22,530.55 550.969 10.1266

1 ......... 91,988.785 1,375,530.41 2,000.814 13.9532 56 ......... 1,870.312 20,505.62 528.824 9.9637

2 ......... 85,873.875 1,283,541.62 1,903.863 13.9468 57 ......... 1,725.863 18,635.30 506.731 9.7977

3 ......... 80,200.450 1,197,667.75 1,848.355 13.9334 58 ......... 1,590.907 16,909.44 484.681 9.6288

4 ......... 74,912.495 1,117,467.30 1,807.158 13.9170 59 ......... 1,464.855 15,318.53 462.708 9.4574

5 ......... 69,982.445 1,042,554.80 1,777.926 13.8974 60 ......... 1,347.141 13,853.68 440.825 9.2838

6 ......... 65,378.834 972,572.36 1,752.605 13.8760 61 ......... 1,237.382 12,506.54 419.197 9.1073

7 ......... 61,081.163 907,193.52 1,732.054 13.8523 62 ......... 1,135.133 11,269.16 397.899 8.9276

8 ......... 57,068.321 846,112.36 1,715.176 13.8263 63 ......... 1,039.911 10,134.02 376.937 8.7451

9 ......... 53,321.281 789,044.04 1,701.577 13.7979 64 ......... 951.196 9,094.11 356.254 8.5607

10 ......... 49,821.789 735,722.76 1,690.394 13.7671 65 ......... 868.593 8,142.92 335.878 8.3748

11 ......... 46,553.393 685,900.97 1,681.367 13.7336 66 ......... 791.737 7,274.32 315.847 8.1878

12 ......... 43,498.964 639,347.58 1,672.487 13.6980 67 ......... 720.371 6,482.59 296.276 7.9990

13 ......... 40,642.448 595,848.61 1,661.698 13.6607 68 ......... 654.241 5,762.22 277.273 7.8075

14 ......... 37,968.084 555,206.16 1,646.185 13.6230 69 ......... 593.042 5,107.97 258.875 7.6132

15 ......... 35,463.531 517,238.08 1,625.526 13.5851 70 ......... 536.462 4,514.93 241.093 7.4161

16 ......... 33,116.727 481,774.55 1,598.766 13.5478 71 ......... 484.165 3,978.47 223.892 7.2172

17 ......... 30,919.821 448,657.82 1,568.374 13.5104 72 ......... 435.833 3,494.31 207.233 7.0175

18 ......... 28,863.596 417,738.00 1,534.942 13.4728 73 ......... 391.222 3,058.47 191.135 6.8177

19 ......... 26,940.483 388,874.41 1,500.102 13.4346 74 ......... 350.168 2,667.25 175.675 6.6171

20 ......... 25,142.877 361,933.92 1,464.957 13.3951 75 ......... 312.530 2,317.08 160.945 6.4140

21 ......... 23,462.996 336,791.05 1,429.937 13.3541 76 ......... 278.136 2,004.55 146.997 6.2071

22 ......... 21,892.597 313,328.05 1,394.500 13.3121 77 ......... 246.774 1,726.42 133.831 5.9959

23 ......... 20,425.354 291,435.45 1,359.483 13.2683 78 ......... 218.218 1,479.64 121.418 5.7806

24 ......... 19,055.207 271,010.10 1,325.574 13.2224 79 ......... 192.189 1,261.43 109.666 5.5635

25 ......... 17,775.808 251,954.89 1,292.778 13.1740 80 ......... 168.444 1,069.24 98.494 5.3477

26 ......... 16,581.737 234,179.08 1,261.610 13.1227 81 ......... 146.776 900.79 87.845 5.1372

27 ......... 15,467.018 217,597.35 1,231.677 13.0685 82 ......... 127.058 754.02 77.729 4.9344

28 ......... 14,426.129 202,130.33 1,202.650 13.0114 83 ......... 109.240 626.96 68.224 4.7393

29 ......... 13,453.970 187,704.20 1,174.256 12.9516 84 ......... 93.333 517.72 59.464 4.5470

30 ......... 12,545.560 174,250.23 1,146.012 12.8894 85 ......... 79.304 424.39 51.540 4.3514

31 ......... 11,696.830 161,704.67 1,118.020 12.8247 86 ......... 66.987 345.08 44.411 4.1515

32 ......... 10,904.079 150,007.84 1,090.482 12.7570 87 ......... 56.183 278.10 37.990 3.9498

33 ......... 10,163.598 139,103.76 1,063.351 12.6865 88 ......... 46.738 221.91 32.220 3.7480

34 ......... 9,471.830 128,940.16 1,036.493 12.6130 89 ......... 38.496 175.17 27.036 3.5504

35 ......... 8,825.765 119,468.33 1,010.080 12.5363 90 ......... 31.340 136.68 22.398 3.3612

36 ......... 8,222.293 110,642.57 983.994 12.4564 91 ......... 25.166 105.34 18.275 3.1857

37 ......... 7,658.616 102,420.28 958.224 12.3732 92 ......... 19.912 80.17 14.667 3.0263

38 ......... 7,132.202 94,761.66 932.841 12.2865 93 ......... 15.523 60.26 11.580 2.8820

39 ......... 6,640.886 87,629.46 908.117 12.1954 94 ......... 11.946 44.74 9.019 2.7450

40 ......... 6,182.327 80,988.57 884.009 12.1000 95 ......... 9.090 32.79 6.945 2.6072

41 ......... 5,754.472 74,806.25 860.605 11.9997 96 ......... 6.832 23.70 5.281 2.4692

42 ......... 5,355.146 69,051.77 837.740 11.8945 97 ......... 5.055 16.87 3.951 2.3372

43 ......... 4,982.405 63,696.63 815.336 11.7843 95 ......... 3.681 11.81 2.908 2.2098

44 ......... 4,634.342 58,714.22 793.225 11.6694 99 ......... 2.636 8.13 2.104 2.0855

45 ......... 4,309.211 54,079.88 771.275 11.5498 100 ......... 1.854 5.50 1.495 1.9645

46 ......... 4,005.407 49,770.67 749.382 11.4259 101 ......... 1.280 3.64 1.041 1.8467

47 ......... 3,721.454 45,765.26 727.465 11.2977 102 ......... 0.865 2.36 0.710 1.7322

48 ......... 3,455.996 42,043.81 705.467 11.1655 103 ......... 0.572 1.50 0.474 1.6209

49 ......... 3,207.818 38,587.81 683.382 11.0293 104 ......... 0.369 0.93 0.308 1.5129

50 ......... 2,975.895 35,379.99 661.315 10.8889 105 ......... 0.232 0.56 0.195 1.4081

51 ......... 2,759.191 32,404.10 639.297 10.7441 106 ......... 0.141 0.33 0.120 1.3066

52 ......... 2,556.653 29,644.91 617.266 10.5952 107 ......... 0.084 0.18 0.072 1.2083

53 ......... 2,367.337 27,088.26 595.208 10.4425 108 ......... 0.048 0.10 0.041 1.1132

54 ......... 2,190.373 24,720.92 573.116 10.2862 109 ......... 0.026 0.05 0.023 1.0213

x x x x x x x x

82
Table 7.H. -- Actuarial Functions at 8.0 Percent Interest for 1989-91 United States 

Total Other than White Population

x D N M a x D N M a

0 ......... 100,000.000 1,311,000.55 2,888.848 12.1100 55 ......... 1,213.979 12,502.35 287.879 9.2987

1 ......... 91,137.037 1,211,000.55 1,433.293 12.2877 56 ......... 1,110.901 11,288.37 274.725 9.1615

2 ......... 84,290.981 1,119,863.51 1,338.128 12.2857 57 ......... 1,015.612 10,177.47 261.725 9.0210

3 ......... 77,993.224 1,035,572.53 1,284.148 12.2777 58 ......... 927.526 9,161.86 248.869 8.8777

4 ......... 72,176.256 957,579.30 1,244.456 12.2672 59 ......... 846.128 8,234.34 236.177 8.7318

5 ......... 66,801.963 885,403.05 1,216.552 12.2541 60 ......... 770.929 7,388.21 223.654 8.5835

6 ......... 61,829.723 818,601.08 1,192.606 12.2396 61 ......... 701.561 6,617.28 211.392 8.4322

7 ......... 57,230.488 756,771.36 1,173.351 12.2232 62 ......... 637.629 5,915.72 199.428 8.2777

8 ......... 52,975.525 699,540.87 1,157.683 12.2050 63 ......... 578.732 5,278.09 187.762 8.1201

9 ......... 49,038.906 646,565.35 1,145.177 12.1847 64 ......... 524.459 4,699.36 176.358 7.9604

10 ......... 45,396.204 597,526.44 1,134.986 12.1625 65 ......... 474.480 4,174.90 165.228 7.7989

11 ......... 42,025.374 552,130.24 1,126.838 12.1380 66 ......... 428.492 3,700.42 154.387 7.6359

12 ......... 38,904.441 510,104.86 1,118.895 12.1117 67 ......... 386.258 3,271.93 143.893 7.4708

13 ......... 36,013.070 471,200.42 1,109.335 12.0842 68 ......... 347.551 2,885.67 133.798 7.3029

14 ......... 33,331.817 435,187.35 1,095.717 12.0562 69 ......... 312.124 2,538.12 124.115 7.1318

15 ......... 30,844.825 401,855.54 1,077.748 12.0283 70 ......... 279.731 2,225.99 114.843 6.9576

16 ......... 28,536.963 371,010.71 1,054.689 12.0011 71 ......... 250.124 1,946.26 105.956 6.7812

17 ......... 26,397.168 342,473.75 1,028.743 11.9739 72 ......... 223.070 1,696.14 97.430 6.6036

18 ......... 24,413.545 316,076.58 1,000.465 11.9468 73 ......... 198.383 1,473.07 89.267 6.4254

19 ......... 22,575.938 291,663.04 971.269 11.9192 74 ......... 175.921 1,274.68 81.500 6.2458

20 ......... 20,874.468 269,087.10 942.090 11.8907 75 ......... 155.558 1,098.76 74.168 6.0634

21 ......... 19,299.406 248,212.63 913.285 11.8612 76 ......... 137.157 943.21 67.290 5.8768

22 ......... 17,840.942 228,913.22 884.407 11.8308 77 ......... 120.565 806.05 60.858 5.6856

23 ......... 16,491.118 211,072.28 856.134 11.7991 78 ......... 105.626 685.48 54.850 5.4897

24 ......... 15,242.429 194,581.16 829.010 11.7658 79 ......... 92.166 579.86 49.213 5.2915

25 ......... 14,087.369 179,338.73 803.019 11.7305 80 ......... 80.031 487.69 43.906 5.0938

26 ......... 13,019.389 165,251.36 778.547 11.6927 81 ......... 69.090 407.66 38.893 4.9004

27 ......... 12,031.705 152,231.98 755.262 11.6526 82 ......... 59.255 338.57 34.175 4.7138

28 ......... 11,118.096 140,200.27 732.891 11.6101 83 ......... 50.474 279.32 29.784 4.5339

29 ......... 10,272.853 129,082.17 711.211 11.5654 84 ......... 42.725 228.84 25.773 4.3562

30 ......... 9,490.535 118,809.32 689.845 11.5187 85 ......... 35.966 186.12 22.180 4.1748

31 ......... 8,766.553 109,318.79 668.865 11.4700 86 ......... 30.099 150.15 18.977 3.9886

32 ......... 8,096.731 100,552.23 648.417 11.4189 87 ......... 25.011 120.05 16.118 3.8000

33 ......... 7,477.014 92,455.50 628.458 11.3653 88 ......... 20.613 95.04 13.573 3.6106

34 ......... 6,903.585 84,978.49 608.882 11.3093 89 ......... 16.821 74.43 11.308 3.4246

35 ......... 6,373.135 78,074.90 589.809 11.2506 90 ......... 13.567 57.61 9.300 3.2460

36 ......... 5,882.389 71,701.77 571.147 11.1892 91 ......... 10.794 44.04 7.532 3.0800

37 ......... 5,428.391 65,819.38 552.882 11.1250 92 ......... 8.461 33.25 5.999 2.9291

38 ......... 5,008.463 60,390.99 535.056 11.0578 93 ......... 6.535 24.78 4.699 2.7924

39 ......... 4,620.265 55,382.52 517.855 10.9869 94 ......... 4.983 18.25 3.631 2.6625

40 ......... 4,261.406 50,762.26 501.238 10.9121 95 ......... 3.757 13.27 2.774 2.5315

41 ......... 3,929.763 46,500.85 485.255 10.8330 96 ......... 2.797 9.51 2.093 2.3999

42 ......... 3,623.200 42,571.09 469.785 10.7496 97 ......... 2.050 6.71 1.553 2.2738

43 ......... 3,339.796 38,947.89 454.767 10.6618 95 ......... 1.479 4.66 1.134 2.1520

44 ......... 3,077.720 35,608.10 440.083 10.5696 99 ......... 1.050 3.18 0.814 2.0329

45 ......... 2,835.298 32,530.38 425.641 10.4734 100 ......... 0.731 2.13 0.573 1.9167

46 ......... 2,611.005 29,695.08 411.369 10.3730 101 ......... 0.500 1.40 0.396 1.8035

47 ......... 2,403.442 27,084.07 397.215 10.2689 102 ......... 0.335 0.90 0.268 1.6931

48 ......... 2,211.334 24,680.63 383.139 10.1610 103 ......... 0.219 0.57 0.177 1.5857

49 ......... 2,033.531 22,469.30 369.139 10.0494 104 ......... 0.140 0.35 0.114 1.4813

50 ......... 1,869.040 20,435.77 355.280 9.9338 105 ......... 0.087 0.21 0.072 1.3798

51 ......... 1,716.892 18,566.73 341.579 9.8141 106 ......... 0.053 0.12 0.044 1.2814

52 ......... 1,576.133 16,849.83 327.997 9.6906 107 ......... 0.031 0.07 0.026 1.1859

53 ......... 1,445.910 15,273.70 314.525 9.5634 108 ......... 0.018 0.04 0.015 1.0934

54 ......... 1,325.437 13,827.79 301.157 9.4326 109 ......... 0.010 0.02 0.008 1.0039

x x x x x x x x

83
Table 7.I. -- Actuarial Functions at 9.0 Percent Interest for 1989-91 United States 

Total Other than White Population

x D N M a x D N M a

0 ......... 100,000.000 1,180,580.25 2,520.897 10.8058 55 ......... 731.241 7,008.04 152.595 8.5838

1 ......... 90,300.917 1,080,580.25 1,078.695 10.9664 56 ......... 663.013 6,276.80 144.745 8.4671

2 ......... 82,751.452 990,279.33 985.269 10.9669 57 ......... 600.581 5,613.79 137.057 8.3473

3 ......... 75,866.255 907,527.88 932.760 10.9622 58 ......... 543.459 5,013.21 129.524 8.2246

4 ......... 69,563.814 831,661.62 894.505 10.9554 59 ......... 491.218 4,469.75 122.156 8.0993

5 ......... 63,793.365 762,097.81 867.858 10.9463 60 ......... 443.455 3,978.53 114.953 7.9717

6 ......... 58,503.365 698,304.44 845.200 10.9361 61 ......... 399.851 3,535.08 107.964 7.8410

7 ......... 53,654.760 639,801.08 827.148 10.9244 62 ......... 360.079 3,135.23 101.208 7.7070

8 ......... 49,209.996 586,146.32 812.594 10.9111 63 ......... 323.821 2,775.15 94.680 7.5700

9 ......... 45,135.275 536,936.32 801.083 10.8962 64 ......... 290.761 2,451.33 88.358 7.4307

10 ......... 41,399.216 491,801.05 791.790 10.8795 65 ......... 260.639 2,160.56 82.244 7.2895

11 ......... 37,973.569 450,401.83 784.427 10.8609 66 ......... 233.218 1,899.93 76.343 7.1466

12 ......... 34,831.026 412,428.26 777.316 10.8408 67 ......... 208.302 1,666.71 70.684 7.0014

13 ......... 31,946.589 377,597.24 768.835 10.8196 68 ......... 185.709 1,458.41 65.290 6.8532

14 ......... 29,296.827 345,650.65 756.866 10.7982 69 ......... 165.248 1,272.70 60.163 6.7017

15 ......... 26,862.175 316,353.82 741.217 10.7769 70 ......... 146.740 1,107.45 55.299 6.5470

16 ......... 24,624.299 289,491.65 721.319 10.7563 71 ......... 130.005 960.71 50.681 6.3898

17 ......... 22,568.917 264,867.35 699.136 10.7359 72 ......... 114.880 830.70 46.290 6.2311

18 ......... 20,681.473 242,298.43 675.181 10.7157 73 ......... 101.229 715.82 42.124 6.0713

19 ......... 18,949.323 221,616.96 650.675 10.6952 74 ......... 88.944 614.59 38.197 5.9099

20 ......... 17,360.433 202,667.63 626.409 10.6741 75 ......... 77.927 525.65 34.525 5.7454

21 ......... 15,903.267 185,307.20 602.672 10.6521 76 ......... 68.079 447.72 31.111 5.5766

22 ......... 14,566.575 169,403.93 579.094 10.6296 77 ......... 59.294 379.65 27.947 5.4028

23 ......... 13,340.958 154,837.36 556.222 10.6062 78 ......... 51.470 320.35 25.019 5.2240

24 ......... 12,217.670 141,496.40 534.481 10.5813 79 ......... 44.499 268.88 22.298 5.0424

25 ......... 11,188.229 129,278.73 513.838 10.5549 80 ......... 38.286 224.38 19.759 4.8607

26 ......... 10,245.173 118,090.50 494.581 10.5265 81 ......... 32.749 186.10 17.383 4.6825

27 ......... 9,381.086 107,845.33 476.426 10.4960 82 ......... 27.829 153.35 15.167 4.5103

28 ......... 8,589.218 98,464.24 459.143 10.4637 83 ......... 23.488 125.52 13.124 4.3440

29 ......... 7,863.422 89,875.02 442.548 10.4295 84 ......... 19.699 102.03 11.275 4.1794

30 ......... 7,197.944 82,011.60 426.343 10.3938 85 ......... 16.431 82.33 9.633 4.0108

31 ......... 6,587.852 74,813.66 410.578 10.3563 86 ......... 13.624 65.90 8.183 3.8370

32 ......... 6,028.676 68,225.81 395.352 10.3169 87 ......... 11.217 52.28 6.901 3.6603

33 ......... 5,516.171 62,197.13 380.628 10.2754 88 ......... 9.160 41.06 5.770 3.4823

34 ......... 5,046.397 56,680.96 366.318 10.2320 89 ......... 7.407 31.90 4.773 3.3068

35 ......... 4,615.908 51,634.56 352.504 10.1862 90 ......... 5.919 24.49 3.897 3.1378

36 ......... 4,221.386 47,018.66 339.111 10.1382 91 ......... 4.666 18.57 3.132 2.9806

37 ......... 3,859.843 42,797.27 326.124 10.0878 92 ......... 3.624 13.91 2.476 2.8375

38 ......... 3,528.582 38,937.43 313.565 10.0349 93 ......... 2.773 10.28 1.924 2.7079

39 ......... 3,225.224 35,408.84 301.558 9.9787 94 ......... 2.095 7.51 1.475 2.5845

40 ......... 2,947.428 32,183.62 290.065 9.9192 95 ......... 1.565 5.41 1.118 2.4598

41 ......... 2,693.109 29,236.19 279.111 9.8559 96 ......... 1.155 3.85 0.837 2.3342

42 ......... 2,460.238 26,543.08 268.607 9.7888 97 ......... 0.839 2.70 0.616 2.2136

43 ......... 2,246.995 24,082.85 258.503 9.7178 95 ......... 0.599 1.86 0.446 2.0970

44 ......... 2,051.674 21,835.85 248.714 9.6429 99 ......... 0.421 1.26 0.318 1.9827

45 ......... 1,872.731 19,784.18 239.175 9.5643 100 ......... 0.291 0.84 0.222 1.8711

46 ......... 1,708.762 17,911.45 229.835 9.4821 101 ......... 0.197 0.54 0.152 1.7621

47 ......... 1,558.493 16,202.68 220.657 9.3964 102 ......... 0.131 0.35 0.102 1.6556

48 ......... 1,420.766 14,644.19 211.613 9.3072 103 ......... 0.085 0.22 0.067 1.5519

49 ......... 1,294.543 13,223.42 202.700 9.2147 104 ......... 0.054 0.13 0.043 1.4509

50 ......... 1,178.912 11,928.88 193.959 9.1185 105 ......... 0.033 0.08 0.027 1.3526

51 ......... 1,073.008 10,749.97 185.396 9.0185 106 ......... 0.020 0.04 0.016 1.2571

52 ......... 976.001 9,676.96 176.986 8.9149 107 ......... 0.012 0.02 0.009 1.1643

53 ......... 887.148 8,700.96 168.720 8.8078 108 ......... 0.006 0.01 0.005 1.0742

54 ......... 805.770 7,813.81 160.593 8.6973 109 ......... 0.004 0.01 0.003 0.9870

x x x x x x x x

84
Table 7.J. -- Actuarial Functions at 10.0 Percent Interest for 1989-91 United States 

Total Other than White Population

x D N M a x D N M a

0 ......... 100,000.000 1,074,960.37 2,276.330 9.7496 55 ......... 442.507 3,965.74 81.985 7.9620

1 ......... 89,480.000 974,960.37 847.239 9.8958 56 ......... 397.572 3,523.23 77.278 7.8619

2 ......... 81,253.719 885,480.37 755.504 9.8977 57 ......... 356.861 3,125.66 72.710 7.7588

3 ......... 73,815.928 804,226.65 704.415 9.8950 58 ......... 319.984 2,768.80 68.275 7.6529

4 ......... 67,068.506 730,410.72 667.532 9.8905 59 ......... 286.595 2,448.81 63.976 7.5445

5 ......... 60,945.912 663,342.21 642.074 9.8841 60 ......... 256.377 2,162.22 59.811 7.4338

6 ......... 55,383.924 602,396.30 620.624 9.8767 61 ......... 229.066 1,905.84 55.808 7.3201

7 ......... 50,332.088 547,012.38 603.690 9.8681 62 ......... 204.406 1,676.78 51.972 7.2031

8 ......... 45,742.915 496,680.29 590.161 9.8581 63 ......... 182.152 1,472.37 48.301 7.0832

9 ......... 41,573.865 450,937.37 579.559 9.8467 64 ......... 162.069 1,290.22 44.777 6.9609

10 ......... 37,785.941 409,363.51 571.077 9.8338 65 ......... 143.958 1,128.15 41.400 6.8366

11 ......... 34,344.196 371,577.57 564.417 9.8192 66 ......... 127.642 984.19 38.170 6.7106

12 ......... 31,215.624 337,233.37 558.045 9.8034 67 ......... 112.969 856.55 35.101 6.5821

13 ......... 28,370.309 306,017.75 550.513 9.7865 68 ......... 99.800 743.58 32.202 6.4507

14 ......... 25,780.656 277,647.44 539.980 9.7696 69 ......... 87.998 643.78 29.472 6.3159

15 ......... 23,423.315 251,866.78 526.335 9.7528 70 ......... 77.431 555.78 26.906 6.1777

16 ......... 21,276.730 228,443.47 509.142 9.7368 71 ......... 67.977 478.35 24.491 6.0369

17 ......... 19,323.489 207,166.74 490.149 9.7210 72 ......... 59.522 410.37 22.216 5.8945

18 ......... 17,546.484 187,843.25 469.825 9.7055 73 ......... 51.972 350.85 20.077 5.7507

19 ......... 15,930.747 170,296.76 449.223 9.6898 74 ......... 45.250 298.88 18.079 5.6051

20 ......... 14,462.282 154,366.02 429.007 9.6737 75 ......... 39.285 253.63 16.228 5.4562

21 ......... 13,127.935 139,903.74 409.414 9.6569 76 ......... 34.008 214.34 14.522 5.3028

22 ......... 11,915.200 126,775.80 390.127 9.6398 77 ......... 29.350 180.34 12.956 5.1442

23 ......... 10,813.461 114,860.60 371.588 9.6220 78 ......... 25.246 150.99 11.520 4.9805

24 ......... 9,812.957 104,047.14 354.126 9.6030 79 ......... 21.628 125.74 10.198 4.8136

25 ......... 8,904.441 94,234.18 337.697 9.5828 80 ......... 18.439 104.11 8.975 4.6462

26 ......... 8,079.759 85,329.74 322.510 9.5609 81 ......... 15.629 85.67 7.841 4.4816

27 ......... 7,331.048 77,249.98 308.323 9.5374 82 ......... 13.160 70.04 6.793 4.3222

28 ......... 6,651.206 69,918.93 294.939 9.5122 83 ......... 11.006 56.88 5.835 4.1681

29 ......... 6,033.817 63,267.73 282.205 9.4855 84 ......... 9.147 45.88 4.977 4.0153

30 ......... 5,472.967 57,233.91 269.884 9.4576 85 ......... 7.560 36.73 4.221 3.8581

31 ......... 4,963.546 51,760.95 258.005 9.4282 86 ......... 6.212 29.17 3.560 3.6956

32 ......... 4,500.947 46,797.40 246.638 9.3972 87 ......... 5.068 22.96 2.981 3.5297

33 ......... 4,080.877 42,296.45 235.745 9.3645 88 ......... 4.101 17.89 2.475 3.3620

34 ......... 3,699.398 38,215.57 225.255 9.3302 89 ......... 3.286 13.79 2.032 3.1962

35 ......... 3,353.054 34,516.18 215.220 9.2940 90 ......... 2.602 10.50 1.647 3.0362

36 ......... 3,038.591 31,163.12 205.580 9.2558 91 ......... 2.032 7.90 1.314 2.8870

37 ......... 2,753.092 28,124.53 196.316 9.2156 92 ......... 1.564 5.87 1.031 2.7511

38 ......... 2,493.935 25,371.44 187.441 9.1733 93 ......... 1.186 4.30 0.795 2.6280

39 ......... 2,258.804 22,877.50 179.031 9.1281 94 ......... 0.888 3.12 0.605 2.5107

40 ......... 2,045.482 20,618.70 171.055 9.0801 95 ......... 0.657 2.23 0.455 2.3918

41 ......... 1,851.997 18,573.22 163.523 9.0288 96 ......... 0.480 1.57 0.338 2.2717

42 ......... 1,676.475 16,721.22 156.365 8.9740 97 ......... 0.346 1.09 0.247 2.1564

43 ......... 1,517.246 15,044.75 149.542 8.9158 95 ......... 0.245 0.75 0.177 2.0445

44 ......... 1,372.765 13,527.50 142.992 8.8542 99 ......... 0.171 0.50 0.125 1.9349

45 ......... 1,241.644 12,154.73 136.668 8.7892 100 ......... 0.117 0.33 0.087 1.8275

46 ......... 1,122.631 10,913.09 130.531 8.7210 101 ......... 0.078 0.21 0.059 1.7224

47 ......... 1,014.598 9,790.46 124.556 8.6496 102 ......... 0.052 0.14 0.039 1.6197

48 ......... 916.528 8,775.86 118.722 8.5751 103 ......... 0.033 0.08 0.026 1.5195

49 ......... 827.510 7,859.33 113.025 8.4976 104 ......... 0.021 0.05 0.016 1.4217

50 ......... 746.745 7,031.82 107.488 8.4166 105 ......... 0.013 0.03 0.010 1.3264

51 ......... 673.484 6,285.08 102.114 8.3322 106 ......... 0.008 0.02 0.006 1.2336

52 ......... 607.028 5,611.60 96.883 8.2444 107 ......... 0.004 0.01 0.003 1.1434

53 ......... 546.749 5,004.57 91.788 8.1533 108 ......... 0.002 0.00 0.002 1.0557

54 ......... 492.081 4,457.82 86.825 8.0591 109 ......... 0.001 0.00 0.001 0.9706

x x x x x x x x

85
Table 7.K. -- Actuarial Functions at 11.0 Percent Interest for 1989-91 United States 

Total Other than White Population

x D N M a x D N M a

0 ......... 100,000.000 987,839.50 2,105.995 8.8784 55 ......... 269.001 2,264.31 44.610 7.4175

1 ......... 88,673.874 887,839.50 689.779 9.0124 56 ......... 239.507 1,995.31 41.774 7.3309

2 ......... 79,796.283 799,165.63 599.689 9.0151 57 ......... 213.045 1,755.80 39.047 7.2414

3 ......... 71,838.822 719,369.34 549.968 9.0137 58 ......... 189.309 1,542.75 36.423 7.1494

4 ......... 64,684.088 647,530.52 514.397 9.0107 59 ......... 168.028 1,353.44 33.903 7.0549

5 ......... 58,249.622 582,846.43 490.065 9.0060 60 ......... 148.957 1,185.42 31.483 6.9581

6 ......... 52,456.820 524,596.81 469.749 9.0005 61 ......... 131.890 1,036.46 29.178 6.8585

7 ......... 47,242.502 472,139.99 453.854 8.9940 62 ......... 116.632 904.57 26.990 6.7558

8 ......... 42,548.229 424,897.49 441.270 8.9863 63 ......... 102.997 787.94 24.913 6.6501

9 ......... 38,321.964 382,349.26 431.497 8.9773 64 ......... 90.816 684.94 22.939 6.5421

10 ......... 34,516.544 344,027.30 423.749 8.9670 65 ......... 79.941 594.12 21.063 6.4321

11 ......... 31,089.957 309,510.75 417.721 8.9553 66 ......... 70.241 514.18 19.286 6.3202

12 ......... 28,003.254 278,420.79 412.004 8.9424 67 ......... 61.607 443.94 17.613 6.2061

13 ......... 25,221.461 250,417.54 405.308 8.9287 68 ......... 53.935 382.34 16.046 6.0888

14 ......... 22,712.757 225,196.08 396.029 8.9150 69 ......... 47.128 328.40 14.584 5.9682

15 ......... 20,450.030 202,483.32 384.115 8.9014 70 ......... 41.096 281.27 13.222 5.8443

16 ......... 18,408.576 182,033.29 369.240 8.8885 71 ......... 35.753 240.18 11.952 5.7177

17 ......... 16,568.018 163,624.72 352.956 8.8759 72 ......... 31.024 204.42 10.766 5.5892

18 ......... 14,908.873 147,056.70 335.687 8.8637 73 ......... 26.845 173.40 9.661 5.4593

19 ......... 13,414.070 132,147.83 318.339 8.8514 74 ......... 23.162 146.56 8.638 5.3274

20 ......... 12,067.879 118,733.76 301.471 8.8388 75 ......... 19.927 123.39 7.699 5.1921

21 ......... 10,855.760 106,665.88 285.268 8.8257 76 ......... 17.095 103.47 6.842 5.0523

22 ......... 9,764.159 95,810.12 269.463 8.8124 77 ......... 14.621 86.37 6.062 4.9072

23 ......... 8,781.485 86,045.96 254.408 8.7986 78 ......... 12.463 71.75 5.353 4.7569

24 ......... 7,897.194 77,264.47 240.355 8.7838 79 ......... 10.581 59.29 4.706 4.6030

25 ......... 7,101.487 69,367.28 227.253 8.7680 80 ......... 8.940 48.70 4.113 4.4482

26 ......... 6,385.734 62,265.79 215.250 8.7508 81 ......... 7.509 39.77 3.568 4.2957

27 ......... 5,741.801 55,880.06 204.138 8.7321 82 ......... 6.266 32.26 3.069 4.1479

28 ......... 5,162.406 50,138.26 193.750 8.7122 83 ......... 5.193 25.99 2.618 4.0048

29 ......... 4,641.022 44,975.85 183.956 8.6909 84 ......... 4.277 20.80 2.216 3.8625

30 ......... 4,171.709 40,334.83 174.564 8.6687 85 ......... 3.503 16.52 1.866 3.7158

31 ......... 3,749.324 36,163.12 165.591 8.6452 86 ......... 2.852 13.02 1.562 3.5635

32 ......... 3,369.260 32,413.79 157.082 8.6204 87 ......... 2.306 10.16 1.299 3.4075

33 ......... 3,027.289 29,044.53 149.001 8.5942 88 ......... 1.849 7.86 1.071 3.2493

34 ......... 2,719.575 26,017.25 141.290 8.5667 89 ......... 1.468 6.01 0.873 3.0924

35 ......... 2,442.757 23,297.67 133.979 8.5374 90 ......... 1.152 4.54 0.702 2.9406

36 ......... 2,193.723 20,854.91 127.019 8.5066 91 ......... 0.892 3.39 0.556 2.7988

37 ......... 1,969.699 18,661.19 120.392 8.4741 92 ......... 0.680 2.50 0.433 2.6695

38 ......... 1,768.211 16,691.49 114.099 8.4398 93 ......... 0.511 1.82 0.331 2.5524

39 ......... 1,587.074 14,923.28 108.190 8.4030 94 ......... 0.379 1.30 0.250 2.4407

40 ......... 1,424.243 13,336.21 102.636 8.3637 95 ......... 0.278 0.93 0.186 2.3272

41 ......... 1,277.904 11,911.96 97.439 8.3215 96 ......... 0.202 0.65 0.137 2.2124

42 ......... 1,146.370 10,634.06 92.544 8.2763 97 ......... 0.144 0.45 0.100 2.1019

43 ......... 1,028.143 9,487.69 87.921 8.2280 95 ......... 0.101 0.30 0.071 1.9946

44 ......... 921.856 8,459.55 83.523 8.1766 99 ......... 0.070 0.20 0.050 1.8892

45 ......... 826.292 7,537.69 79.314 8.1223 100 ......... 0.047 0.13 0.034 1.7858

46 ......... 740.361 6,711.40 75.267 8.0650 101 ......... 0.031 0.08 0.023 1.6845

47 ......... 663.087 5,971.04 71.362 8.0049 102 ......... 0.020 0.05 0.015 1.5853

48 ......... 593.597 5,307.95 67.584 7.9420 103 ......... 0.013 0.03 0.010 1.4883

49 ......... 531.115 4,714.36 63.927 7.8763 104 ......... 0.008 0.02 0.006 1.3936

50 ......... 474.960 4,183.24 60.405 7.8076 105 ......... 0.005 0.01 0.004 1.3011

51 ......... 424.505 3,708.28 57.018 7.7355 106 ......... 0.003 0.01 0.002 1.2110

52 ......... 379.169 3,283.77 53.750 7.6604 107 ......... 0.002 0.00 0.001 1.1232

53 ......... 338.441 2,904.61 50.597 7.5823 108 ......... 0.001 0.00 0.001 1.0378

54 ......... 301.857 2,566.16 47.552 7.5013 109 ......... 0.000 0.00 0.000 0.9548

x x x x x x x x

86
Table 7.L. -- Actuarial Functions at 12.0 Percent Interest for 1989-91 United States 

Total Other than White Population

x D N M a x D N M a

0 ......... 100,000.000 914,834.08 1,982.063 8.1483 55 ......... 164.258 1,303.82 24.563 6.9376

1 ......... 87,882.143 814,834.08 578.491 8.2719 56 ......... 144.943 1,139.56 22.847 6.8621

2 ......... 78,377.710 726,951.94 490.003 8.2750 57 ......... 127.778 994.61 21.212 6.7840

3 ......... 69,931.698 648,574.23 441.602 8.2744 58 ......... 112.527 866.84 19.652 6.7033

4 ......... 62,404.698 578,642.53 407.284 8.2724 59 ......... 98.986 754.31 18.167 6.6204

5 ......... 55,695.216 516,237.83 384.019 8.2690 60 ......... 86.968 655.32 16.754 6.5353

6 ......... 49,708.619 460,542.62 364.767 8.2648 61 ......... 76.316 568.36 15.421 6.4474

7 ......... 44,367.768 410,834.00 349.840 8.2597 62 ......... 66.884 492.04 14.166 6.3566

8 ......... 39,602.366 366,466.23 338.127 8.2536 63 ......... 58.538 425.16 12.986 6.2629

9 ......... 35,350.240 326,863.86 329.112 8.2464 64 ......... 51.154 366.62 11.873 6.1670

10 ......... 31,555.631 291,513.62 322.029 8.2381 65 ......... 44.626 315.46 10.827 6.0690

11 ......... 28,169.208 259,957.99 316.566 8.2284 66 ......... 38.862 270.84 9.843 5.9693

12 ......... 25,145.946 231,788.78 311.433 8.2177 67 ......... 33.780 231.98 8.926 5.8672

13 ......... 22,445.779 206,642.84 305.474 8.2063 68 ......... 29.310 198.20 8.074 5.7622

14 ......... 20,032.689 184,197.06 297.290 8.1948 69 ......... 25.382 168.89 7.287 5.6538

15 ......... 17,875.916 164,164.37 286.876 8.1836 70 ......... 21.935 143.50 6.560 5.5422

16 ......... 15,947.752 146,288.45 273.989 8.1730 71 ......... 18.913 121.57 5.888 5.4278

17 ......... 14,225.083 130,340.70 260.008 8.1627 72 ......... 16.265 102.66 5.266 5.3115

18 ......... 12,686.272 116,115.62 245.313 8.1529 73 ......... 13.948 86.39 4.692 5.1937

19 ......... 11,312.399 103,429.35 230.684 8.1430 74 ......... 11.927 72.44 4.166 5.0737

20 ......... 10,086.258 92,116.95 216.585 8.1329 75 ......... 10.170 60.52 3.686 4.9504

21 ......... 8,992.166 82,030.69 203.164 8.1225 76 ......... 8.647 50.35 3.253 4.8225

22 ......... 8,015.745 73,038.52 190.189 8.1119 77 ......... 7.329 41.70 2.862 4.6894

23 ......... 7,144.666 65,022.78 177.940 8.1009 78 ......... 6.192 34.37 2.509 4.5508

24 ......... 6,367.835 57,878.11 166.608 8.0891 79 ......... 5.210 28.18 2.191 4.4086

25 ......... 5,675.096 51,510.28 156.138 8.0765 80 ......... 4.362 22.97 1.901 4.2651

26 ......... 5,057.544 45,835.18 146.632 8.0627 81 ......... 3.631 18.61 1.638 4.1235

27 ......... 4,506.942 40,777.64 137.909 8.0477 82 ......... 3.003 14.97 1.399 3.9860

28 ......... 4,015.975 36,270.70 129.829 8.0316 83 ......... 2.467 11.97 1.184 3.8528

29 ......... 3,578.140 32,254.72 122.277 8.0144 84 ......... 2.014 9.50 0.995 3.7201

30 ......... 3,187.592 28,676.58 115.101 7.9963 85 ......... 1.634 7.49 0.832 3.5828

31 ......... 2,839.269 25,488.99 108.306 7.9773 86 ......... 1.319 5.86 0.692 3.4398

32 ......... 2,528.676 22,649.72 101.920 7.9571 87 ......... 1.057 4.54 0.571 3.2929

33 ......... 2,251.735 20,121.04 95.909 7.9358 88 ......... 0.840 3.48 0.467 3.1434

34 ......... 2,004.793 17,869.31 90.224 7.9133 89 ......... 0.661 2.64 0.378 2.9946

35 ......... 1,784.653 15,864.52 84.883 7.8894 90 ......... 0.514 1.98 0.302 2.8504

36 ......... 1,588.401 14,079.86 79.844 7.8642 91 ......... 0.394 1.47 0.237 2.7155

37 ......... 1,413.459 12,491.46 75.088 7.8375 92 ......... 0.298 1.07 0.183 2.5924

38 ......... 1,257.541 11,078.00 70.613 7.8093 93 ......... 0.222 0.77 0.139 2.4808

39 ......... 1,118.640 9,820.46 66.448 7.7789 94 ......... 0.163 0.55 0.104 2.3743

40 ......... 994.906 8,701.82 62.568 7.7464 95 ......... 0.119 0.39 0.077 2.2659

41 ......... 884.711 7,706.91 58.970 7.7112 96 ......... 0.085 0.27 0.056 2.1559

42 ......... 786.562 6,822.20 55.612 7.6734 97 ......... 0.060 0.18 0.041 2.0499

43 ......... 699.144 6,035.64 52.468 7.6329 95 ......... 0.042 0.12 0.029 1.9468

44 ......... 621.271 5,336.50 49.504 7.5896 99 ......... 0.029 0.08 0.020 1.8454

45 ......... 551.895 4,715.23 46.693 7.5437 100 ......... 0.019 0.05 0.014 1.7458

46 ......... 490.085 4,163.33 44.014 7.4951 101 ......... 0.013 0.03 0.009 1.6481

47 ......... 435.014 3,673.25 41.452 7.4440 102 ......... 0.008 0.02 0.006 1.5522

48 ......... 385.949 3,238.23 38.995 7.3903 103 ......... 0.005 0.01 0.004 1.4583

49 ......... 342.241 2,852.28 36.639 7.3341 104 ......... 0.003 0.01 0.002 1.3665

50 ......... 303.323 2,510.04 34.390 7.2751 105 ......... 0.002 0.00 0.001 1.2768

51 ......... 268.680 2,206.72 32.246 7.2132 106 ......... 0.001 0.00 0.001 1.1892

52 ......... 237.843 1,938.04 30.196 7.1484 107 ......... 0.001 0.00 0.000 1.1037

53 ......... 210.400 1,700.20 28.236 7.0808 108 ......... 0.000 0.00 0.000 1.0204

54 ......... 185.981 1,489.80 26.360 7.0105 109 ......... 0.000 0.00 0.000 0.9394

x x x x x x x x

87
Table 8.A. -- Actuarial Functions at 1.0 Percent Interest for 1989-91 United States 

Males Other than White

x D N M a x D N M a

0 ......... 100,000.000 4,827,953.75 52,198.478 47.2795 55 ......... 45,305.691 834,541.84 37,042.900 17.4202

1 ......... 97,314.851 4,727,953.75 50,503.428 47.5841 56 ......... 44,154.867 789,236.15 36,340.648 16.8743

2 ......... 96,234.683 4,630,638.89 50,386.773 47.1182 57 ......... 42,975.318 745,081.28 35,598.276 16.3374

3 ......... 95,209.070 4,534,404.21 50,313.979 46.6258 58 ......... 41,767.632 702,105.96 34,816.087 15.8098

4 ......... 94,205.864 4,439,195.14 50,253.437 46.1223 59 ......... 40,533.502 660,338.33 33,995.499 15.2912

5 ......... 93,228.414 4,344,989.28 50,208.718 45.6058 60 ......... 39,275.681 619,804.83 33,139.000 14.7809

6 ......... 92,265.794 4,251,760.86 50,169.152 45.0817 61 ......... 37,999.008 580,529.15 32,251.195 14.2775

7 ......... 91,317.761 4,159,495.07 50,134.642 44.5497 62 ......... 36,704.375 542,530.14 31,332.790 13.7811

8 ......... 90,382.226 4,068,177.31 50,103.243 44.0108 63 ......... 35,391.584 505,825.76 30,383.408 13.2923

9 ......... 89,460.837 3,977,795.08 50,076.727 43.4641 64 ......... 34,056.757 470,434.18 29,398.993 12.8132

10 ......... 88,554.265 3,888,334.24 50,055.906 42.9091 65 ......... 32,699.327 436,377.42 28,378.759 12.3451

11 ......... 87,660.460 3,799,779.98 50,038.876 42.3466 66 ......... 31,323.437 403,678.09 27,326.624 11.8874

12 ......... 86,774.785 3,712,119.52 50,021.127 41.7788 67 ......... 29,935.647 372,354.66 26,248.968 11.4385

13 ......... 85,888.390 3,625,344.74 49,993.888 41.2100 68 ......... 28,540.751 342,419.01 25,150.464 10.9975

14 ......... 84,991.032 3,539,456.34 49,946.910 40.6451 69 ......... 27,141.855 313,878.26 24,034.149 10.5644

15 ......... 84,077.184 3,454,465.31 49,874.557 40.0868 70 ......... 25,739.457 286,736.40 22,900.483 10.1400

16 ......... 83,144.103 3,370,388.13 49,773.924 39.5367 71 ......... 24,332.073 260,996.95 21,747.945 9.7265

17 ......... 82,195.082 3,287,244.03 49,648.112 38.9932 72 ......... 22,918.771 236,664.87 20,575.554 9.3262

18 ......... 81,234.966 3,205,048.94 49,501.809 38.4541 73 ......... 21,504.952 213,746.10 19,388.654 8.9394

19 ......... 80,268.423 3,123,813.98 49,339.572 37.9171 74 ......... 20,102.517 192,241.15 18,199.139 8.5630

20 ......... 79,301.582 3,043,545.55 49,167.467 37.3794 75 ......... 18,724.796 172,138.63 17,020.453 8.1931

21 ......... 78,332.223 2,964,243.97 48,983.273 36.8419 76 ......... 17,380.836 153,413.84 15,861.887 7.8266

22 ......... 77,361.431 2,885,911.75 48,788.047 36.3043 77 ......... 16,072.344 136,033.00 14,725.482 7.4638

23 ......... 76,391.048 2,808,550.32 48,583.619 35.7654 78 ......... 14,801.404 119,960.66 13,613.674 7.1047

24 ......... 75,425.208 2,732,159.27 48,374.126 35.2234 79 ......... 13,563.623 105,159.26 12,522.442 6.7530

25 ......... 74,467.886 2,656,734.06 48,163.589 34.6762 80 ......... 12,356.571 91,595.63 11,449.684 6.4127

26 ......... 73,518.267 2,582,266.18 47,951.275 34.1241 81 ......... 11,177.005 79,239.06 10,392.460 6.0895

27 ......... 72,577.859 2,508,747.91 47,738.771 33.5663 82 ......... 10,029.315 68,062.06 9,355.433 5.7863

28 ......... 71,642.812 2,436,170.05 47,522.316 33.0044 83 ......... 8,926.461 58,032.74 8,351.879 5.5012

29 ......... 70,710.173 2,364,527.24 47,299.012 32.4397 84 ......... 7,888.248 49,106.28 7,402.047 5.2252

30 ......... 69,777.108 2,293,817.07 47,066.048 31.8735 85 ......... 6,929.380 41,218.03 6,521.281 4.9483

31 ......... 68,843.101 2,224,039.96 46,822.903 31.3059 86 ......... 6,049.498 34,288.65 5,710.006 4.6680

32 ......... 67,909.839 2,155,196.86 46,571.256 30.7362 87 ......... 5,240.639 28,239.16 4,961.043 4.3885

33 ......... 66,976.067 2,087,287.02 46,309.859 30.1647 88 ......... 4,497.612 22,998.52 4,269.904 4.1135

34 ......... 66,039.869 2,020,310.95 46,036.790 29.5923 89 ......... 3,814.570 18,500.90 3,631.392 3.8501

35 ......... 65,101.525 1,954,271.08 45,752.307 29.0188 90 ......... 3,189.127 14,686.34 3,043.718 3.6051

36 ......... 64,159.913 1,889,169.56 45,455.263 28.4447 91 ......... 2,621.791 11,497.21 2,507.957 3.3853

37 ......... 63,213.264 1,825,009.64 45,143.861 27.8707 92 ......... 2,115.419 8,875.42 2,027.544 3.1956

38 ......... 62,264.683 1,761,796.38 44,821.154 27.2953 93 ......... 1,675.500 6,760.00 1,608.570 3.0346

39 ......... 61,317.156 1,699,531.70 44,490.110 26.7171 94 ......... 1,307.271 5,084.50 1,256.929 2.8894

40 ......... 60,370.871 1,638,214.54 44,150.925 26.1358 95 ......... 1,008.728 3,777.23 971.330 2.7445

41 ......... 59,426.673 1,577,843.67 43,804.458 25.5511 96 ......... 769.999 2,768.50 742.588 2.5955

42 ......... 58,483.402 1,518,417.00 43,449.570 24.9632 97 ......... 579.039 1,998.50 559.252 2.4514

43 ......... 57,538.643 1,459,933.60 43,083.855 24.3731 95 ......... 428.546 1,419.46 414.492 2.3123

44 ......... 56,590.077 1,402,394.95 42,704.978 23.7816 99 ......... 311.808 990.91 301.997 2.1780

45 ......... 55,634.843 1,345,804.88 42,310.042 23.1900 100 ......... 222.779 679.11 216.055 2.0483

46 ......... 54,670.199 1,290,170.03 41,896.238 22.5991 101 ......... 156.100 456.33 151.582 1.9233

47 ......... 53,692.892 1,235,499.84 41,460.220 22.0105 102 ......... 107.118 300.23 104.146 1.8028

48 ......... 52,702.286 1,181,806.94 41,001.227 21.4242 103 ......... 71.880 193.11 69.968 1.6866

49 ......... 51,697.169 1,129,104.66 40,517.915 20.8407 104 ......... 47.087 121.23 45.887 1.5746

50 ......... 50,678.212 1,077,407.49 40,010.811 20.2598 105 ......... 30.057 74.14 29.323 1.4668

51 ......... 49,644.263 1,026,729.28 39,478.627 19.6817 106 ......... 18.657 44.09 18.221 1.3630

52 ......... 48,593.037 977,085.01 38,918.928 19.1075 107 ......... 11.237 25.43 10.985 1.2630

53 ......... 47,522.352 928,491.98 38,329.362 18.5380 108 ......... 6.550 14.19 6.409 1.1669

54 ......... 46,427.787 880,969.62 37,705.315 17.9751 109 ......... 3.684 7.64 3.609 1.0745

x x x x x x x x

88
Table 8.B. -- Actuarial Functions at 2.0 Percent Interest for 1989-91 United States 

Males Other than White

x D N M a x D N M a

0 ......... 100,000.000 3,632,045.42 28,783.423 35.3205 55 ......... 26,352.321 433,527.17 17,851.788 15.4512

1 ......... 96,360.784 3,532,045.42 27,104.992 35.6544 56 ......... 25,431.144 407,174.85 17,447.323 15.0109

2 ......... 94,356.978 3,435,684.64 26,990.613 35.4116 57 ......... 24,509.114 381,743.70 17,023.944 14.5756

3 ......... 92,436.167 3,341,327.66 26,919.939 35.1474 58 ......... 23,586.829 357,234.59 16,582.230 14.1455

4 ......... 90,565.491 3,248,891.49 26,861.736 34.8734 59 ......... 22,665.487 333,647.76 16,123.374 13.7205

5 ......... 88,747.128 3,158,326.00 26,819.167 34.5879 60 ......... 21,746.824 310,982.27 15,649.133 13.3001

6 ......... 86,969.693 3,069,578.87 26,781.872 34.2948 61 ......... 20,833.661 289,235.45 15,162.377 12.8831

7 ......... 85,232.194 2,982,609.18 26,749.661 33.9939 62 ......... 19,926.561 268,401.79 14,663.781 12.4695

8 ......... 83,531.956 2,897,376.98 26,720.643 33.6859 63 ......... 19,025.485 248,475.23 14,153.421 12.0601

9 ......... 81,869.809 2,813,845.03 26,696.377 33.3698 64 ......... 18,128.431 229,449.74 13,629.416 11.6569

10 ......... 80,245.650 2,731,975.22 26,677.509 33.0452 65 ......... 17,235.225 211,321.31 13,091.670 11.2610

11 ......... 78,656.925 2,651,729.57 26,662.228 32.7126 66 ......... 16,348.155 194,086.09 12,542.545 10.8720

12 ......... 77,098.863 2,573,072.64 26,646.458 32.3737 67 ......... 15,470.672 177,737.93 11,985.615 10.4887

13 ......... 75,563.156 2,495,973.78 26,622.494 32.0316 68 ......... 14,605.188 162,267.26 11,423.477 10.1102

14 ......... 74,040.601 2,420,410.63 26,581.569 31.6903 69 ......... 13,753.159 147,662.07 10,857.824 9.7366

15 ......... 72,526.411 2,346,370.02 26,519.155 31.3519 70 ......... 12,914.676 133,908.91 10,289.011 9.3687

16 ......... 71,018.368 2,273,843.61 26,433.199 31.0177 71 ......... 12,088.835 120,994.24 9,716.399 9.0088

17 ......... 69,519.440 2,202,825.25 26,326.789 30.6865 72 ......... 11,275.034 108,905.40 9,139.634 8.6590

18 ......... 68,033.786 2,133,305.81 26,204.261 30.3566 73 ......... 10,475.776 97,630.37 8,561.456 8.3196

19 ......... 66,565.250 2,065,272.02 26,069.720 30.0263 74 ......... 9,696.598 87,154.59 7,987.684 7.9882

20 ......... 65,118.725 1,998,706.77 25,928.396 29.6933 75 ......... 8,943.494 77,457.99 7,424.710 7.6608

21 ......... 63,692.118 1,933,588.04 25,778.627 29.3584 76 ......... 8,220.193 68,514.50 6,876.771 7.3349

22 ......... 62,286.071 1,869,895.93 25,621.445 29.0211 77 ......... 7,526.824 60,294.31 6,344.583 7.0106

23 ......... 60,901.798 1,807,609.85 25,458.467 28.6807 78 ......... 6,863.674 52,767.48 5,829.018 6.6879

24 ......... 59,542.267 1,746,708.06 25,293.089 28.3356 79 ......... 6,228.030 45,903.81 5,327.955 6.3705

25 ......... 58,210.198 1,687,165.79 25,128.516 27.9840 80 ......... 5,618.161 39,675.78 4,840.204 6.0621

26 ......... 56,904.487 1,628,955.59 24,964.182 27.6261 81 ......... 5,032.025 34,057.62 4,364.229 5.7682

27 ......... 55,625.843 1,572,051.10 24,801.312 27.2612 82 ......... 4,471.053 29,025.59 3,901.924 5.4919

28 ......... 54,370.870 1,516,425.26 24,637.041 26.8904 83 ......... 3,940.389 24,554.54 3,458.927 5.2315

29 ......... 53,136.967 1,462,054.39 24,469.233 26.5148 84 ......... 3,447.954 20,614.15 3,043.755 4.9787

30 ......... 51,921.715 1,408,917.42 24,295.883 26.1354 85 ......... 2,999.139 17,166.20 2,662.547 4.7237

31 ......... 50,724.490 1,356,995.71 24,116.731 25.7523 86 ......... 2,592.643 14,167.06 2,314.857 4.4643

32 ......... 49,546.293 1,306,271.22 23,933.132 25.3647 87 ......... 2,223.969 11,574.41 1,997.020 4.2044

33 ......... 48,385.954 1,256,724.93 23,744.289 24.9729 88 ......... 1,889.939 9,350.44 1,706.597 3.9475

34 ......... 47,241.869 1,208,338.97 23,548.948 24.5777 89 ......... 1,587.203 7,460.51 1,440.919 3.7004

35 ......... 46,114.047 1,161,097.10 23,347.437 24.1788 90 ......... 1,313.953 5,873.30 1,198.791 3.4699

36 ......... 45,001.505 1,114,983.06 23,139.092 23.7766 91 ......... 1,069.615 4,559.35 980.216 3.2626

37 ......... 43,902.847 1,069,981.55 22,922.817 23.3716 92 ......... 854.569 3,489.73 786.143 3.0836

38 ......... 42,820.078 1,026,078.71 22,700.888 22.9626 93 ......... 670.218 2,635.17 618.548 2.9318

39 ......... 41,755.038 983,258.63 22,475.457 22.5483 94 ......... 517.796 1,964.95 479.267 2.7948

40 ......... 40,707.602 941,503.59 22,246.747 22.1284 95 ......... 395.629 1,447.15 367.254 2.6578

41 ......... 39,678.084 900,795.99 22,015.418 21.7026 96 ......... 299.038 1,051.52 278.419 2.5164

42 ......... 38,665.454 861,117.90 21,780.789 21.2710 97 ......... 222.672 752.48 207.917 2.3793

43 ......... 37,667.890 822,452.45 21,541.372 20.8343 95 ......... 163.183 529.81 152.795 2.2467

44 ......... 36,683.703 784,784.56 21,295.771 20.3933 99 ......... 117.567 366.63 110.378 2.1185

45 ......... 35,710.913 748,100.86 21,042.269 19.9488 100 ......... 83.175 249.06 78.292 1.9944

46 ......... 34,747.691 712,389.94 20,779.260 19.5018 101 ......... 57.709 165.89 54.456 1.8746

47 ......... 33,791.953 677,642.25 20,504.850 19.0534 102 ......... 39.213 108.18 37.092 1.7588

48 ......... 32,843.328 643,850.30 20,218.812 18.6037 103 ......... 26.055 68.97 24.703 1.6469

49 ......... 31,901.100 611,006.97 19,920.572 18.1532 104 ......... 16.901 42.91 16.059 1.5390

50 ......... 30,965.734 579,105.87 19,610.717 17.7015 105 ......... 10.682 26.01 10.172 1.4349

51 ......... 30,036.572 548,140.14 19,288.726 17.2491 106 ......... 6.566 15.33 6.265 1.3344

52 ......... 29,112.302 518,103.56 18,953.409 16.7967 107 ......... 3.916 8.76 3.744 1.2376

53 ......... 28,191.724 488,991.26 18,603.660 16.3452 108 ......... 2.260 4.85 2.165 1.1444

54 ......... 27,272.371 460,799.54 18,237.085 15.8962 109 ......... 1.259 2.59 1.208 1.0545

x x x x x x x x

89
Table 8.C. -- Actuarial Functions at 3.0 Percent Interest for 1989-91 United States 

Males Other than White

x D N M a x D N M a

0 ......... 100,000.000 2,852,545.41 16,916.153 27.5255 55 ......... 15,409.231 228,348.20 8,758.312 13.8189

1 ......... 95,425.243 2,752,545.41 15,254.017 27.8450 56 ......... 14,726.208 212,938.97 8,524.102 13.4599

2 ......... 92,533.698 2,657,120.16 15,141.848 27.7152 57 ......... 14,054.506 198,212.76 8,281.319 13.1031

3 ......... 89,769.906 2,564,586.46 15,073.213 27.5684 58 ......... 13,394.315 184,158.26 8,030.482 12.7490

4 ......... 87,099.274 2,474,816.56 15,017.238 27.4137 59 ......... 12,746.147 170,763.94 7,772.440 12.3973

5 ......... 84,521.859 2,387,717.28 14,976.695 27.2497 60 ......... 12,110.795 158,017.79 7,508.335 12.0477

6 ......... 82,024.883 2,303,195.43 14,941.521 27.0792 61 ......... 11,489.612 145,907.00 7,239.893 11.6990

7 ......... 79,605.724 2,221,170.54 14,911.437 26.9021 62 ......... 10,882.660 134,417.39 6,967.591 11.3515

8 ......... 77,260.271 2,141,564.82 14,884.597 26.7188 63 ......... 10,289.669 123,534.73 6,691.570 11.0057

9 ......... 74,987.746 2,064,304.55 14,862.371 26.5286 64 ......... 9,709.320 113,245.06 6,410.921 10.6635

10 ......... 72,786.523 1,989,316.80 14,845.257 26.3308 65 ......... 9,141.312 103,535.74 6,125.708 10.3261

11 ......... 70,652.801 1,916,530.28 14,831.531 26.1260 66 ......... 8,586.640 94,394.43 5,837.288 9.9932

12 ......... 68,580.925 1,845,877.48 14,817.503 25.9153 67 ......... 8,046.864 85,807.79 5,547.608 9.6635

13 ......... 66,562.313 1,777,296.55 14,796.394 25.7012 68 ......... 7,522.939 77,760.92 5,258.058 9.3365

14 ......... 64,587.904 1,710,734.24 14,760.693 25.4869 69 ......... 7,015.293 70,237.98 4,969.526 9.0121

15 ......... 62,652.787 1,646,146.34 14,706.777 25.2741 70 ......... 6,523.638 63,222.69 4,682.200 8.6913

16 ......... 60,754.414 1,583,493.55 14,633.243 25.0638 71 ......... 6,047.191 56,699.05 4,395.762 8.3761

17 ......... 58,894.721 1,522,739.14 14,543.096 24.8553 72 ......... 5,585.346 50,651.86 4,110.049 8.0687

18 ......... 57,076.547 1,463,844.41 14,440.302 24.6470 73 ......... 5,139.032 45,066.52 3,826.415 7.7695

19 ......... 55,302.347 1,406,767.87 14,328.525 24.4378 74 ......... 4,710.613 39,927.48 3,547.677 7.4761

20 ......... 53,575.327 1,351,465.52 14,212.254 24.2255 75 ......... 4,302.573 35,216.87 3,276.839 7.1851

21 ......... 51,892.857 1,297,890.19 14,090.230 24.0110 76 ......... 3,916.210 30,914.30 3,015.794 6.8939

22 ......... 50,254.595 1,245,997.34 13,963.410 23.7937 77 ......... 3,551.066 26,998.09 2,764.713 6.6028

23 ......... 48,660.649 1,195,742.74 13,833.190 23.5731 78 ......... 3,206.761 23,447.02 2,523.838 6.3117

24 ......... 47,112.494 1,147,082.09 13,702.336 23.3477 79 ......... 2,881.532 20,240.26 2,292.010 6.0241

25 ......... 45,611.332 1,099,969.60 13,573.382 23.1161 80 ......... 2,574.127 17,358.73 2,068.533 5.7435

26 ......... 44,155.330 1,054,358.27 13,445.866 22.8784 81 ......... 2,283.187 14,784.60 1,852.568 5.4754

27 ......... 42,744.100 1,010,202.94 13,320.714 22.6337 82 ......... 2,008.961 12,501.41 1,644.842 5.2228

28 ......... 41,374.123 967,458.84 13,195.710 22.3832 83 ......... 1,753.330 10,492.45 1,447.725 4.9843

29 ......... 40,042.596 926,084.71 13,069.255 22.1275 84 ......... 1,519.319 8,739.12 1,264.782 4.7520

30 ......... 38,746.943 886,042.12 12,939.891 21.8674 85 ......... 1,308.721 7,219.80 1,098.435 4.5167

31 ......... 37,485.995 847,295.18 12,807.495 21.6030 86 ......... 1,120.356 5,911.08 948.189 4.2761

32 ......... 36,259.806 809,809.18 12,673.130 21.3335 87 ......... 951.711 4,790.73 812.175 4.0338

33 ......... 35,066.834 773,549.38 12,536.270 21.0593 88 ......... 800.916 3,839.02 689.100 3.7933

34 ......... 33,905.275 738,482.54 12,396.075 20.7808 89 ......... 666.093 3,038.10 577.605 3.5611

35 ......... 32,774.523 704,577.27 12,252.855 20.4977 90 ......... 546.066 2,372.01 476.979 3.3438

36 ......... 31,673.287 671,802.74 12,106.216 20.2104 91 ......... 440.206 1,825.94 387.023 3.1479

37 ......... 30,600.021 640,129.46 11,955.474 19.9192 92 ......... 348.288 1,385.73 307.926 2.9787

38 ......... 29,555.577 609,529.44 11,802.293 19.6232 93 ......... 270.502 1,037.45 240.285 2.8353

39 ......... 28,540.647 579,973.86 11,648.205 19.3210 94 ......... 206.955 766.95 184.617 2.7059

40 ......... 27,554.555 551,433.21 11,493.394 19.0124 95 ......... 156.592 559.99 140.281 2.5761

41 ......... 26,596.931 523,878.66 11,338.329 18.6970 96 ......... 117.211 403.40 105.462 2.4416

42 ......... 25,666.514 497,281.72 11,182.580 18.3747 97 ......... 86.431 286.19 78.096 2.3112

43 ......... 24,761.561 471,615.21 11,025.196 18.0463 95 ......... 62.726 199.76 56.907 2.1846

44 ......... 23,880.468 446,853.65 10,865.314 17.7121 99 ......... 44.753 137.03 40.761 2.0620

45 ......... 23,021.498 422,973.18 10,701.890 17.3730 100 ......... 31.354 92.28 28.666 1.9431

46 ......... 22,183.063 399,951.68 10,533.985 17.0296 101 ......... 21.543 60.92 19.768 1.8281

47 ......... 21,363.470 377,768.62 10,360.501 16.6829 102 ......... 14.496 39.38 13.349 1.7168

48 ......... 20,562.154 356,405.15 10,181.422 16.3331 103 ......... 9.538 24.89 8.814 1.6090

49 ......... 19,778.351 335,843.00 9,996.516 15.9803 104 ......... 6.127 15.35 5.680 1.5049

50 ......... 19,012.041 316,064.65 9,806.274 15.6244 105 ......... 3.835 9.22 3.567 1.4043

51 ......... 18,262.519 297,052.60 9,610.501 15.2657 106 ......... 2.334 5.39 2.177 1.3071

52 ......... 17,528.704 278,790.09 9,408.604 14.9048 107 ......... 1.379 3.05 1.290 1.2132

53 ......... 16,809.617 261,261.38 9,200.062 14.5424 108 ......... 0.788 1.67 0.739 1.1226

54 ......... 16,103.565 244,451.77 8,983.611 14.1800 109 ......... 0.435 0.88 0.409 1.0353

x x x x x x x x

90
Table 8.D. -- Actuarial Functions at 4.0 Percent Interest for 1989-91 United States 

Males Other than White

x D N M a x D N M a

0 ......... 100,000.000 2,322,389.12 10,677.341 22.2239 55 ......... 9,057.215 121,845.64 4,370.844 12.4529

1 ......... 94,507.692 2,222,389.12 9,031.188 22.5154 56 ......... 8,572.520 112,788.43 4,234.504 12.1570

2 ......... 90,762.759 2,127,881.43 8,921.165 22.4444 57 ......... 8,102.836 104,215.91 4,094.532 11.8617

3 ......... 87,205.209 2,037,118.67 8,854.491 22.3601 58 ......... 7,647.964 96,113.07 3,951.308 11.5671

4 ......... 83,797.310 1,949,913.46 8,800.638 22.2694 59 ......... 7,207.890 88,465.11 3,805.386 11.2734

5 ......... 80,535.706 1,866,116.16 8,762.007 22.1713 60 ......... 6,782.750 81,257.22 3,657.472 10.9800

6 ......... 77,404.985 1,785,580.45 8,728.814 22.0680 61 ......... 6,372.977 74,474.47 3,508.575 10.6860

7 ......... 74,399.754 1,708,175.46 8,700.697 21.9594 62 ......... 5,978.276 68,101.49 3,358.988 10.3915

8 ......... 71,513.381 1,633,775.71 8,675.854 21.8457 63 ......... 5,598.171 62,123.21 3,208.817 10.0971

9 ......... 68,742.491 1,562,262.33 8,655.479 21.7263 64 ......... 5,231.636 56,525.04 3,057.596 9.8045

10 ......... 66,083.011 1,493,519.84 8,639.941 21.6007 65 ......... 4,878.216 51,293.41 2,905.393 9.5148

11 ......... 63,529.015 1,427,436.83 8,627.599 21.4691 66 ......... 4,538.159 46,415.19 2,752.959 9.2278

12 ......... 61,073.100 1,363,907.81 8,615.107 21.3324 67 ......... 4,211.986 41,877.03 2,601.331 8.9423

13 ......... 58,705.516 1,302,834.71 8,596.489 21.1927 68 ......... 3,899.885 37,665.04 2,451.229 8.6580

14 ......... 56,416.428 1,244,129.20 8,565.305 21.0526 69 ......... 3,601.753 33,765.16 2,303.093 8.3746

15 ......... 54,199.923 1,187,712.77 8,518.663 20.9136 70 ......... 3,317.125 30,163.41 2,156.994 8.0932

16 ......... 52,052.310 1,133,512.84 8,455.662 20.7764 71 ......... 3,045.296 26,846.28 2,012.747 7.8157

17 ......... 49,973.805 1,081,460.53 8,379.169 20.6405 72 ......... 2,785.671 23,800.99 1,870.248 7.5441

18 ......... 47,965.351 1,031,486.73 8,292.784 20.5048 73 ......... 2,538.429 21,015.32 1,730.147 7.2789

19 ......... 46,027.500 983,521.38 8,199.754 20.3681 74 ......... 2,304.438 18,476.89 1,593.788 7.0180

20 ......... 44,161.370 937,493.88 8,103.913 20.2288 75 ......... 2,084.585 16,172.45 1,462.568 6.7581

21 ......... 42,363.241 893,332.51 8,004.298 20.0874 76 ......... 1,879.149 14,087.86 1,337.308 6.4969

22 ......... 40,631.350 850,969.27 7,901.763 19.9437 77 ......... 1,687.555 12,208.71 1,217.989 6.2346

23 ......... 38,964.334 810,337.92 7,797.491 19.7969 78 ......... 1,509.279 10,521.16 1,104.619 5.9710

24 ......... 37,361.934 771,373.58 7,693.719 19.6460 79 ......... 1,343.168 9,011.88 996.558 5.7094

25 ......... 35,823.655 734,011.65 7,592.437 19.4896 80 ......... 1,188.340 7,668.71 893.390 5.4533

26 ......... 34,346.632 698,188.00 7,493.248 19.3277 81 ......... 1,043.894 6,480.37 794.649 5.2079

27 ......... 32,929.193 663,841.36 7,396.833 19.1597 82 ......... 909.683 5,436.48 700.588 4.9762

28 ......... 31,567.311 630,912.17 7,301.458 18.9863 83 ......... 786.296 4,526.79 612.189 4.7571

29 ......... 30,257.629 599,344.86 7,205.904 18.8081 84 ......... 674.801 3,740.50 530.935 4.5431

30 ......... 28,997.062 569,087.23 7,109.092 18.6257 85 ......... 575.675 3,065.70 457.763 4.3254

31 ......... 27,783.662 540,090.17 7,010.964 18.4391 86 ......... 488.079 2,490.02 392.309 4.1017

32 ......... 26,616.430 512,306.51 6,912.334 18.2478 87 ......... 410.623 2,001.94 333.625 3.8754

33 ......... 25,493.225 485,690.08 6,812.837 18.0517 88 ......... 342.239 1,591.32 281.034 3.6497

34 ......... 24,411.776 460,196.85 6,711.897 17.8514 89 ......... 281.891 1,249.08 233.849 3.4311

35 ......... 23,370.735 435,785.07 6,609.771 17.6466 90 ......... 228.873 967.19 191.673 3.2259

36 ......... 22,368.301 412,414.34 6,506.211 17.4374 91 ......... 182.730 738.32 154.333 3.0405

37 ......... 21,402.548 390,046.04 6,400.778 17.2243 92 ......... 143.184 555.59 121.816 2.8802

38 ......... 20,473.264 368,643.49 6,294.668 17.0061 93 ......... 110.137 412.40 94.275 2.7445

39 ......... 19,580.120 348,170.23 6,188.957 16.7818 94 ......... 83.453 302.27 71.827 2.6220

40 ......... 18,721.852 328,590.11 6,083.772 16.5512 95 ......... 62.537 218.82 54.121 2.4990

41 ......... 17,897.436 309,868.25 5,979.427 16.3136 96 ......... 46.360 156.28 40.349 2.3710

42 ......... 17,105.276 291,970.82 5,875.629 16.0691 97 ......... 33.857 109.92 29.629 2.2466

43 ......... 16,343.501 274,865.54 5,771.749 15.8180 95 ......... 24.335 76.06 21.409 2.1256

44 ......... 15,610.392 258,522.04 5,667.236 15.5609 99 ......... 17.195 51.73 15.206 2.0083

45 ......... 14,904.191 242,911.65 5,561.436 15.2982 100 ......... 11.931 34.53 10.603 1.8943

46 ......... 14,223.296 228,007.46 5,453.778 15.0306 101 ......... 8.119 22.60 7.250 1.7838

47 ......... 13,566.081 213,784.16 5,343.614 14.7587 102 ......... 5.411 14.48 4.854 1.6766

48 ......... 12,931.685 200,218.08 5,230.989 14.4828 103 ......... 3.526 9.07 3.177 1.5728

49 ......... 12,319.142 187,286.40 5,115.819 14.2029 104 ......... 2.243 5.55 2.030 1.4722

50 ......... 11,727.974 174,967.25 4,998.465 13.9188 105 ......... 1.391 3.30 1.264 1.3749

51 ......... 11,157.293 163,239.28 4,878.859 13.6307 106 ......... 0.838 1.91 0.765 1.2807

52 ......... 10,606.005 152,081.99 4,756.698 13.3392 107 ......... 0.490 1.07 0.449 1.1897

53 ......... 10,073.114 141,475.98 4,631.730 13.0449 108 ......... 0.278 0.58 0.255 1.1017

54 ......... 9,557.226 131,402.87 4,503.269 12.7491 109 ......... 0.152 0.31 0.140 1.0167

x x x x x x x x

91
Table 8.E. -- Actuarial Functions at 5.0 Percent Interest for 1989-91 United States 

Males Other than White

x D N M a x D N M a

0 ......... 100,000.000 1,947,403.06 7,266.521 18.4740 55 ......... 5,350.777 65,810.98 2,216.921 11.2993

1 ......... 93,607.619 1,847,403.06 5,636.045 18.7356 56 ......... 5,016.199 60,460.20 2,137.142 11.0530

2 ......... 89,042.177 1,753,795.44 5,528.108 18.6962 57 ......... 4,696.208 55,444.01 2,056.018 10.8061

3 ......... 84,737.285 1,664,753.26 5,463.321 18.6461 58 ......... 4,390.361 50,747.80 1,973.799 10.5589

4 ......... 80,650.346 1,580,015.98 5,411.490 18.5909 59 ......... 4,098.326 46,357.44 1,890.829 10.3113

5 ......... 76,773.028 1,499,365.63 5,374.665 18.5298 60 ......... 3,819.867 42,259.11 1,807.528 10.0630

6 ......... 73,085.828 1,422,592.60 5,343.324 18.4647 61 ......... 3,554.912 38,439.24 1,724.472 9.8130

7 ......... 69,579.256 1,349,506.77 5,317.028 18.3952 62 ......... 3,302.984 34,884.33 1,641.825 9.5615

8 ......... 66,242.945 1,279,927.52 5,294.016 18.3217 63 ......... 3,063.520 31,581.35 1,559.646 9.3088

9 ......... 63,069.826 1,213,684.57 5,275.322 18.2435 64 ......... 2,835.672 28,517.83 1,477.681 9.0568

10 ......... 60,052.381 1,150,614.75 5,261.202 18.1602 65 ......... 2,618.929 25,682.16 1,395.969 8.8064

11 ......... 57,181.634 1,090,562.37 5,250.093 18.0719 66 ......... 2,413.161 23,063.23 1,314.912 8.5573

12 ......... 54,447.563 1,033,380.73 5,238.956 17.9794 67 ......... 2,218.389 20,650.07 1,235.052 8.3086

13 ......... 51,838.382 978,933.17 5,222.517 17.8843 68 ......... 2,034.447 18,431.68 1,156.749 8.0598

14 ......... 49,342.614 927,094.79 5,195.243 17.7889 69 ......... 1,861.027 16,397.23 1,080.207 7.8108

15 ......... 46,952.560 877,752.17 5,154.837 17.6944 70 ......... 1,697.636 14,536.20 1,005.436 7.5626

16 ......... 44,662.667 830,799.61 5,100.780 17.6017 71 ......... 1,543.677 12,838.57 932.317 7.3169

17 ......... 42,470.865 786,136.95 5,035.772 17.5100 72 ......... 1,398.623 11,294.89 860.771 7.0757

18 ......... 40,375.727 743,666.08 4,963.056 17.4186 73 ......... 1,262.350 9,896.27 791.100 6.8396

19 ......... 38,375.509 703,290.36 4,885.492 17.3265 74 ......... 1,135.073 8,633.92 723.935 6.6065

20 ......... 36,468.957 664,914.85 4,806.345 17.2324 75 ......... 1,017.004 7,498.84 659.916 6.3735

21 ......... 34,650.860 628,445.89 4,724.865 17.1365 76 ......... 908.047 6,481.84 599.388 6.1382

22 ......... 32,917.750 593,795.03 4,641.796 17.0387 77 ......... 807.698 5,573.79 542.279 5.9008

23 ......... 31,266.566 560,877.28 4,558.124 16.9386 78 ......... 715.492 4,766.09 488.535 5.6613

24 ......... 29,695.204 529,610.71 4,475.646 16.8349 79 ......... 630.681 4,050.60 437.795 5.4226

25 ......... 28,201.415 499,915.51 4,395.914 16.7266 80 ......... 552.668 3,419.92 389.814 5.1880

26 ......... 26,781.149 471,714.10 4,318.573 16.6137 81 ......... 480.865 2,867.25 344.330 4.9627

27 ......... 25,431.394 444,932.95 4,244.111 16.4954 82 ......... 415.051 2,386.39 301.413 4.7496

28 ......... 24,147.419 419,501.55 4,171.154 16.3725 83 ......... 355.338 1,971.34 261.465 4.5478

29 ......... 22,925.144 395,354.13 4,098.756 16.2454 84 ......... 302.047 1,616.00 225.095 4.3502

30 ......... 21,760.818 372,428.99 4,026.104 16.1147 85 ......... 255.224 1,313.95 192.654 4.1482

31 ......... 20,651.649 350,668.17 3,953.165 15.9802 86 ......... 214.327 1,058.73 163.912 3.9398

32 ......... 19,595.624 330,016.52 3,880.551 15.8413 87 ......... 178.597 844.40 138.388 3.7280

33 ......... 18,589.945 310,420.90 3,807.997 15.6983 88 ......... 147.436 665.80 115.731 3.5159

34 ......... 17,631.804 291,830.95 3,735.092 15.5514 89 ......... 120.282 518.37 95.598 3.3096

35 ......... 16,719.134 274,199.15 3,662.032 15.4003 90 ......... 96.729 398.08 77.773 3.1154

36 ......... 15,849.605 257,480.02 3,588.652 15.2452 91 ......... 76.492 301.36 62.142 2.9397

37 ......... 15,020.866 241,630.41 3,514.656 15.0863 92 ......... 59.367 224.86 48.660 2.7877

38 ......... 14,231.826 226,609.54 3,440.895 14.9227 93 ......... 45.230 165.50 37.349 2.6590

39 ......... 13,481.336 212,377.72 3,368.111 14.7535 94 ......... 33.945 120.27 28.218 2.5429

40 ......... 12,767.634 198,896.38 3,296.378 14.5782 95 ......... 25.195 86.32 21.085 2.4260

41 ......... 12,089.170 186,128.75 3,225.896 14.3963 96 ......... 18.500 61.13 15.589 2.3041

42 ......... 11,444.051 174,039.58 3,156.451 14.2079 97 ......... 13.382 42.63 11.352 2.1853

43 ......... 10,830.259 162,595.53 3,087.614 14.0131 95 ......... 9.527 29.24 8.134 2.0696

44 ......... 10,245.934 151,765.27 3,019.017 13.8122 99 ......... 6.667 19.72 5.729 1.9571

45 ......... 9,689.251 141,519.34 2,950.235 13.6058 100 ......... 4.582 13.05 3.961 1.8477

46 ......... 9,158.537 131,830.08 2,880.914 13.3942 101 ......... 3.088 8.47 2.685 1.7414

47 ......... 8,652.155 122,671.55 2,810.653 13.1781 102 ......... 2.039 5.38 1.783 1.6382

48 ......... 8,169.003 114,019.39 2,739.508 12.9576 103 ......... 1.316 3.34 1.157 1.5381

49 ......... 7,707.942 105,850.39 2,667.447 12.7326 104 ......... 0.829 2.02 0.733 1.4409

50 ......... 7,268.169 98,142.45 2,594.719 12.5030 105 ......... 0.509 1.19 0.452 1.3467

51 ......... 6,848.649 90,874.28 2,521.302 12.2689 106 ......... 0.304 0.69 0.271 1.2554

52 ......... 6,448.251 84,025.63 2,447.030 12.0308 107 ......... 0.176 0.38 0.158 1.1670

53 ......... 6,065.937 77,577.38 2,371.776 11.7890 108 ......... 0.099 0.21 0.089 1.0815

54 ......... 5,700.461 71,511.44 2,295.155 11.5449 109 ......... 0.053 0.11 0.048 0.9987

x x x x x x x x

92
Table 8.F. -- Actuarial Functions at 6.0 Percent Interest for 1989-91 United States 

Males Other than White

x D N M a x D N M a

0 ......... 100,000.000 1,672,630.64 5,322.794 15.7263 55 ......... 3,176.916 35,952.97 1,141.842 10.3169

1 ......... 92,724.528 1,572,630.64 3,707.699 15.9602 56 ......... 2,950.170 32,776.06 1,094.922 10.1099

2 ......... 87,370.061 1,479,906.12 3,601.790 15.9384 57 ......... 2,735.918 29,825.89 1,047.660 9.9016

3 ......... 82,361.614 1,392,536.05 3,538.818 15.9076 58 ......... 2,533.608 27,089.97 1,000.213 9.6923

4 ......... 77,649.734 1,310,174.44 3,488.916 15.8729 59 ......... 2,342.767 24,556.36 952.785 9.4818

5 ......... 73,219.345 1,232,524.71 3,453.795 15.8333 60 ......... 2,162.989 22,213.59 905.615 9.2699

6 ......... 69,045.245 1,159,305.36 3,424.187 15.7905 61 ......... 1,993.968 20,050.60 859.029 9.0556

7 ......... 65,112.417 1,090,260.12 3,399.580 15.7443 62 ......... 1,835.183 18,056.64 813.109 8.8391

8 ......... 61,405.476 1,025,147.70 3,378.248 15.6947 63 ......... 1,686.076 16,221.45 767.880 8.6208

9 ......... 57,912.529 963,742.22 3,361.083 15.6413 64 ......... 1,545.951 14,535.38 723.194 8.4022

10 ......... 54,621.619 905,829.69 3,348.240 15.5837 65 ......... 1,414.317 12,989.43 679.067 8.1842

11 ......... 51,519.820 851,208.08 3,338.231 15.5220 66 ......... 1,290.901 11,575.11 635.706 7.9667

12 ......... 48,593.664 799,688.26 3,328.291 15.4566 67 ......... 1,175.514 10,284.21 593.389 7.7487

13 ......... 45,828.546 751,094.59 3,313.757 15.3892 68 ......... 1,067.874 9,108.69 552.287 7.5297

14 ......... 43,210.593 705,266.05 3,289.873 15.3216 69 ......... 967.631 8,040.82 512.490 7.3098

15 ......... 40,729.660 662,055.45 3,254.823 15.2549 70 ......... 874.349 7,073.19 473.980 7.0897

16 ......... 38,377.757 621,325.79 3,208.373 15.1897 71 ......... 787.554 6,198.84 436.676 6.8710

17 ......... 36,150.098 582,948.04 3,153.039 15.1258 72 ......... 706.819 5,411.29 400.519 6.6558

18 ......... 34,042.556 546,797.94 3,091.729 15.0622 73 ......... 631.932 4,704.47 365.642 6.4446

19 ......... 32,050.838 512,755.38 3,026.949 14.9982 74 ......... 562.857 4,072.54 332.336 6.2355

20 ......... 30,171.161 480,704.54 2,961.470 14.9326 75 ......... 499.551 3,509.68 300.890 6.0257

21 ......... 28,396.586 450,533.38 2,894.696 14.8658 76 ......... 441.824 3,010.13 271.439 5.8130

22 ......... 26,721.798 422,136.80 2,827.263 14.7975 77 ......... 389.290 2,568.30 243.914 5.5974

23 ......... 25,141.962 395,415.00 2,759.981 14.7273 78 ......... 341.596 2,179.01 218.255 5.3789

24 ......... 23,653.136 370,273.04 2,694.284 14.6543 79 ......... 298.264 1,837.42 194.259 5.1604

25 ......... 22,251.369 346,619.90 2,631.375 14.5775 80 ......... 258.904 1,539.15 171.782 4.9449

26 ......... 20,931.410 324,368.53 2,570.927 14.4967 81 ......... 223.142 1,280.25 150.675 4.7374

27 ......... 19,688.965 303,437.12 2,513.279 14.4115 82 ......... 190.784 1,057.11 130.948 4.5408

28 ......... 18,518.545 283,748.16 2,457.329 14.3224 83 ......... 161.796 866.32 112.758 4.3544

29 ......... 17,415.328 265,229.61 2,402.331 14.2297 84 ......... 136.233 704.53 96.354 4.1715

30 ......... 16,374.884 247,814.29 2,347.660 14.1338 85 ......... 114.028 568.29 81.861 3.9838

31 ......... 15,393.635 231,439.40 2,293.292 14.0347 86 ......... 94.853 454.27 69.140 3.7891

32 ......... 14,468.682 216,045.77 2,239.676 13.9320 87 ......... 78.295 359.41 57.951 3.5905

33 ......... 13,596.634 201,577.08 2,186.611 13.8255 88 ......... 64.025 281.12 48.112 3.3908

34 ......... 12,774.194 187,980.45 2,133.791 13.7156 89 ......... 51.740 217.09 39.452 3.1958

35 ......... 11,998.694 175,206.26 2,081.358 13.6021 90 ......... 41.216 165.35 31.857 3.0118

36 ......... 11,267.357 163,207.56 2,029.193 13.4850 91 ......... 32.286 124.14 25.259 2.8449

37 ......... 10,577.476 151,940.21 1,977.087 13.3645 92 ......... 24.821 91.85 19.622 2.7005

38 ......... 9,927.299 141,362.73 1,925.635 13.2398 93 ......... 18.732 67.03 14.938 2.5783

39 ......... 9,315.085 131,435.43 1,875.344 13.1100 94 ......... 13.926 48.30 11.192 2.4682

40 ......... 8,738.719 122,120.35 1,826.247 12.9746 95 ......... 10.239 34.37 8.293 2.3570

41 ......... 8,196.289 113,381.63 1,778.461 12.8333 96 ......... 7.447 24.13 6.081 2.2406

42 ......... 7,685.710 105,185.34 1,731.823 12.6858 97 ......... 5.336 16.69 4.391 2.1271

43 ......... 7,204.875 97,499.63 1,686.029 12.5325 95 ......... 3.763 11.35 3.120 2.0163

44 ......... 6,751.848 90,294.75 1,640.824 12.3733 99 ......... 2.609 7.59 2.179 1.9084

45 ......... 6,324.770 83,542.90 1,595.927 12.2088 100 ......... 1.776 4.98 1.494 1.8033

46 ......... 5,921.941 77,218.13 1,551.103 12.0393 101 ......... 1.186 3.20 1.004 1.7010

47 ......... 5,541.734 71,296.19 1,506.101 11.8653 102 ......... 0.775 2.02 0.661 1.6015

48 ......... 5,182.912 65,754.46 1,460.962 11.6868 103 ......... 0.496 1.24 0.425 1.5048

49 ......... 4,844.252 60,571.55 1,415.673 11.5038 104 ......... 0.309 0.75 0.267 1.4108

50 ......... 4,524.772 55,727.30 1,370.397 11.3160 105 ......... 0.188 0.44 0.163 1.3196

51 ......... 4,223.378 51,202.52 1,325.122 11.1236 106 ......... 0.111 0.25 0.097 1.2310

52 ......... 3,938.950 46,979.14 1,279.753 10.9268 107 ......... 0.064 0.14 0.056 1.1452

53 ......... 3,670.455 43,040.19 1,234.217 10.7261 108 ......... 0.035 0.07 0.031 1.0620

54 ......... 3,416.768 39,369.74 1,188.292 10.5225 109 ......... 0.019 0.04 0.017 0.9814

x x x x x x x x

93
Table 8.G. -- Actuarial Functions at 7.0 Percent Interest for 1989-91 United States 

Males Other than White

x D N M a x D N M a

0 ......... 100,000.000 1,464,889.20 4,166.127 13.6489 55 ......... 1,895.486 19,852.64 596.715 9.4736

1 ......... 91,857.944 1,364,889.20 2,566.127 13.8587 56 ......... 1,743.749 17,957.15 568.982 9.2980

2 ......... 85,744.607 1,273,031.26 2,462.188 13.8468 57 ......... 1,601.998 16,213.40 541.308 9.1207

3 ......... 80,073.924 1,187,286.65 2,400.965 13.8274 58 ......... 1,469.672 14,611.41 513.786 8.9420

4 ......... 74,787.381 1,107,212.73 2,352.903 13.8048 59 ......... 1,346.270 13,141.73 486.531 8.7616

5 ......... 69,861.238 1,032,425.35 2,319.393 13.7782 60 ......... 1,231.344 11,795.46 459.678 8.5793

6 ......... 65,262.890 962,564.11 2,291.406 13.7490 61 ......... 1,124.516 10,564.12 433.405 8.3944

7 ......... 60,970.313 897,301.22 2,268.365 13.7170 62 ......... 1,025.295 9,439.60 407.751 8.2067

8 ......... 56,961.813 836,330.90 2,248.576 13.6823 63 ......... 933.187 8,414.31 382.718 8.0167

9 ......... 53,219.565 779,369.09 2,232.802 13.6444 64 ......... 847.636 7,481.12 358.217 7.8259

10 ......... 49,726.219 726,149.53 2,221.110 13.6030 65 ......... 768.215 6,633.49 334.248 7.6349

11 ......... 46,464.075 676,423.31 2,212.083 13.5580 66 ......... 694.626 5,865.27 310.916 7.4438

12 ......... 43,415.489 629,959.23 2,203.203 13.5100 67 ......... 626.625 5,170.65 288.358 7.2516

13 ......... 40,562.360 586,543.74 2,190.339 13.4603 68 ......... 563.926 4,544.02 266.653 7.0578

14 ......... 37,887.805 545,981.38 2,169.397 13.4105 69 ......... 506.213 3,980.09 245.833 6.8625

15 ......... 35,378.718 508,093.58 2,138.952 13.3616 70 ......... 453.139 3,473.88 225.875 6.6663

16 ......... 33,024.252 472,714.86 2,098.981 13.3142 71 ......... 404.342 3,020.74 206.723 6.4708

17 ......... 30,816.617 439,690.61 2,051.811 13.2680 72 ......... 359.499 2,616.40 188.333 6.2779

18 ......... 28,748.801 408,873.99 2,000.035 13.2223 73 ......... 318.407 2,256.90 170.760 6.0881

19 ......... 26,813.843 380,125.19 1,945.840 13.1765 74 ......... 280.952 1,938.49 154.135 5.8997

20 ......... 25,005.398 353,311.35 1,891.572 13.1294 75 ......... 247.023 1,657.54 138.585 5.7101

21 ......... 23,314.707 328,305.95 1,836.748 13.0815 76 ......... 216.435 1,410.52 124.158 5.5170

22 ......... 21,734.598 304,991.24 1,781.900 13.0325 77 ......... 188.918 1,194.08 110.801 5.3206

23 ......... 20,258.495 283,256.64 1,727.686 12.9821 78 ......... 164.224 1,005.17 98.465 5.1207

24 ......... 18,880.732 262,998.15 1,675.245 12.9294 79 ......... 142.051 840.94 87.037 4.9200

25 ......... 17,595.796 244,117.42 1,625.498 12.8736 80 ......... 122.153 698.89 76.432 4.7214

26 ......... 16,397.316 226,521.62 1,578.144 12.8146 81 ......... 104.297 576.74 66.566 4.5298

27 ......... 15,279.856 210,124.30 1,533.406 12.7517 82 ......... 88.339 472.44 57.432 4.3480

28 ......... 14,237.224 194,844.45 1,490.391 12.6856 83 ......... 74.216 384.10 49.088 4.1754

29 ......... 13,263.929 180,607.22 1,448.503 12.6164 84 ......... 61.907 309.88 41.634 4.0057

30 ......... 12,354.946 167,343.30 1,407.254 12.5446 85 ......... 51.332 247.98 35.109 3.8308

31 ......... 11,506.041 154,988.35 1,366.616 12.4702 86 ......... 42.301 196.65 29.437 3.6487

32 ......... 10,713.609 143,482.31 1,326.915 12.3925 87 ......... 34.590 154.34 24.493 3.4621

33 ......... 9,973.792 132,768.70 1,287.989 12.3118 88 ......... 28.021 119.75 20.187 3.2737

34 ......... 9,282.917 122,794.91 1,249.605 12.2281 89 ......... 22.433 91.73 16.432 3.0891

35 ......... 8,637.877 113,511.99 1,211.859 12.1412 90 ......... 17.703 69.30 13.170 2.9145

36 ......... 8,035.580 104,874.11 1,174.657 12.0512 91 ......... 13.738 51.60 10.362 2.7558

37 ......... 7,473.074 96,838.53 1,137.843 11.9583 92 ......... 10.463 37.86 7.986 2.6183

38 ......... 6,948.170 89,365.46 1,101.831 11.8617 93 ......... 7.822 27.40 6.030 2.5022

39 ......... 6,458.747 82,417.29 1,066.961 11.7606 94 ......... 5.761 19.57 4.481 2.3975

40 ......... 6,002.488 75,958.54 1,033.237 11.6545 95 ......... 4.196 13.81 3.293 2.2916

41 ......... 5,577.285 69,956.06 1,000.721 11.5430 96 ......... 3.023 9.62 2.394 2.1804

42 ......... 5,180.977 64,378.77 969.282 11.4260 97 ......... 2.146 6.59 1.715 2.0717

43 ......... 4,811.453 59,197.79 938.700 11.3035 95 ......... 1.499 4.45 1.208 1.9656

44 ......... 4,466.779 54,386.34 908.795 11.1757 99 ......... 1.030 2.95 0.837 1.8619

45 ......... 4,145.135 49,919.56 879.369 11.0429 100 ......... 0.694 1.92 0.569 1.7608

46 ......... 3,844.856 45,774.43 850.267 10.9054 101 ......... 0.459 1.22 0.379 1.6623

47 ......... 3,564.378 41,929.57 821.322 10.7635 102 ......... 0.298 0.76 0.248 1.5663

48 ......... 3,302.433 38,365.19 792.561 10.6172 103 ......... 0.188 0.47 0.158 1.4728

49 ......... 3,057.799 35,062.76 763.974 10.4667 104 ......... 0.117 0.28 0.098 1.3819

50 ......... 2,829.444 32,004.96 735.662 10.3114 105 ......... 0.070 0.16 0.060 1.2935

51 ......... 2,616.294 29,175.51 707.615 10.1515 106 ......... 0.041 0.09 0.035 1.2076

52 ......... 2,417.292 26,559.22 679.772 9.9872 107 ......... 0.023 0.05 0.020 1.1241

53 ......... 2,231.467 24,141.93 652.089 9.8189 108 ......... 0.013 0.03 0.011 1.0432

54 ......... 2,057.824 21,910.46 624.429 9.6474 109 ......... 0.007 0.01 0.006 0.9646

x x x x x x x x

94
Table 8.H. -- Actuarial Functions at 8.0 Percent Interest for 1989-91 United States 

Males Other than White

x D N M a x D N M a

0 ......... 100,000.000 1,303,469.42 3,446.710 12.0347 55 ......... 1,136.375 11,073.21 316.138 8.7443

1 ......... 91,007.407 1,203,469.42 1,861.525 12.2239 56 ......... 1,035.727 9,936.83 299.665 8.5941

2 ......... 84,164.095 1,112,462.01 1,759.501 12.2178 57 ......... 942.721 8,901.11 283.380 8.4419

3 ......... 77,870.180 1,028,297.91 1,699.964 12.2053 58 ......... 856.844 7,958.38 267.334 8.2880

4 ......... 72,055.711 950,427.73 1,653.657 12.1902 59 ......... 777.631 7,101.54 251.591 8.1323

5 ......... 66,686.264 878,372.02 1,621.670 12.1717 60 ......... 704.662 6,323.91 236.224 7.9744

6 ......... 61,720.074 811,685.76 1,595.203 12.1511 61 ......... 637.569 5,619.25 221.328 7.8136

7 ......... 57,126.627 749,965.69 1,573.613 12.1281 62 ......... 575.931 4,981.68 206.917 7.6498

8 ......... 52,876.656 692,839.06 1,555.244 12.1029 63 ......... 519.338 4,405.75 192.986 7.4834

9 ......... 48,945.359 639,962.40 1,540.737 12.0750 64 ......... 467.359 3,886.41 179.477 7.3157

10 ......... 45,309.124 591,017.04 1,530.084 12.0441 65 ......... 419.647 3,419.05 166.384 7.1474

11 ......... 41,944.744 545,707.92 1,521.935 12.0102 66 ......... 375.935 2,999.40 153.756 6.9785

12 ......... 38,829.783 503,763.18 1,513.993 11.9736 67 ......... 335.992 2,623.47 141.661 6.8081

13 ......... 35,942.104 464,933.39 1,502.594 11.9356 68 ......... 299.574 2,287.48 130.131 6.6358

14 ......... 33,261.341 428,991.29 1,484.209 11.8976 69 ......... 266.425 1,987.90 119.173 6.4614

15 ......... 30,771.058 395,729.95 1,457.729 11.8605 70 ......... 236.283 1,721.48 108.766 6.2857

16 ......... 28,457.277 364,958.89 1,423.286 11.8248 71 ......... 208.886 1,485.20 98.872 6.1101

17 ......... 26,309.061 336,501.61 1,383.016 11.7903 72 ......... 184.001 1,276.31 89.459 5.9364

18 ......... 24,316.448 310,192.55 1,339.222 11.7565 73 ......... 161.460 1,092.31 80.548 5.7652

19 ......... 22,469.814 285,876.10 1,293.806 11.7227 74 ......... 141.148 930.85 72.196 5.5948

20 ......... 20,760.328 263,406.29 1,248.751 11.6880 75 ......... 122.953 789.70 64.456 5.4228

21 ......... 19,177.431 242,645.96 1,203.656 11.6527 76 ......... 106.731 666.75 57.342 5.2470

22 ......... 17,712.183 223,468.53 1,158.959 11.6167 77 ......... 92.299 560.02 50.816 5.0674

23 ......... 16,356.399 205,756.35 1,115.188 11.5796 78 ......... 79.491 467.72 44.845 4.8839

24 ......... 15,102.866 189,399.95 1,073.240 11.5407 79 ......... 68.122 388.23 39.364 4.6990

25 ......... 13,944.710 174,297.08 1,033.815 11.4992 80 ......... 58.037 320.11 34.326 4.5155

26 ......... 12,874.588 160,352.37 996.635 11.4550 81 ......... 49.094 262.07 29.682 4.3380

27 ......... 11,886.113 147,477.78 961.833 11.4076 82 ......... 41.198 212.97 25.422 4.1695

28 ......... 10,972.509 135,591.67 928.681 11.3574 83 ......... 34.291 171.78 21.567 4.0093

29 ......... 10,127.747 124,619.16 896.698 11.3047 84 ......... 28.339 137.48 18.155 3.8515

30 ......... 9,346.339 114,491.41 865.493 11.2499 85 ......... 23.280 109.15 15.196 3.6883

31 ......... 8,623.560 105,145.08 835.036 11.1928 86 ......... 19.007 85.87 12.647 3.5175

32 ......... 7,955.299 96,521.52 805.557 11.1330 87 ......... 15.398 66.86 10.446 3.3419

33 ......... 7,337.381 88,566.22 776.920 11.0705 88 ......... 12.359 51.46 8.547 3.1638

34 ......... 6,765.895 81,228.84 748.944 11.0056 89 ......... 9.802 39.10 6.906 2.9889

35 ......... 6,237.460 74,462.94 721.687 10.9380 90 ......... 7.664 29.30 5.494 2.8229

36 ......... 5,748.811 68,225.48 695.071 10.8678 91 ......... 5.892 21.63 4.290 2.6717

37 ......... 5,296.879 62,476.67 668.978 10.7950 92 ......... 4.446 15.74 3.280 2.5407

38 ......... 4,879.230 57,179.79 643.690 10.7190 93 ......... 3.293 11.30 2.456 2.4301

39 ......... 4,493.545 52,300.56 619.430 10.6390 94 ......... 2.403 8.00 1.810 2.3305

40 ......... 4,137.444 47,807.02 596.184 10.5547 95 ......... 1.734 5.60 1.319 2.2295

41 ......... 3,808.761 43,669.57 573.978 10.4656 96 ......... 1.238 3.87 0.951 2.1232

42 ......... 3,505.360 39,860.81 552.707 10.3714 97 ......... 0.871 2.63 0.676 2.0191

43 ......... 3,225.204 36,355.45 532.208 10.2723 95 ......... 0.603 1.76 0.472 1.9172

44 ......... 2,966.439 33,130.25 512.347 10.1684 99 ......... 0.410 1.16 0.324 1.8176

45 ......... 2,727.343 30,163.81 492.986 10.0598 100 ......... 0.274 0.75 0.219 1.7203

46 ......... 2,506.346 27,436.46 474.016 9.9468 101 ......... 0.179 0.47 0.145 1.6252

47 ......... 2,301.998 24,930.12 455.322 9.8298 102 ......... 0.115 0.29 0.094 1.5326

48 ......... 2,113.076 22,628.12 436.919 9.7086 103 ......... 0.072 0.18 0.059 1.4422

49 ......... 1,938.430 20,515.04 418.797 9.5833 104 ......... 0.044 0.10 0.037 1.3541

50 ......... 1,777.060 18,576.62 401.015 9.4536 105 ......... 0.026 0.06 0.022 1.2683

51 ......... 1,627.975 16,799.55 383.563 9.3193 106 ......... 0.015 0.03 0.013 1.1849

52 ......... 1,490.219 15,171.58 366.399 9.1808 107 ......... 0.009 0.02 0.007 1.1038

53 ......... 1,362.924 13,681.36 349.490 9.0382 108 ......... 0.005 0.01 0.004 1.0250

54 ......... 1,245.229 12,318.44 332.753 8.8925 109 ......... 0.002 0.00 0.002 0.9484

x x x x x x x x

95
Table 8.I. -- Actuarial Functions at 9.0 Percent Interest for 1989-91 United States 

Males Other than White

x D N M a x D N M a

0 ......... 100,000.000 1,175,030.96 2,979.095 10.7503 55 ......... 684.496 6,235.19 169.664 8.1092

1 ......... 90,172.477 1,075,030.96 1,408.453 10.9219 56 ......... 618.147 5,550.69 159.833 7.9796

2 ......... 82,626.883 984,858.48 1,308.293 10.9193 57 ......... 557.477 4,932.54 150.203 7.8480

3 ......... 75,746.566 902,231.60 1,250.380 10.9112 58 ......... 502.045 4,375.07 140.801 7.7145

4 ......... 69,447.632 826,485.03 1,205.749 10.9008 59 ......... 451.452 3,873.02 131.662 7.5790

5 ......... 63,682.877 757,037.40 1,175.202 10.8876 60 ......... 405.337 3,421.57 122.822 7.4413

6 ......... 58,399.615 693,354.52 1,150.159 10.8726 61 ......... 363.379 3,016.23 114.332 7.3005

7 ......... 53,557.388 634,954.91 1,129.918 10.8556 62 ......... 325.237 2,652.85 106.194 7.1567

8 ......... 49,118.155 581,397.52 1,112.855 10.8367 63 ......... 290.588 2,327.62 98.399 7.0100

9 ......... 45,049.175 532,279.36 1,099.503 10.8155 64 ......... 259.105 2,037.03 90.910 6.8618

10 ......... 41,319.803 487,230.19 1,089.787 10.7917 65 ......... 230.518 1,777.92 83.717 6.7127

11 ......... 37,900.713 445,910.39 1,082.424 10.7652 66 ......... 204.612 1,547.40 76.845 6.5626

12 ......... 34,764.185 408,009.67 1,075.313 10.7365 67 ......... 181.195 1,342.79 70.322 6.4108

13 ......... 31,883.637 373,245.49 1,065.202 10.7065 68 ......... 160.073 1,161.60 64.161 6.2567

14 ......... 29,234.883 341,361.85 1,049.043 10.6765 69 ......... 141.054 1,001.53 58.359 6.1003

15 ......... 26,797.933 312,126.97 1,025.981 10.6474 70 ......... 123.948 860.47 52.900 5.9422

16 ......... 24,555.539 285,329.03 996.261 10.6197 71 ......... 108.571 736.52 47.758 5.7838

17 ......... 22,493.587 260,773.50 961.831 10.5932 72 ......... 94.759 627.95 42.910 5.6268

18 ......... 20,599.220 238,279.91 924.732 10.5674 73 ......... 82.388 533.19 38.363 5.4717

19 ......... 18,860.247 217,680.69 886.612 10.5418 74 ......... 71.363 450.80 34.140 5.3171

20 ......... 17,265.508 198,820.44 849.141 10.5155 75 ......... 61.593 379.44 30.263 5.1604

21 ......... 15,802.756 181,554.93 811.982 10.4888 76 ......... 52.976 317.85 26.732 4.9998

22 ......... 14,461.447 165,752.18 775.488 10.4617 77 ......... 45.393 264.87 23.522 4.8351

23 ......... 13,231.973 151,290.73 740.078 10.4337 78 ......... 38.735 219.48 20.613 4.6662

24 ......... 12,105.801 138,058.76 706.454 10.4043 79 ......... 32.891 180.74 17.967 4.4953

25 ......... 11,074.928 125,952.96 675.143 10.3728 80 ......... 27.764 147.85 15.556 4.3253

26 ......... 10,131.227 114,878.03 645.885 10.3390 81 ......... 23.271 120.09 13.355 4.1605

27 ......... 9,267.568 104,746.80 618.750 10.3025 82 ......... 19.349 96.82 11.354 4.0039

28 ......... 8,476.746 95,479.23 593.139 10.2637 83 ......... 15.957 77.47 9.561 3.8549

29 ......... 7,752.349 87,002.49 568.657 10.2227 84 ......... 13.066 61.51 7.987 3.7078

30 ......... 7,088.580 79,250.14 544.991 10.1800 85 ......... 10.636 48.45 6.635 3.5552

31 ......... 6,480.396 72,161.56 522.103 10.1354 86 ......... 8.604 37.81 5.482 3.3948

32 ......... 5,923.368 65,681.16 500.153 10.0885 87 ......... 6.906 29.21 4.495 3.2292

33 ......... 5,413.156 59,757.79 479.026 10.0394 88 ......... 5.492 22.30 3.651 3.0607

34 ......... 4,945.748 54,344.64 458.576 9.9882 89 ......... 4.316 16.81 2.928 2.8946

35 ......... 4,517.642 49,398.89 438.835 9.9347 90 ......... 3.344 12.49 2.312 2.7365

36 ......... 4,125.526 44,881.25 419.735 9.8789 91 ......... 2.547 9.15 1.792 2.5923

37 ......... 3,766.332 40,755.72 401.181 9.8211 92 ......... 1.904 6.60 1.359 2.4673

38 ......... 3,437.534 36,989.39 383.365 9.7604 93 ......... 1.398 4.70 1.010 2.3619

39 ......... 3,136.766 33,551.86 366.430 9.6963 94 ......... 1.010 3.30 0.738 2.2669

40 ......... 2,861.689 30,415.09 350.352 9.6284 95 ......... 0.722 2.29 0.533 2.1706

41 ......... 2,610.185 27,553.40 335.134 9.5561 96 ......... 0.511 1.57 0.382 2.0687

42 ......... 2,380.222 24,943.21 320.690 9.4794 97 ......... 0.356 1.06 0.269 1.9689

43 ......... 2,169.898 22,562.99 306.898 9.3982 95 ......... 0.244 0.70 0.186 1.8710

44 ......... 1,977.492 20,393.10 293.659 9.3126 99 ......... 0.165 0.46 0.127 1.7752

45 ......... 1,801.425 18,415.60 280.871 9.2228 100 ......... 0.109 0.29 0.085 1.6814

46 ......... 1,640.268 16,614.18 268.456 9.1289 101 ......... 0.071 0.18 0.056 1.5897

47 ......... 1,492.712 14,973.91 256.334 9.0313 102 ......... 0.045 0.11 0.036 1.5002

48 ......... 1,357.636 13,481.20 244.510 8.9299 103 ......... 0.028 0.07 0.022 1.4127

49 ......... 1,234.001 12,123.56 232.974 8.8246 104 ......... 0.017 0.04 0.014 1.3274

50 ......... 1,120.895 10,889.56 221.757 8.7151 105 ......... 0.010 0.02 0.008 1.2442

51 ......... 1,017.437 9,768.66 210.851 8.6012 106 ......... 0.006 0.01 0.005 1.1631

52 ......... 922.800 8,751.23 200.222 8.4833 107 ......... 0.003 0.01 0.003 1.0842

53 ......... 836.231 7,828.43 189.847 8.3616 108 ......... 0.002 0.00 0.001 1.0074

54 ......... 757.009 6,992.20 179.672 8.2366 109 ......... 0.001 0.00 0.001 0.9327

x x x x x x x x

96
Table 8.J. -- Actuarial Functions at 10.0 Percent Interest for 1989-91 United States 

Males Other than White

x D N M a x D N M a

0 ......... 100,000.000 1,070,719.49 2,661.864 9.7072 55 ......... 414.220 3,542.56 92.168 7.5524

1 ......... 89,352.727 970,719.49 1,105.501 9.8639 56 ......... 370.668 3,128.34 86.273 7.4397

2 ......... 81,131.405 881,366.77 1,007.154 9.8634 57 ......... 331.249 2,757.68 80.551 7.3251

3 ......... 73,699.474 800,235.36 950.805 9.8581 58 ......... 295.600 2,426.43 75.015 7.2085

4 ......... 66,956.492 726,535.89 907.775 9.8509 59 ......... 263.395 2,130.83 69.683 7.0899

5 ......... 60,840.355 659,579.39 878.592 9.8411 60 ......... 234.339 1,867.43 64.573 6.9689

6 ......... 55,285.706 598,739.04 854.884 9.8299 61 ......... 208.172 1,633.09 59.709 6.8449

7 ......... 50,240.746 543,453.33 835.897 9.8170 62 ......... 184.628 1,424.92 55.089 6.7178

8 ......... 45,657.544 493,212.59 820.036 9.8024 63 ......... 163.458 1,240.29 50.704 6.5878

9 ......... 41,494.559 447,555.04 807.737 9.7859 64 ......... 144.424 1,076.84 46.530 6.4561

10 ......... 37,713.459 406,060.48 798.869 9.7670 65 ......... 127.322 932.41 42.557 6.3233

11 ......... 34,278.303 368,347.03 792.210 9.7458 66 ......... 111.986 805.09 38.796 6.1892

12 ......... 31,155.721 334,068.72 785.837 9.7225 67 ......... 98.268 693.10 35.258 6.0532

13 ......... 28,314.403 302,913.00 776.858 9.6982 68 ......... 86.023 594.84 31.947 5.9148

14 ......... 25,726.147 274,598.60 762.638 9.6739 69 ......... 75.114 508.81 28.858 5.7739

15 ......... 23,367.297 248,872.45 742.529 9.6505 70 ......... 65.404 433.70 25.977 5.6310

16 ......... 21,217.317 225,505.15 716.849 9.6284 71 ......... 56.770 368.30 23.288 5.4875

17 ......... 19,258.991 204,287.84 687.370 9.6074 72 ......... 49.097 311.53 20.777 5.3451

18 ......... 17,476.699 185,028.84 655.895 9.5872 73 ......... 42.299 262.43 18.442 5.2041

19 ......... 15,855.860 167,552.15 623.847 9.5672 74 ......... 36.306 220.13 16.294 5.0632

20 ......... 14,383.203 151,696.29 592.632 9.5468 75 ......... 31.051 183.82 14.339 4.9201

21 ......... 13,044.965 137,313.08 561.957 9.5261 76 ......... 26.464 152.77 12.575 4.7729

22 ......... 11,829.207 124,268.12 532.106 9.5052 77 ......... 22.469 126.31 10.987 4.6214

23 ......... 10,725.124 112,438.91 503.404 9.4837 78 ......... 18.999 103.84 9.559 4.4654

24 ......... 9,723.107 101,713.79 476.399 9.4610 79 ......... 15.986 84.84 8.273 4.3072

25 ......... 8,814.268 91,990.68 451.479 9.4366 80 ......... 13.372 68.85 7.112 4.1492

26 ......... 7,989.897 83,176.41 428.405 9.4102 81 ......... 11.106 55.48 6.062 3.9958

27 ......... 7,242.337 75,186.52 407.200 9.3815 82 ......... 9.150 44.38 5.116 3.8499

28 ......... 6,564.111 67,944.18 387.367 9.3509 83 ......... 7.478 35.23 4.275 3.7110

29 ......... 5,948.588 61,380.07 368.582 9.3184 84 ......... 6.067 27.75 3.545 3.5736

30 ......... 5,389.812 55,431.48 350.587 9.2845 85 ......... 4.894 21.68 2.923 3.4306

31 ......... 4,882.585 50,041.67 333.342 9.2490 86 ......... 3.923 16.79 2.397 3.2798

32 ......... 4,422.326 45,159.08 316.955 9.2116 87 ......... 3.120 12.87 1.951 3.1233

33 ......... 4,004.667 40,736.76 301.325 9.1723 88 ......... 2.459 9.75 1.573 2.9636

34 ......... 3,625.614 36,732.09 286.333 9.1313 89 ......... 1.915 7.29 1.252 2.8057

35 ......... 3,281.673 33,106.48 271.993 9.0883 90 ......... 1.470 5.37 0.981 2.6550

36 ......... 2,969.590 29,824.80 258.245 9.0434 91 ......... 1.109 3.90 0.755 2.5173

37 ......... 2,686.394 26,855.21 245.011 8.9968 92 ......... 0.822 2.79 0.568 2.3978

38 ......... 2,429.584 24,168.82 232.419 8.9477 93 ......... 0.598 1.97 0.419 2.2972

39 ......... 2,196.852 21,739.23 220.558 8.8956 94 ......... 0.428 1.37 0.303 2.2066

40 ......... 1,985.981 19,542.38 209.400 8.8402 95 ......... 0.303 0.94 0.217 2.1145

41 ......... 1,794.972 17,556.40 198.935 8.7809 96 ......... 0.213 0.64 0.154 2.0169

42 ......... 1,621.950 15,761.43 189.093 8.7176 97 ......... 0.147 0.43 0.108 1.9210

43 ......... 1,465.188 14,139.48 179.780 8.6503 95 ......... 0.100 0.28 0.074 1.8269

44 ......... 1,323.130 12,674.29 170.922 8.5790 99 ......... 0.067 0.18 0.050 1.7347

45 ......... 1,194.367 11,351.16 162.443 8.5039 100 ......... 0.044 0.12 0.033 1.6442

46 ......... 1,077.632 10,156.79 154.287 8.4251 101 ......... 0.028 0.07 0.022 1.5557

47 ......... 971.774 9,079.16 146.395 8.3429 102 ......... 0.018 0.04 0.014 1.4691

48 ......... 875.803 8,107.39 138.768 8.2571 103 ......... 0.011 0.03 0.009 1.3844

49 ......... 788.810 7,231.59 131.393 8.1677 104 ......... 0.007 0.02 0.005 1.3016

50 ......... 709.996 6,442.78 124.289 8.0744 105 ......... 0.004 0.01 0.003 1.2208

51 ......... 638.605 5,732.78 117.443 7.9770 106 ......... 0.002 0.00 0.002 1.1420

52 ......... 573.939 5,094.18 110.832 7.8758 107 ......... 0.001 0.00 0.001 1.0652

53 ......... 515.369 4,520.24 104.439 7.7709 108 ......... 0.001 0.00 0.001 0.9904

54 ......... 462.303 4,004.87 98.225 7.6629 109 ......... 0.000 0.00 0.000 0.9175

x x x x x x x x

97
Table 8.K. -- Actuarial Functions at 11.0 Percent Interest for 1989-91 United States 

Males Other than White

x D N M a x D N M a

0 ......... 100,000.000 984,491.75 2,437.755 8.8449 55 ......... 251.805 2,029.88 50.646 7.0613

1 ......... 88,547.748 884,491.75 895.413 8.9889 56 ......... 223.300 1,778.08 47.094 6.9627

2 ......... 79,676.163 795,944.00 798.830 8.9897 57 ......... 197.755 1,554.78 43.678 6.8621

3 ......... 71,725.487 716,267.83 743.990 8.9862 58 ......... 174.883 1,357.02 40.403 6.7596

4 ......... 64,576.056 644,542.35 702.490 8.9811 59 ......... 154.426 1,182.14 37.277 6.6551

5 ......... 58,148.735 579,966.29 674.598 8.9738 60 ......... 136.153 1,027.71 34.308 6.5482

6 ......... 52,363.793 521,817.56 652.143 8.9652 61 ......... 119.860 891.56 31.507 6.4383

7 ......... 47,156.767 469,453.76 634.322 8.9552 62 ......... 105.346 771.70 28.871 6.3254

8 ......... 42,468.820 422,297.00 619.568 8.9437 63 ......... 92.427 666.35 26.392 6.2095

9 ......... 38,248.861 379,828.18 608.231 8.9304 64 ......... 80.928 573.93 24.053 6.0918

10 ......... 34,450.334 341,579.32 600.131 8.9151 65 ......... 70.702 493.00 21.847 5.9729

11 ......... 31,030.308 307,128.98 594.103 8.8977 66 ......... 61.626 422.30 19.777 5.8526

12 ......... 27,949.516 276,098.67 588.386 8.8785 67 ......... 53.590 360.67 17.848 5.7302

13 ......... 25,171.761 248,149.16 580.403 8.8582 68 ......... 46.490 307.08 16.058 5.6053

14 ......... 22,664.734 222,977.40 567.875 8.8381 69 ......... 40.228 260.59 14.404 5.4778

15 ......... 20,401.123 200,312.66 550.319 8.8187 70 ......... 34.713 220.36 12.875 5.3482

16 ......... 18,357.172 179,911.54 528.100 8.8006 71 ......... 29.858 185.65 11.461 5.2177

17 ......... 16,512.717 161,554.37 502.825 8.7836 72 ......... 25.590 155.79 10.151 5.0879

18 ......... 14,849.578 145,041.65 476.081 8.7674 73 ......... 21.848 130.20 8.946 4.9593

19 ......... 13,351.013 130,192.07 449.096 8.7515 74 ......... 18.584 108.35 7.846 4.8305

20 ......... 12,001.893 116,841.06 423.049 8.7352 75 ......... 15.751 89.77 6.855 4.6994

21 ......... 10,787.151 104,839.17 397.684 8.7189 76 ......... 13.303 74.02 5.968 4.5641

22 ......... 9,693.691 94,052.01 373.221 8.7024 77 ......... 11.193 60.72 5.176 4.4243

23 ......... 8,709.747 84,358.32 349.913 8.6855 78 ......... 9.379 49.52 4.472 4.2799

24 ......... 7,824.886 75,648.58 328.180 8.6677 79 ......... 7.821 40.14 3.843 4.1329

25 ......... 7,029.572 67,823.69 308.306 8.6483 80 ......... 6.483 32.32 3.280 3.9858

26 ......... 6,314.712 60,794.12 290.069 8.6274 81 ......... 5.336 25.84 2.775 3.8427

27 ......... 5,672.321 54,479.41 273.461 8.6044 82 ......... 4.357 20.50 2.325 3.7064

28 ......... 5,094.806 48,807.09 258.068 8.5798 83 ......... 3.528 16.15 1.928 3.5767

29 ......... 4,575.466 43,712.28 243.619 8.5536 84 ......... 2.837 12.62 1.586 3.4481

30 ......... 4,108.325 39,136.81 229.902 8.5262 85 ......... 2.268 9.78 1.298 3.3139

31 ......... 3,688.168 35,028.49 216.876 8.4975 86 ......... 1.801 7.51 1.057 3.1718

32 ......... 3,310.407 31,340.32 204.609 8.4672 87 ......... 1.420 5.71 0.854 3.0238

33 ......... 2,970.754 28,029.91 193.015 8.4353 88 ......... 1.109 4.29 0.683 2.8722

34 ......... 2,665.334 25,059.16 181.994 8.4019 89 ......... 0.856 3.18 0.540 2.7218

35 ......... 2,390.755 22,393.83 171.547 8.3668 90 ......... 0.651 2.33 0.420 2.5779

36 ......... 2,143.907 20,003.07 161.621 8.3302 91 ......... 0.487 1.68 0.321 2.4462

37 ......... 1,921.980 17,859.16 152.153 8.2921 92 ......... 0.357 1.19 0.239 2.3320

38 ......... 1,722.586 15,937.18 143.225 8.2519 93 ......... 0.258 0.83 0.175 2.2358

39 ......... 1,543.545 14,214.60 134.892 8.2091 94 ......... 0.183 0.58 0.126 2.1492

40 ......... 1,382.812 12,671.05 127.122 8.1632 95 ......... 0.128 0.39 0.089 2.0611

41 ......... 1,238.556 11,288.24 119.901 8.1140 96 ......... 0.089 0.26 0.063 1.9675

42 ......... 1,109.086 10,049.68 113.171 8.0612 97 ......... 0.061 0.18 0.044 1.8753

43 ......... 992.866 8,940.60 106.861 8.0048 95 ......... 0.041 0.11 0.030 1.7848

44 ......... 888.525 7,947.73 100.912 7.9449 99 ......... 0.027 0.07 0.020 1.6959

45 ......... 794.831 7,059.21 95.270 7.8814 100 ......... 0.018 0.05 0.013 1.6086

46 ......... 710.684 6,264.38 89.890 7.8146 101 ......... 0.011 0.03 0.008 1.5230

47 ......... 635.099 5,553.69 84.733 7.7446 102 ......... 0.007 0.02 0.005 1.4392

48 ......... 567.221 4,918.59 79.793 7.6714 103 ......... 0.004 0.01 0.003 1.3571

49 ......... 506.277 4,351.37 75.060 7.5948 104 ......... 0.003 0.01 0.002 1.2769

50 ......... 451.587 3,845.10 70.541 7.5146 105 ......... 0.001 0.00 0.001 1.1984

51 ......... 402.520 3,393.51 66.226 7.4307 106 ......... 0.001 0.00 0.001 1.1217

52 ......... 358.501 2,990.99 62.097 7.3430 107 ......... 0.000 0.00 0.000 1.0469

53 ......... 319.016 2,632.49 58.139 7.2519 108 ......... 0.000 0.00 0.000 0.9739

54 ......... 283.590 2,313.47 54.327 7.1578 109 ......... 0.000 0.00 0.000 0.9028

x x x x x x x x

98
Table 8.L. -- Actuarial Functions at 12.0 Percent Interest for 1989-91 United States 

Males Other than White

x D N M a x D N M a

0 ......... 100,000.000 912,115.15 2,273.377 8.1212 55 ......... 153.758 1,172.52 28.131 6.6257

1 ......... 87,757.143 812,115.15 744.805 8.2541 56 ......... 135.135 1,018.76 25.982 6.5389

2 ......... 78,259.726 724,358.01 649.939 8.2558 57 ......... 118.607 883.63 23.933 6.4500

3 ......... 69,821.372 646,098.28 596.556 8.2536 58 ......... 103.952 765.02 21.986 6.3593

4 ......... 62,300.473 576,276.91 556.518 8.2500 59 ......... 90.973 661.07 20.144 6.2666

5 ......... 55,598.753 513,976.44 529.849 8.2444 60 ......... 79.492 570.09 18.411 6.1717

6 ......... 49,620.465 458,377.69 508.570 8.2377 61 ......... 69.355 490.60 16.790 6.0738

7 ......... 44,287.250 408,757.22 491.834 8.2297 62 ......... 60.412 421.25 15.279 5.9728

8 ......... 39,528.455 364,469.97 478.101 8.2204 63 ......... 52.530 360.83 13.870 5.8690

9 ......... 35,282.806 324,941.51 467.644 8.2096 64 ......... 45.585 308.30 12.552 5.7633

10 ......... 31,495.100 289,658.71 460.238 8.1969 65 ......... 39.469 262.72 11.321 5.6563

11 ......... 28,115.163 258,163.61 454.776 8.1824 66 ......... 34.095 223.25 10.175 5.5479

12 ......... 25,097.691 230,048.45 449.643 8.1661 67 ......... 29.384 189.15 9.118 5.4373

13 ......... 22,401.548 204,950.75 442.538 8.1490 68 ......... 25.263 159.77 8.145 5.3242

14 ......... 19,990.333 182,549.21 431.489 8.1319 69 ......... 21.666 134.51 7.254 5.2083

15 ......... 17,833.165 162,558.87 416.143 8.1155 70 ......... 18.528 112.84 6.438 5.0902

16 ......... 15,903.220 144,725.71 396.894 8.1004 71 ......... 15.795 94.31 5.690 4.9711

17 ......... 14,177.603 128,822.49 375.193 8.0863 72 ......... 13.416 78.52 5.004 4.8525

18 ......... 12,635.817 114,644.89 352.436 8.0730 73 ......... 11.352 65.10 4.377 4.7347

19 ......... 11,259.222 102,009.07 329.679 8.0600 74 ......... 9.570 53.75 3.811 4.6167

20 ......... 10,031.107 90,749.85 307.909 8.0468 75 ......... 8.038 44.18 3.305 4.4961

21 ......... 8,935.335 80,718.74 286.898 8.0337 76 ......... 6.729 36.14 2.856 4.3713

22 ......... 7,957.895 71,783.41 266.816 8.0204 77 ......... 5.611 29.41 2.460 4.2421

23 ......... 7,086.300 63,825.51 247.853 8.0069 78 ......... 4.660 23.80 2.110 4.1080

24 ......... 6,309.529 56,739.21 230.328 7.9926 79 ......... 3.851 19.14 1.800 3.9711

25 ......... 5,617.626 50,429.68 214.446 7.9770 80 ......... 3.163 15.29 1.525 3.8338

26 ......... 5,001.294 44,812.06 200.002 7.9601 81 ......... 2.580 12.13 1.281 3.7000

27 ......... 4,452.405 39,810.76 186.966 7.9414 82 ......... 2.088 9.55 1.065 3.5725

28 ......... 3,963.387 35,358.36 174.991 7.9212 83 ......... 1.676 7.46 0.877 3.4510

29 ......... 3,527.598 31,394.97 163.851 7.8998 84 ......... 1.336 5.78 0.716 3.3306

30 ......... 3,139.160 27,867.37 153.371 7.8773 85 ......... 1.058 4.45 0.581 3.2044

31 ......... 2,792.957 24,728.21 143.506 7.8538 86 ......... 0.833 3.39 0.470 3.0702

32 ......... 2,484.505 21,935.25 134.300 7.8288 87 ......... 0.651 2.56 0.377 2.9300

33 ......... 2,209.684 19,450.75 125.676 7.8025 88 ......... 0.504 1.91 0.299 2.7859

34 ......... 1,964.808 17,241.06 117.551 7.7749 89 ......... 0.385 1.40 0.235 2.6425

35 ......... 1,746.660 15,276.26 109.919 7.7460 90 ......... 0.290 1.02 0.181 2.5050

36 ......... 1,552.331 13,529.60 102.732 7.7157 91 ......... 0.215 0.73 0.137 2.3789

37 ......... 1,379.216 11,977.26 95.937 7.6841 92 ......... 0.157 0.51 0.102 2.2695

38 ......... 1,225.093 10,598.05 89.588 7.6508 93 ......... 0.112 0.36 0.074 2.1774

39 ......... 1,087.959 9,372.96 83.714 7.6152 94 ......... 0.079 0.24 0.053 2.0946

40 ......... 965.965 8,285.00 78.287 7.5769 95 ......... 0.055 0.16 0.037 2.0102

41 ......... 857.470 7,319.03 73.288 7.5356 96 ......... 0.038 0.11 0.026 1.9203

42 ......... 760.980 6,461.56 68.670 7.4911 97 ......... 0.026 0.07 0.018 1.8317

43 ......... 675.155 5,700.58 64.379 7.4434 95 ......... 0.017 0.05 0.012 1.7445

44 ......... 598.808 5,025.43 60.370 7.3924 99 ......... 0.011 0.03 0.008 1.6587

45 ......... 530.882 4,426.62 56.601 7.3382 100 ......... 0.007 0.02 0.005 1.5744

46 ......... 470.441 3,895.74 53.040 7.2810 101 ......... 0.005 0.01 0.003 1.4917

47 ......... 416.653 3,425.30 49.657 7.2210 102 ......... 0.003 0.01 0.002 1.4105

48 ......... 368.799 3,008.64 46.445 7.1579 103 ......... 0.002 0.00 0.001 1.3309

49 ......... 326.235 2,639.84 43.395 7.0918 104 ......... 0.001 0.00 0.001 1.2530

50 ......... 288.396 2,313.61 40.509 7.0223 105 ......... 0.001 0.00 0.000 1.1767

51 ......... 254.765 2,025.21 37.778 6.9493 106 ......... 0.000 0.00 0.000 1.1021

52 ......... 224.879 1,770.45 35.188 6.8729 107 ......... 0.000 0.00 0.000 1.0292

53 ......... 198.324 1,545.57 32.728 6.7931 108 ......... 0.000 0.00 0.000 0.9580

54 ......... 174.727 1,347.24 30.379 6.7106 109 ......... 0.000 0.00 0.000 0.8885

x x x x x x x x

99
Table 9.A. -- Actuarial Functions at 1.0 Percent Interest for 1989-91 United States 

Females Other than White

x D N M a x D N M a

0 ......... 100,000.000 5,262,360.01 47,897.426 51.6236 55 ......... 51,333.375 1,149,646.52 39,950.736 21.3957

1 ......... 97,596.040 5,162,360.01 46,483.564 51.8952 56 ......... 50,397.242 1,098,313.15 39,522.854 20.7931

2 ......... 96,530.732 5,064,763.97 46,384.554 51.4679 57 ......... 49,443.989 1,047,915.91 39,068.584 20.1940

3 ......... 95,515.776 4,968,233.23 46,325.348 51.0148 58 ......... 48,471.543 998,471.92 38,585.683 19.5991

4 ......... 94,525.871 4,872,717.46 46,281.143 50.5490 59 ......... 47,474.589 950,000.37 38,068.645 19.0107

5 ......... 93,557.621 4,778,191.59 46,248.793 50.0722 60 ......... 46,451.893 902,525.79 37,515.994 18.4293

6 ......... 92,599.278 4,684,633.97 46,216.764 49.5904 61 ......... 45,403.918 856,073.89 36,927.939 17.8546

7 ......... 91,656.338 4,592,034.69 46,190.648 49.1006 62 ......... 44,333.830 810,669.97 36,307.395 17.2856

8 ......... 90,725.762 4,500,378.35 46,167.561 48.6042 63 ......... 43,240.412 766,336.14 35,652.925 16.7227

9 ......... 89,808.286 4,409,652.59 46,148.360 48.1007 64 ......... 42,123.039 723,095.73 34,963.676 16.1663

10 ......... 88,900.990 4,319,844.30 46,130.254 47.5916 65 ......... 40,980.084 680,972.69 34,237.781 15.6172

11 ......... 88,003.752 4,230,943.31 46,113.224 47.0769 66 ......... 39,813.112 639,992.61 33,476.551 15.0749

12 ......... 87,114.678 4,142,939.56 46,095.475 46.5573 67 ......... 38,623.131 600,179.50 32,680.759 14.5394

13 ......... 86,233.705 4,055,824.88 46,077.023 46.0329 68 ......... 37,413.669 561,556.37 31,853.705 14.0094

14 ......... 85,358.157 3,969,591.18 46,055.274 45.5051 69 ......... 36,187.127 524,142.70 30,997.595 13.4842

15 ......... 84,486.325 3,884,233.02 46,028.572 44.9747 70 ......... 34,942.834 487,955.57 30,111.591 12.9644

16 ......... 83,619.125 3,799,746.70 45,997.870 44.4411 71 ......... 33,680.164 453,012.74 29,194.889 12.4504

17 ......... 82,755.749 3,716,127.57 45,962.406 43.9048 72 ......... 32,395.595 419,332.57 28,243.787 11.9441

18 ......... 81,895.420 3,633,371.82 45,921.442 43.3660 73 ......... 31,088.665 386,936.98 27,257.606 11.4462

19 ......... 81,040.704 3,551,476.40 45,877.571 42.8234 74 ......... 29,760.383 355,848.31 26,237.132 10.9571

20 ......... 80,190.787 3,470,435.70 45,830.038 42.2772 75 ......... 28,415.528 326,087.93 25,186.935 10.4757

21 ......... 79,344.888 3,390,244.91 45,778.106 41.7280 76 ......... 27,060.588 297,672.40 24,113.337 10.0002

22 ......... 78,504.664 3,310,900.02 45,723.475 41.1746 77 ......... 25,699.017 270,611.81 23,019.692 9.5300

23 ......... 77,667.732 3,232,395.36 45,663.817 40.6183 78 ......... 24,330.923 244,912.80 21,906.044 9.0659

24 ......... 76,834.951 3,154,727.63 45,600.024 40.0585 79 ......... 22,951.406 220,581.87 20,767.427 8.6108

25 ......... 76,007.149 3,077,892.68 45,532.964 39.4948 80 ......... 21,554.866 197,630.47 19,598.129 8.1687

26 ......... 75,184.347 3,001,885.53 45,462.708 38.9270 81 ......... 20,136.386 176,075.60 18,393.063 7.7442

27 ......... 74,365.036 2,926,701.18 45,387.796 38.3559 82 ......... 18,699.217 155,939.21 17,155.264 7.3393

28 ......... 73,550.037 2,852,336.14 45,309.085 37.7809 83 ......... 17,254.380 137,240.00 15,895.568 6.9539

29 ......... 72,737.893 2,778,786.11 45,225.159 37.2027 84 ......... 15,824.615 119,985.62 14,636.639 6.5822

30 ......... 71,927.201 2,706,048.21 45,134.645 36.6220 85 ......... 14,430.915 104,161.00 13,399.617 6.2179

31 ......... 71,117.352 2,634,121.01 45,036.946 36.0391 86 ......... 13,080.260 89,730.09 12,191.843 5.8600

32 ......... 70,309.942 2,563,003.66 44,933.669 35.4529 87 ......... 11,771.766 76,649.83 11,012.857 5.5113

33 ......... 69,504.349 2,492,693.72 44,824.213 34.8639 88 ......... 10,509.148 64,878.06 9,866.791 5.1735

34 ......... 68,700.685 2,423,189.37 44,708.711 34.2717 89 ......... 9,295.126 54,368.92 8,756.820 4.8492

35 ......... 67,899.769 2,354,488.68 44,588.000 33.6759 90 ......... 8,132.702 45,073.79 7,686.427 4.5423

36 ......... 67,100.989 2,286,588.92 44,461.494 33.0768 91 ......... 7,025.137 36,941.09 6,659.384 4.2584

37 ......... 66,303.066 2,219,487.93 44,327.938 32.4749 92 ......... 5,983.545 29,915.95 5,687.348 3.9997

38 ......... 65,506.828 2,153,184.86 44,188.166 31.8696 93 ......... 5,023.726 23,932.40 4,786.771 3.7639

39 ......... 64,712.396 2,087,678.03 44,042.317 31.2609 94 ......... 4,165.134 18,908.68 3,977.920 3.5398

40 ......... 63,917.871 2,022,965.64 43,888.508 30.6495 95 ......... 3,412.423 14,743.54 3,266.448 3.3205

41 ......... 63,124.090 1,959,047.77 43,727.577 30.0349 96 ......... 2,759.063 11,331.12 2,646.873 3.1069

42 ......... 62,329.885 1,895,923.68 43,558.364 29.4176 97 ......... 2,194.083 8,572.06 2,109.211 2.9069

43 ......... 61,534.137 1,833,593.79 43,379.743 28.7980 95 ......... 1,714.231 6,377.97 1,651.082 2.7206

44 ......... 60,735.773 1,772,059.65 43,190.628 28.1765 99 ......... 1,314.408 4,663.74 1,268.232 2.5482

45 ......... 59,933.765 1,711,323.88 42,989.964 27.5536 100 ......... 990.217 3,349.34 957.056 2.3824

46 ......... 59,124.602 1,651,390.12 42,774.204 26.9307 101 ......... 731.918 2,359.12 708.560 2.2232

47 ......... 58,307.418 1,592,265.51 42,542.413 26.3081 102 ......... 529.981 1,627.20 513.870 2.0703

48 ......... 57,480.152 1,533,958.10 42,292.448 25.6867 103 ......... 375.300 1,097.22 364.436 1.9236

49 ......... 56,641.443 1,476,477.94 42,022.850 25.0671 104 ......... 259.414 721.92 252.266 1.7829

50 ......... 55,791.818 1,419,836.50 41,734.031 24.4488 105 ......... 174.660 462.51 170.081 1.6480

51 ......... 54,929.385 1,364,044.68 41,423.992 23.8327 106 ......... 114.276 287.85 111.426 1.5189

52 ......... 54,052.333 1,309,115.30 41,090.795 23.2194 107 ......... 72.466 173.57 70.747 1.3952

53 ......... 53,161.297 1,255,062.96 40,734.931 22.6086 108 ......... 44.405 101.10 43.404 1.2769

54 ......... 52,255.144 1,201,901.67 40,355.127 22.0006 109 ......... 26.205 56.70 25.643 1.1637

x x x x x x x x

100
Table 9.B. -- Actuarial Functions at 2.0 Percent Interest for 1989-91 United States 

Females Other than White

x D N M a x D N M a

0 ......... 100,000.000 3,865,654.08 24,202.861 37.6565 55 ......... 29,858.359 585,889.56 18,370.328 18.6223

1 ......... 96,639.216 3,765,654.08 22,802.861 37.9661 56 ......... 29,026.461 556,031.20 18,123.888 18.1560

2 ......... 94,647.251 3,669,014.86 22,705.783 37.7651 57 ......... 28,198.241 527,004.74 17,864.815 17.6893

3 ......... 92,733.941 3,574,367.61 22,648.302 37.5443 58 ......... 27,372.632 498,806.50 17,592.113 17.2228

4 ......... 90,873.131 3,481,633.67 22,605.805 37.3131 59 ......... 26,546.798 471,433.87 17,302.996 16.7586

5 ......... 89,060.511 3,390,760.54 22,575.010 37.0725 60 ......... 25,720.271 444,887.07 16,996.995 16.2971

6 ......... 87,284.035 3,301,700.03 22,544.819 36.8271 61 ......... 24,893.540 419,166.80 16,674.583 15.8384

7 ......... 85,548.208 3,214,415.99 22,520.443 36.5743 62 ......... 24,068.542 394,273.26 16,337.694 15.3813

8 ......... 83,849.455 3,128,867.78 22,499.106 36.3153 63 ......... 23,244.786 370,204.72 15,985.870 14.9264

9 ......... 82,187.776 3,045,018.33 22,481.534 36.0495 64 ......... 22,422.118 346,959.93 15,618.982 14.4740

10 ......... 80,559.844 2,962,830.55 22,465.127 35.7780 65 ......... 21,599.862 324,537.81 15,236.376 14.0250

11 ......... 78,964.958 2,882,270.71 22,449.846 35.5006 66 ......... 20,779.039 302,937.95 14,839.079 13.5790

12 ......... 77,400.856 2,803,305.75 22,434.076 35.2180 67 ......... 19,960.343 282,158.91 14,427.816 13.1360

13 ......... 75,866.958 2,725,904.90 22,417.842 34.9301 68 ......... 19,145.735 262,198.57 14,004.586 12.6949

14 ......... 74,360.424 2,650,037.94 22,398.896 34.6377 69 ......... 18,336.525 243,052.83 13,570.783 12.2551

15 ......... 72,879.343 2,575,677.51 22,375.862 34.3417 70 ......... 17,532.436 224,716.31 13,126.234 11.8172

16 ......... 71,424.112 2,502,798.17 22,349.638 34.0414 71 ......... 16,733.221 207,183.87 12,670.792 11.3816

17 ......... 69,993.644 2,431,374.06 22,319.643 33.7371 72 ......... 15,937.218 190,450.65 12,202.891 10.9501

18 ......... 68,586.912 2,361,380.41 22,285.335 33.4290 73 ......... 15,144.321 174,513.43 11,722.489 10.5234

19 ......... 67,205.690 2,292,793.50 22,248.955 33.1161 74 ......... 14,355.141 159,369.11 11,230.256 10.1019

20 ......... 65,848.899 2,225,587.81 22,209.922 32.7984 75 ......... 13,572.064 145,013.97 10,728.652 9.6847

21 ......... 64,515.518 2,159,738.91 22,167.697 32.4763 76 ......... 12,798.191 131,441.91 10,220.899 9.2704

22 ......... 63,206.523 2,095,223.40 22,123.712 32.1488 77 ......... 12,035.083 118,643.72 9,708.735 8.8582

23 ......... 61,919.618 2,032,016.87 22,076.150 31.8170 78 ......... 11,282.682 106,608.63 9,192.316 8.4489

24 ......... 60,655.148 1,970,097.25 22,025.790 31.4803 79 ......... 10,538.632 95,325.95 8,669.496 8.0454

25 ......... 59,413.412 1,909,442.11 21,973.371 31.1382 80 ......... 9,800.348 84,787.32 8,137.851 7.6515

26 ......... 58,194.063 1,850,028.69 21,918.991 30.7907 81 ......... 9,065.649 74,986.97 7,595.316 7.2716

27 ......... 56,995.589 1,791,834.63 21,861.577 30.4381 82 ......... 8,336.082 65,921.32 7,043.507 6.9080

28 ......... 55,818.293 1,734,839.04 21,801.842 30.0801 83 ......... 7,616.564 57,585.24 6,487.442 6.5605

29 ......... 54,660.749 1,679,020.75 21,738.773 29.7171 84 ......... 6,916.942 49,968.68 5,937.164 6.2241

30 ......... 53,521.616 1,624,360.00 21,671.420 29.3496 85 ......... 6,245.914 43,051.74 5,401.763 5.8928

31 ......... 52,400.187 1,570,838.38 21,599.435 28.9777 86 ......... 5,605.828 36,805.82 4,884.145 5.5656

32 ......... 51,297.383 1,518,438.20 21,524.085 28.6007 87 ......... 4,995.583 31,199.99 4,383.819 5.2455

33 ......... 50,212.477 1,467,140.81 21,445.010 28.2187 88 ......... 4,416.043 26,204.41 3,902.231 4.9339

34 ......... 49,145.294 1,416,928.34 21,362.385 27.8314 89 ......... 3,867.606 21,788.37 3,440.384 4.6336

35 ......... 48,096.156 1,367,783.04 21,276.881 27.4385 90 ......... 3,350.758 17,920.76 2,999.370 4.3483

36 ......... 47,064.364 1,319,686.89 21,188.150 27.0400 91 ......... 2,866.053 14,570.00 2,580.366 4.0836

37 ......... 46,048.775 1,272,622.52 21,095.392 26.6364 92 ......... 2,417.181 11,703.95 2,187.692 3.8420

38 ......... 45,049.736 1,226,573.75 20,999.270 26.2271 93 ......... 2,009.545 9,286.77 1,827.451 3.6213

39 ......... 44,067.089 1,181,524.01 20,899.951 25.8119 94 ......... 1,649.765 7,277.22 1,507.074 3.4111

40 ......... 43,099.316 1,137,456.92 20,796.239 25.3915 95 ......... 1,338.373 5,627.46 1,228.030 3.2047

41 ......... 42,146.781 1,094,357.61 20,688.789 24.9654 96 ......... 1,071.512 4,289.09 987.412 3.0028

42 ......... 41,208.501 1,052,210.82 20,576.916 24.5338 97 ......... 843.742 3,217.57 780.652 2.8135

43 ......... 40,283.556 1,011,002.32 20,459.981 24.0971 95 ......... 652.750 2,373.83 606.205 2.6367

44 ......... 39,371.091 970,718.77 20,337.390 23.6556 99 ......... 495.597 1,721.08 461.851 2.4727

45 ......... 38,470.307 931,347.68 20,208.588 23.2095 100 ......... 369.701 1,225.49 345.672 2.3148

46 ......... 37,578.853 892,877.37 20,071.454 22.7601 101 ......... 270.585 855.78 253.805 2.1627

47 ......... 36,696.133 855,298.52 19,925.574 22.3076 102 ......... 194.009 585.20 182.535 2.0163

48 ......... 35,820.827 818,602.38 19,769.800 21.8527 103 ......... 136.039 391.19 128.368 1.8756

49 ......... 34,952.095 782,781.56 19,603.437 21.3958 104 ......... 93.110 255.15 88.107 1.7403

50 ......... 34,090.284 747,829.46 19,426.961 20.9367 105 ......... 62.075 162.04 58.898 1.6104

51 ......... 33,234.262 713,739.18 19,239.376 20.4760 106 ......... 40.216 99.97 38.256 1.4857

52 ......... 32,382.990 680,504.92 19,039.756 20.0143 107 ......... 25.252 59.75 24.081 1.3661

53 ......... 31,536.920 648,121.93 18,828.647 19.5512 108 ......... 15.322 34.50 14.646 1.2514

54 ......... 30,695.447 616,585.01 18,605.544 19.0872 109 ......... 8.953 19.17 8.577 1.1415

x x x x x x x x

101
Table 9.C. -- Actuarial Functions at 3.0 Percent Interest for 1989-91 United States 

Females Other than White

x D N M a x D N M a

0 ......... 100,000.000 2,983,929.50 13,089.432 28.8393 55 ......... 17,459.348 303,395.57 8,622.584 16.3773

1 ......... 95,700.971 2,883,929.50 11,703.024 29.1348 56 ......... 16,808.119 285,936.22 8,479.880 16.0118

2 ......... 92,818.362 2,788,228.53 11,607.822 29.0396 57 ......... 16,169.999 269,128.10 8,331.317 15.6437

3 ......... 90,059.091 2,695,410.17 11,551.998 28.9294 58 ......... 15,544.168 252,958.10 8,176.457 15.2735

4 ......... 87,395.140 2,605,351.08 11,511.128 28.8112 59 ......... 14,928.838 237,413.93 8,013.869 14.9030

5 ......... 84,820.322 2,517,955.94 11,481.799 28.6858 60 ......... 14,323.606 222,485.09 7,843.457 14.5328

6 ......... 82,321.352 2,433,135.62 11,453.325 28.5566 61 ......... 13,728.606 208,161.49 7,665.650 14.1626

7 ......... 79,900.877 2,350,814.27 11,430.558 28.4216 62 ......... 13,144.755 194,432.88 7,481.661 13.7917

8 ......... 77,553.931 2,270,913.39 11,410.823 28.2817 63 ......... 12,571.619 181,288.13 7,291.382 13.4204

9 ......... 75,278.984 2,193,359.46 11,394.728 28.1364 64 ......... 12,008.956 168,716.51 7,094.883 13.0492

10 ......... 73,071.511 2,118,080.47 11,379.846 27.9864 65 ......... 11,456.252 156,707.55 6,891.954 12.6788

11 ......... 70,929.488 2,045,008.96 11,366.120 27.8316 66 ......... 10,913.900 145,251.30 6,683.279 12.3088

12 ......... 68,849.553 1,974,079.48 11,352.093 27.6724 67 ......... 10,382.106 134,337.40 6,469.366 11.9393

13 ......... 66,829.926 1,905,229.92 11,337.793 27.5086 68 ......... 9,861.715 123,955.29 6,251.366 11.5693

14 ......... 64,866.896 1,838,400.00 11,321.265 27.3411 69 ......... 9,353.204 114,093.58 6,030.090 11.1983

15 ......... 62,957.671 1,773,533.10 11,301.367 27.1702 70 ......... 8,856.223 104,740.38 5,805.533 10.8268

16 ......... 61,101.518 1,710,575.43 11,278.933 26.9956 71 ......... 8,370.449 95,884.15 5,577.707 10.4551

17 ......... 59,296.452 1,649,473.91 11,253.522 26.8174 72 ......... 7,894.865 87,513.70 5,345.922 10.0849

18 ......... 57,540.588 1,590,177.46 11,224.740 26.6358 73 ......... 7,429.250 79,618.84 5,110.254 9.7169

19 ......... 55,834.424 1,532,636.87 11,194.515 26.4497 74 ......... 6,973.737 72,189.59 4,871.127 9.3516

20 ......... 54,176.065 1,476,802.45 11,162.402 26.2593 75 ......... 6,529.304 65,215.85 4,629.814 8.9882

21 ......... 52,563.718 1,422,626.38 11,127.999 26.0648 76 ......... 6,097.230 58,686.55 4,387.913 8.6251

22 ......... 50,997.248 1,370,062.66 11,092.510 25.8654 77 ......... 5,678.008 52,589.32 4,146.280 8.2619

23 ......... 49,473.889 1,319,065.42 11,054.508 25.6619 78 ......... 5,271.354 46,911.31 3,905.006 7.8993

24 ......... 47,993.055 1,269,591.53 11,014.661 25.4537 79 ......... 4,875.926 41,639.96 3,663.111 7.5399

25 ......... 46,554.125 1,221,598.47 10,973.587 25.2404 80 ......... 4,490.320 36,764.03 3,419.523 7.1874

26 ......... 45,155.984 1,175,044.35 10,931.391 25.0219 81 ......... 4,113.368 32,273.71 3,173.357 6.8461

27 ......... 43,796.642 1,129,888.36 10,887.273 24.7985 82 ......... 3,745.619 28,160.34 2,925.415 6.5182

28 ......... 42,475.556 1,086,091.72 10,841.817 24.5698 83 ......... 3,389.095 24,414.72 2,677.986 6.2039

29 ......... 41,190.877 1,043,616.16 10,794.290 24.3361 84 ......... 3,047.907 21,025.63 2,435.510 5.8984

30 ......... 39,940.880 1,002,425.29 10,744.027 24.0977 85 ......... 2,725.502 17,977.72 2,201.879 5.5961

31 ......... 38,724.355 962,484.41 10,690.829 23.8548 86 ......... 2,422.441 15,252.22 1,978.201 5.2962

32 ......... 37,541.318 923,760.05 10,635.685 23.6065 87 ......... 2,137.778 12,829.78 1,764.095 5.0015

33 ......... 36,390.573 886,218.73 10,578.377 23.3530 88 ......... 1,871.426 10,692.00 1,560.008 4.7133

34 ......... 35,271.354 849,828.16 10,519.078 23.0940 89 ......... 1,623.097 8,820.57 1,366.187 4.4344

35 ......... 34,183.263 814,556.81 10,458.307 22.8291 90 ......... 1,392.542 7,197.48 1,182.907 4.1686

36 ......... 33,125.183 780,373.54 10,395.857 22.5583 91 ......... 1,179.539 5,804.94 1,010.463 3.9214

37 ......... 32,095.720 747,248.36 10,331.205 22.2819 92 ......... 985.145 4,625.40 850.425 3.6951

38 ......... 31,094.547 715,152.64 10,264.859 21.9993 93 ......... 811.058 3,640.25 705.031 3.4883

39 ......... 30,120.994 684,058.09 10,196.972 21.7103 94 ......... 659.385 2,829.19 576.981 3.2907

40 ......... 29,173.482 653,937.10 10,126.770 21.4155 95 ......... 529.733 2,169.81 466.535 3.0960

41 ......... 28,251.743 624,763.62 10,054.744 21.1142 96 ......... 419.991 1,640.08 372.222 2.9050

42 ......... 27,354.614 596,511.87 9,980.482 20.8066 97 ......... 327.503 1,220.08 291.967 2.7254

43 ......... 26,481.009 569,157.26 9,903.613 20.4930 95 ......... 250.909 892.58 224.911 2.5574

44 ......... 25,629.912 542,676.25 9,823.808 20.1736 99 ......... 188.652 641.67 169.962 2.4014

45 ......... 24,800.376 517,046.34 9,740.774 19.8483 100 ......... 139.362 453.02 126.168 2.2507

46 ......... 23,990.488 492,245.96 9,653.227 19.5184 101 ......... 101.009 313.66 91.874 2.1052

47 ......... 23,199.510 468,255.47 9,561.001 19.1839 102 ......... 71.721 212.65 65.527 1.9650

48 ......... 22,426.271 445,055.96 9,463.476 18.8453 103 ......... 49.802 140.93 45.697 1.8298

49 ......... 21,669.935 422,629.69 9,360.333 18.5030 104 ......... 33.756 91.13 31.101 1.6996

50 ......... 20,930.421 400,959.76 9,251.982 18.1568 105 ......... 22.286 57.37 20.615 1.5743

51 ......... 20,206.744 380,029.34 9,137.928 17.8071 106 ......... 14.298 35.09 13.276 1.4539

52 ......... 19,498.006 359,822.59 9,017.736 17.4543 107 ......... 8.891 20.79 8.285 1.3381

53 ......... 18,804.226 340,324.59 8,891.860 17.0983 108 ......... 5.342 11.90 4.996 1.2269

54 ......... 18,124.795 321,520.36 8,760.124 16.7393 109 ......... 3.091 6.55 2.900 1.1202

x x x x x x x x

102
Table 9.D. -- Actuarial Functions at 4.0 Percent Interest for 1989-91 United States 

Females Other than White

x D N M a x D N M a

0 ......... 100,000.000 2,399,827.66 7,698.936 22.9983 55 ......... 10,262.229 159,469.83 4,128.774 14.5395

1 ......... 94,780.769 2,299,827.66 6,325.859 23.2647 56 ......... 9,784.456 149,207.60 4,045.703 14.2495

2 ......... 91,041.975 2,205,046.89 6,232.479 23.2201 57 ......... 9,322.480 139,423.14 3,960.052 13.9556

3 ......... 87,486.132 2,114,004.92 6,178.250 23.1639 58 ......... 8,875.500 130,100.66 3,871.629 13.6584

4 ......... 84,081.959 2,026,518.79 6,138.929 23.1017 59 ......... 8,442.193 121,225.16 3,779.686 13.3594

5 ......... 80,820.092 1,942,436.83 6,110.984 23.0341 60 ......... 8,022.052 112,782.97 3,684.246 13.0591

6 ......... 77,684.757 1,861,616.74 6,084.113 22.9637 61 ......... 7,614.887 104,760.92 3,585.621 12.7574

7 ......... 74,675.604 1,783,931.98 6,062.835 22.8891 62 ......... 7,220.934 97,146.03 3,484.549 12.4534

8 ......... 71,785.198 1,709,256.38 6,044.568 22.8107 63 ......... 6,839.683 89,925.10 3,381.026 12.1476

9 ......... 69,009.474 1,637,471.18 6,029.814 22.7282 64 ......... 6,470.739 83,085.41 3,275.147 11.8402

10 ......... 66,341.753 1,568,461.70 6,016.302 22.6422 65 ......... 6,113.573 76,614.67 3,166.855 11.5319

11 ......... 63,777.805 1,502,119.95 6,003.960 22.5524 66 ......... 5,768.148 70,501.10 3,056.567 11.2225

12 ......... 61,312.320 1,438,342.15 5,991.468 22.4593 67 ......... 5,434.327 64,732.95 2,944.598 10.9119

13 ......... 58,941.542 1,377,029.83 5,978.856 22.3626 68 ......... 5,112.304 59,298.62 2,831.587 10.5992

14 ......... 56,660.123 1,318,088.28 5,964.419 22.2631 69 ......... 4,802.070 54,186.32 2,717.981 10.2840

15 ......... 54,463.674 1,261,428.16 5,947.206 22.1609 70 ......... 4,503.193 49,384.25 2,603.799 9.9665

16 ......... 52,349.697 1,206,964.49 5,927.986 22.0558 71 ......... 4,215.263 44,881.06 2,489.068 9.6473

17 ......... 50,314.685 1,154,614.79 5,906.424 21.9479 72 ......... 3,937.535 40,665.80 2,373.466 9.3277

18 ......... 48,355.317 1,104,300.11 5,882.236 21.8372 73 ......... 3,669.683 36,728.26 2,257.058 9.0086

19 ......... 46,470.341 1,055,944.79 5,857.080 21.7230 74 ......... 3,411.560 33,058.58 2,140.077 8.6902

20 ......... 44,656.550 1,009,474.45 5,830.610 21.6053 75 ......... 3,163.431 29,647.02 2,023.161 8.3718

21 ......... 42,910.905 964,817.90 5,802.524 21.4842 76 ......... 2,925.687 26,483.59 1,907.087 8.0521

22 ......... 41,231.793 921,906.99 5,773.831 21.3591 77 ......... 2,698.331 23,557.90 1,792.258 7.7305

23 ......... 39,615.525 880,675.20 5,743.402 21.2306 78 ......... 2,480.991 20,859.57 1,678.700 7.4078

24 ......... 38,060.251 841,059.68 5,711.802 21.0981 79 ......... 2,272.815 18,378.58 1,565.946 7.0863

25 ......... 36,564.135 802,999.42 5,679.542 20.9614 80 ......... 2,072.946 16,105.76 1,453.494 6.7695

26 ......... 35,125.000 766,435.29 5,646.719 20.8202 81 ......... 1,880.669 14,032.82 1,340.945 6.4616

27 ......... 33,740.050 731,310.29 5,612.731 20.6748 82 ......... 1,696.064 12,152.15 1,228.674 6.1649

28 ......... 32,407.674 697,570.24 5,578.050 20.5248 83 ......... 1,519.869 10,456.08 1,117.712 5.8796

29 ......... 31,125.312 665,162.57 5,542.137 20.3705 84 ......... 1,353.718 8,936.21 1,010.017 5.6012

30 ......... 29,890.570 634,037.25 5,504.522 20.2119 85 ......... 1,198.883 7,582.50 907.248 5.3246

31 ......... 28,701.503 604,146.68 5,465.092 20.0493 86 ......... 1,055.328 6,383.61 809.804 5.0489

32 ......... 27,557.121 575,445.18 5,424.614 19.8819 87 ......... 922.360 5,328.29 717.426 4.7768

33 ......... 26,455.570 547,888.06 5,382.952 19.7097 88 ......... 799.677 4,405.93 630.218 4.5096

34 ......... 25,395.352 521,432.49 5,340.256 19.5326 89 ......... 686.895 3,606.25 548.193 4.2501

35 ......... 24,375.274 496,037.14 5,296.922 19.3500 90 ......... 583.657 2,919.35 471.375 4.0018

36 ......... 23,393.659 471,661.86 5,252.818 19.1620 91 ......... 489.628 2,335.70 399.793 3.7704

37 ......... 22,448.684 448,268.20 5,207.599 18.9686 92 ......... 405.003 1,846.07 334.000 3.5582

38 ......... 21,539.315 425,819.52 5,161.641 18.7694 93 ......... 330.227 1,441.07 274.802 3.3639

39 ......... 20,664.306 404,280.21 5,115.067 18.5642 94 ......... 265.891 1,110.84 223.167 3.1778

40 ......... 19,821.827 383,615.90 5,067.369 18.3532 95 ......... 211.556 844.95 179.058 2.9940

41 ......... 19,010.982 363,794.07 5,018.902 18.1360 96 ......... 166.117 633.39 141.755 2.8129

42 ......... 18,230.298 344,783.09 4,969.410 17.9126 97 ......... 128.290 467.27 110.318 2.6423

43 ......... 17,478.397 326,552.79 4,918.674 17.6832 95 ......... 97.341 338.98 84.303 2.4824

44 ......... 16,753.983 309,074.40 4,866.507 17.4478 99 ......... 72.485 241.64 63.191 2.3337

45 ......... 16,055.843 292,320.41 4,812.750 17.2065 100 ......... 53.032 169.16 46.525 2.1898

46 ......... 15,382.177 276,264.57 4,756.617 16.9600 101 ......... 38.067 116.13 33.601 2.0506

47 ......... 14,731.991 260,882.39 4,698.052 16.7086 102 ......... 26.769 78.06 23.767 1.9160

48 ......... 14,104.041 246,150.40 4,636.718 16.4525 103 ......... 18.410 51.29 16.437 1.7861

49 ......... 13,497.334 232,046.36 4,572.474 16.1920 104 ......... 12.358 32.88 11.093 1.6607

50 ......... 12,911.367 218,549.03 4,505.636 15.9269 105 ......... 8.080 20.52 7.291 1.5398

51 ......... 12,345.097 205,637.66 4,435.956 15.6574 106 ......... 5.134 12.44 4.656 1.4233

52 ......... 11,797.561 193,292.56 4,363.232 15.3841 107 ......... 3.162 7.31 2.881 1.3112

53 ......... 11,268.378 181,495.00 4,287.801 15.1066 108 ......... 1.882 4.15 1.722 1.2033

54 ......... 10,756.795 170,226.62 4,209.618 14.8250 109 ......... 1.078 2.26 0.991 1.0996

x x x x x x x x

103
Table 9.E. -- Actuarial Functions at 5.0 Percent Interest for 1989-91 United States 

Females Other than White

x D N M a x D N M a

0 ......... 100,000.000 1,995,288.90 4,986.243 18.9529 55 ......... 6,062.670 84,993.07 2,015.381 13.0191

1 ......... 93,878.095 1,895,288.90 3,626.243 19.1888 56 ......... 5,725.362 78,930.40 1,966.772 12.7861

2 ......... 89,316.100 1,801,410.81 3,534.633 19.1689 57 ......... 5,403.085 73,205.04 1,917.130 12.5487

3 ......... 85,010.258 1,712,094.71 3,481.939 19.1399 58 ......... 5,095.035 67,801.95 1,866.371 12.3075

4 ......... 80,924.306 1,627,084.45 3,444.094 19.1063 59 ......... 4,800.137 62,706.92 1,814.093 12.0636

5 ......... 77,044.128 1,546,160.14 3,417.454 19.0685 60 ......... 4,517.809 57,906.78 1,760.344 11.8174

6 ......... 73,349.989 1,469,116.02 3,392.083 19.0289 61 ......... 4,247.661 53,388.97 1,705.330 11.5690

7 ......... 69,837.233 1,395,766.03 3,372.184 18.9860 62 ......... 3,989.550 49,141.31 1,649.487 11.3175

8 ......... 66,494.729 1,325,928.80 3,355.263 18.9404 63 ......... 3,742.920 45,151.76 1,592.836 11.0632

9 ......... 63,314.777 1,259,434.07 3,341.726 18.8916 64 ......... 3,507.297 41,408.84 1,535.447 10.8065

10 ......... 60,287.509 1,196,119.29 3,329.448 18.8403 65 ......... 3,282.145 37,901.54 1,477.309 10.5478

11 ......... 57,405.567 1,135,831.78 3,318.339 18.7861 66 ......... 3,067.207 34,619.40 1,418.664 10.2869

12 ......... 54,660.831 1,078,426.21 3,307.202 18.7294 67 ......... 2,862.177 31,552.19 1,359.692 10.0238

13 ......... 52,046.798 1,023,765.38 3,296.066 18.6701 68 ......... 2,666.929 28,690.01 1,300.737 9.7577

14 ......... 49,555.752 971,718.58 3,283.439 18.6086 69 ......... 2,481.231 26,023.09 1,242.037 9.4880

15 ......... 47,181.043 922,162.83 3,268.527 18.5452 70 ......... 2,304.641 23,541.85 1,183.601 9.2150

16 ......... 44,917.835 874,981.79 3,252.035 18.4796 71 ......... 2,136.739 21,237.21 1,125.443 8.9391

17 ......... 42,760.566 830,063.95 3,233.711 18.4119 72 ......... 1,976.948 19,100.47 1,067.402 8.6616

18 ......... 40,703.988 787,303.39 3,213.350 18.3422 73 ......... 1,824.919 17,123.53 1,009.513 8.3832

19 ......... 38,744.729 746,599.40 3,192.376 18.2697 74 ......... 1,680.398 15,298.61 951.892 8.1042

20 ......... 36,877.882 707,854.67 3,170.517 18.1946 75 ......... 1,543.339 13,618.21 894.853 7.8239

21 ......... 35,098.820 670,976.79 3,147.545 18.1168 76 ......... 1,413.757 12,074.87 838.764 7.5410

22 ......... 33,404.202 635,877.97 3,124.299 18.0359 77 ......... 1,291.476 10,661.11 783.804 7.2550

23 ......... 31,789.108 602,473.77 3,099.881 17.9522 78 ......... 1,176.144 9,369.64 729.971 6.9664

24 ......... 30,250.225 570,684.66 3,074.765 17.8655 79 ......... 1,067.194 8,193.49 677.027 6.6776

25 ......... 28,784.342 540,434.43 3,049.369 17.7753 80 ......... 964.076 7,126.30 624.728 6.3918

26 ......... 27,388.066 511,650.09 3,023.776 17.6815 81 ......... 866.322 6,162.22 572.883 6.1131

27 ......... 26,057.624 484,262.02 2,997.527 17.5843 82 ......... 773.844 5,295.90 521.658 5.8436

28 ......... 24,790.255 458,204.40 2,970.998 17.4832 83 ......... 686.849 4,522.06 471.513 5.5838

29 ......... 23,582.556 433,414.15 2,943.788 17.3786 84 ......... 605.937 3,835.21 423.308 5.3294

30 ......... 22,431.350 409,831.59 2,915.560 17.2705 85 ......... 531.521 3,229.27 377.746 5.0755

31 ......... 21,333.882 387,400.24 2,886.252 17.1589 86 ......... 463.420 2,697.75 334.956 4.8214

32 ......... 20,288.182 366,066.36 2,856.451 17.0433 87 ......... 401.173 2,234.33 294.777 4.5695

33 ......... 19,291.698 345,778.18 2,826.070 16.9237 88 ......... 344.501 1,833.16 257.208 4.3212

34 ......... 18,342.208 326,486.48 2,795.233 16.7997 89 ......... 293.096 1,488.66 222.208 4.0791

35 ......... 17,437.769 308,144.27 2,764.232 16.6711 90 ......... 246.673 1,195.56 189.742 3.8467

36 ......... 16,576.148 290,706.50 2,732.981 16.5376 91 ......... 204.962 948.89 159.777 3.6296

37 ......... 15,755.071 274,130.35 2,701.245 16.3995 92 ......... 167.923 743.92 132.498 3.4302

38 ......... 14,972.882 258,375.28 2,669.297 16.2562 93 ......... 135.615 576.00 108.187 3.2473

39 ......... 14,227.821 243,402.40 2,637.231 16.1075 94 ......... 108.154 440.39 87.184 3.0718

40 ......... 13,517.777 229,174.58 2,604.702 15.9536 95 ......... 85.233 332.23 69.413 2.8979

41 ......... 12,841.336 215,656.80 2,571.964 15.7940 96 ......... 66.289 247.00 54.527 2.7261

42 ......... 12,196.732 202,815.47 2,538.852 15.6287 97 ......... 50.707 180.71 42.101 2.5638

43 ......... 11,582.314 190,618.74 2,505.231 15.4577 95 ......... 38.108 130.00 31.917 2.4115

44 ......... 10,996.535 179,036.42 2,470.991 15.2812 99 ......... 28.106 91.90 23.730 2.2696

45 ......... 10,437.943 168,039.89 2,436.044 15.0989 100 ......... 20.368 63.79 17.330 2.1319

46 ......... 9,904.753 157,601.94 2,399.899 14.9117 101 ......... 14.481 43.42 12.413 1.9985

47 ......... 9,395.747 147,697.19 2,362.548 14.7196 102 ......... 10.086 28.94 8.708 1.8693

48 ......... 8,909.585 138,301.44 2,323.802 14.5228 103 ......... 6.870 18.85 5.973 1.7443

49 ......... 8,445.123 129,391.86 2,283.606 14.3215 104 ......... 4.568 11.98 3.997 1.6234

50 ......... 8,001.552 120,946.73 2,242.184 14.1154 105 ......... 2.958 7.42 2.605 1.5066

51 ......... 7,577.755 112,945.18 2,199.413 13.9048 106 ......... 1.862 4.46 1.650 1.3939

52 ......... 7,172.694 105,367.43 2,155.198 13.6901 107 ......... 1.136 2.60 1.012 1.2853

53 ......... 6,785.714 98,194.73 2,109.774 13.4708 108 ......... 0.669 1.46 0.600 1.1805

54 ......... 6,415.952 91,409.02 2,063.141 13.2471 109 ......... 0.380 0.79 0.342 1.0797

x x x x x x x x

104
Table 9.F. -- Actuarial Functions at 6.0 Percent Interest for 1989-91 United States 

Females Other than White

x D N M a x D N M a

0 ......... 100,000.000 1,703,692.96 3,564.550 16.0369 55 ......... 3,599.588 45,889.55 1,002.066 11.7486

1 ......... 92,992.453 1,603,692.96 2,217.380 16.2454 56 ......... 3,367.249 42,289.96 973.478 11.5592

2 ......... 87,638.839 1,510,700.51 2,127.490 16.2378 57 ......... 3,147.730 38,922.71 944.558 11.3653

3 ......... 82,626.934 1,423,061.67 2,076.273 16.2227 58 ......... 2,940.264 35,774.98 915.265 11.1673

4 ......... 77,913.501 1,340,434.73 2,039.837 16.2041 59 ......... 2,743.950 32,834.72 885.381 10.9662

5 ......... 73,477.896 1,262,521.23 2,014.430 16.1823 60 ......... 2,558.197 30,090.77 854.946 10.7625

6 ......... 69,294.801 1,189,043.33 1,990.462 16.1592 61 ......... 2,382.535 27,532.57 824.088 10.5560

7 ......... 65,353.832 1,119,748.53 1,971.840 16.1336 62 ......... 2,216.648 25,150.04 793.061 10.3460

8 ......... 61,638.874 1,054,394.70 1,956.155 16.1060 63 ......... 2,059.998 22,933.39 761.882 10.1327

9 ......... 58,137.451 992,755.83 1,943.725 16.0760 64 ......... 1,912.107 20,873.39 730.595 9.9164

10 ......... 54,835.484 934,618.38 1,932.557 16.0440 65 ......... 1,772.478 18,961.28 699.198 9.6976

11 ......... 51,721.580 879,782.89 1,922.548 16.0100 66 ......... 1,640.777 17,188.80 667.826 9.4760

12 ......... 48,784.004 828,061.31 1,912.609 15.9740 67 ......... 1,516.654 15,548.03 636.577 9.2515

13 ......... 46,012.799 779,277.31 1,902.763 15.9361 68 ......... 1,399.861 14,031.37 605.632 9.0234

14 ......... 43,397.244 733,264.51 1,891.705 15.8966 69 ......... 1,290.102 12,631.51 575.111 8.7911

15 ......... 40,927.861 689,867.27 1,878.770 15.8557 70 ......... 1,186.981 11,341.41 545.014 8.5548

16 ......... 38,597.018 648,939.41 1,864.599 15.8132 71 ......... 1,090.122 10,154.43 515.344 8.3149

17 ......... 36,396.684 610,342.39 1,849.002 15.7692 72 ......... 999.085 9,064.31 486.011 8.0726

18 ......... 34,319.327 573,945.70 1,831.835 15.7237 73 ......... 913.554 8,065.22 457.032 7.8284

19 ......... 32,359.207 539,626.38 1,814.318 15.6761 74 ......... 833.271 7,151.67 428.459 7.5826

20 ......... 30,509.469 507,267.17 1,796.233 15.6265 75 ......... 758.087 6,318.40 400.442 7.3347

21 ......... 28,763.692 476,757.70 1,777.407 15.5750 76 ......... 687.885 5,560.31 373.151 7.0832

22 ......... 27,116.688 447,994.01 1,758.537 15.5210 77 ......... 622.459 4,872.42 346.661 6.8277

23 ......... 25,562.146 420,877.32 1,738.902 15.4649 78 ......... 561.524 4,249.97 320.960 6.5686

24 ......... 24,095.227 395,315.17 1,718.897 15.4064 79 ......... 504.701 3,688.44 295.922 6.3082

25 ......... 22,711.309 371,219.95 1,698.859 15.3452 80 ......... 451.633 3,183.74 271.422 6.0494

26 ......... 21,405.760 348,508.64 1,678.856 15.2811 81 ......... 402.011 2,732.11 247.363 5.7961

27 ......... 20,173.791 327,102.88 1,658.534 15.2142 82 ......... 355.709 2,330.10 223.817 5.5506

28 ......... 19,011.533 306,929.09 1,638.188 15.1444 83 ......... 312.742 1,974.39 200.985 5.3131

29 ......... 17,914.738 287,917.55 1,617.518 15.0715 84 ......... 273.298 1,661.64 179.242 5.0800

30 ......... 16,879.455 270,002.82 1,596.277 14.9959 85 ......... 237.472 1,388.35 158.886 4.8464

31 ......... 15,902.168 253,123.36 1,574.431 14.9175 86 ......... 205.093 1,150.87 139.949 4.6115

32 ......... 14,980.041 237,221.19 1,552.427 14.8358 87 ......... 175.870 945.78 122.335 4.3777

33 ......... 14,109.894 222,241.15 1,530.206 14.7507 88 ......... 149.600 769.91 106.020 4.1465

34 ......... 13,288.879 208,131.26 1,507.865 14.6621 89 ......... 126.077 620.31 90.965 3.9201

35 ......... 12,514.431 194,842.38 1,485.617 14.5694 90 ......... 105.107 494.24 77.131 3.7022

36 ......... 11,783.851 182,327.95 1,463.401 14.4727 91 ......... 86.510 389.13 64.484 3.4981

37 ......... 11,094.492 170,544.10 1,441.053 14.3720 92 ......... 70.208 302.62 53.078 3.3103

38 ......... 10,444.217 159,449.61 1,418.768 14.2668 93 ......... 56.165 232.41 43.010 3.1380

39 ......... 9,830.878 149,005.39 1,396.611 14.1569 94 ......... 44.370 176.25 34.394 2.9722

40 ......... 9,252.149 139,174.51 1,374.347 14.0424 95 ......... 34.637 131.88 27.172 2.8074

41 ......... 8,706.247 129,922.36 1,352.151 13.9229 96 ......... 26.684 97.24 21.180 2.6441

42 ......... 8,191.203 121,216.11 1,329.914 13.7983 97 ......... 20.219 70.56 16.225 2.4896

43 ......... 7,705.183 113,024.91 1,307.547 13.6687 95 ......... 15.052 50.34 12.203 2.3442

44 ......... 7,246.477 105,319.73 1,284.983 13.5339 99 ......... 10.997 35.28 9.000 2.2086

45 ......... 6,813.487 98,073.25 1,262.171 13.3940 100 ......... 7.894 24.29 6.519 2.0768

46 ......... 6,404.447 91,259.76 1,238.800 13.2494 101 ......... 5.559 16.39 4.631 1.9489

47 ......... 6,018.007 84,855.32 1,214.876 13.1002 102 ......... 3.836 10.83 3.222 1.8247

48 ......... 5,652.783 78,837.31 1,190.294 12.9466 103 ......... 2.588 7.00 2.192 1.7043

49 ......... 5,307.552 73,184.53 1,165.031 12.7888 104 ......... 1.705 4.41 1.455 1.5877

50 ......... 4,981.337 67,876.97 1,139.244 12.6263 105 ......... 1.094 2.71 0.940 1.4748

51 ......... 4,672.999 62,895.64 1,112.868 12.4594 106 ......... 0.682 1.61 0.590 1.3657

52 ......... 4,381.481 58,222.64 1,085.860 12.2883 107 ......... 0.412 0.93 0.359 1.2603

53 ......... 4,105.987 53,841.16 1,058.374 12.1128 108 ......... 0.240 0.52 0.211 1.1586

54 ......... 3,845.621 49,735.17 1,030.423 11.9329 109 ......... 0.135 0.28 0.119 1.0605

x x x x x x x x

105
Table 9.G. -- Actuarial Functions at 7.0 Percent Interest for 1989-91 United States 

Females Other than White

x D N M a x D N M a

0 ......... 100,000.000 1,485,995.54 2,785.339 13.8600 55 ......... 2,147.670 25,077.86 507.062 10.6768

1 ......... 92,123.364 1,385,995.54 1,450.759 14.0450 56 ......... 1,990.271 22,930.19 490.165 10.5211

2 ......... 86,008.385 1,293,872.17 1,362.542 14.0436 57 ......... 1,843.132 20,939.92 473.231 10.3611

3 ......... 80,331.874 1,207,863.79 1,312.748 14.0359 58 ......... 1,705.562 19,096.79 456.239 10.1968

4 ......... 75,041.425 1,127,531.91 1,277.655 14.0255 59 ......... 1,576.810 17,391.23 439.066 10.0294

5 ......... 70,107.931 1,052,490.49 1,253.413 14.0124 60 ......... 1,456.328 15,814.42 421.740 9.8591

6 ......... 65,498.775 982,382.56 1,230.757 13.9985 61 ......... 1,343.652 14,358.09 404.337 9.6859

7 ......... 61,196.372 916,883.78 1,213.320 13.9826 62 ......... 1,238.415 13,014.44 387.003 9.5089

8 ......... 57,178.320 855,687.41 1,198.770 13.9652 63 ......... 1,140.141 11,776.02 369.746 9.3286

9 ......... 53,426.260 798,509.09 1,187.348 13.9460 64 ......... 1,048.397 10,635.88 352.592 9.1449

10 ......... 49,920.917 745,082.83 1,177.181 13.9253 65 ......... 962.757 9,587.49 335.538 8.9584

11 ......... 46,646.036 695,161.91 1,168.154 13.9029 66 ......... 882.892 8,624.73 318.657 8.7687

12 ......... 43,585.546 648,515.88 1,159.274 13.8792 67 ......... 808.475 7,741.84 301.999 8.5759

13 ......... 40,725.441 604,930.33 1,150.559 13.8539 68 ......... 739.242 6,933.36 285.658 8.3790

14 ......... 38,051.464 564,204.89 1,140.864 13.8274 69 ......... 674.914 6,194.12 269.691 8.1776

15 ......... 35,550.880 526,153.43 1,129.628 13.8000 70 ......... 615.163 5,519.21 254.093 7.9719

16 ......... 33,212.927 490,602.55 1,117.434 13.7714 71 ......... 559.685 4,904.04 238.859 7.7622

17 ......... 31,026.823 457,389.62 1,104.138 13.7417 72 ......... 508.151 4,344.36 223.941 7.5493

18 ......... 28,982.533 426,362.80 1,089.640 13.7110 73 ......... 460.306 3,836.21 209.339 7.3340

19 ......... 27,071.825 397,380.26 1,074.985 13.6787 74 ......... 415.930 3,375.90 195.077 7.1165

20 ......... 25,285.783 370,308.44 1,059.997 13.6449 75 ......... 374.865 2,959.97 181.222 6.8961

21 ......... 23,616.116 345,022.65 1,044.540 13.6096 76 ......... 336.973 2,585.11 167.853 6.6716

22 ......... 22,055.788 321,406.54 1,029.192 13.5724 77 ......... 302.073 2,248.13 154.998 6.4424

23 ......... 20,597.065 299,350.75 1,013.371 13.5337 78 ......... 269.955 1,946.06 142.642 6.2088

24 ......... 19,233.624 278,753.69 997.402 13.4930 79 ......... 240.370 1,676.11 130.718 5.9730

25 ......... 17,959.504 259,520.06 981.556 13.4503 80 ......... 213.085 1,435.74 119.158 5.7379

26 ......... 16,768.914 241,560.56 965.887 13.4053 81 ......... 187.900 1,222.65 107.913 5.5069

27 ......... 15,656.111 224,791.64 950.115 13.3581 82 ......... 164.705 1,034.75 97.011 5.2825

28 ......... 14,616.237 209,135.53 934.474 13.3084 83 ......... 143.456 870.05 86.537 5.0649

29 ......... 13,644.292 194,519.30 918.730 13.2565 84 ......... 124.191 726.59 76.657 4.8506

30 ......... 12,735.648 180,875.00 902.704 13.2023 85 ......... 106.903 602.40 67.494 4.6350

31 ......... 11,886.146 168,139.36 886.375 13.1458 86 ......... 91.464 495.50 59.048 4.4174

32 ......... 11,092.254 156,253.21 870.082 13.0867 87 ......... 77.698 404.03 51.266 4.2000

33 ......... 10,350.293 145,160.96 853.782 13.0248 88 ......... 65.475 326.33 44.126 3.9841

34 ......... 9,656.936 134,810.66 837.546 12.9600 89 ......... 54.664 260.86 37.598 3.7720

35 ......... 9,009.157 125,153.73 821.530 12.8918 90 ......... 45.146 206.20 31.657 3.5673

36 ......... 8,403.929 116,144.57 805.686 12.8203 91 ......... 36.811 161.05 26.275 3.3750

37 ......... 7,838.350 107,740.64 789.897 12.7453 92 ......... 29.595 124.24 21.467 3.1980

38 ......... 7,309.964 99,902.29 774.300 12.6666 93 ......... 23.454 94.64 17.263 3.0352

39 ......... 6,816.379 92,592.33 758.937 12.5838 94 ......... 18.355 71.19 13.698 2.8784

40 ......... 6,355.155 85,775.95 743.644 12.4971 95 ......... 14.195 52.83 10.739 2.7220

41 ......... 5,924.294 79,420.79 728.541 12.4060 96 ......... 10.834 38.64 8.306 2.5666

42 ......... 5,521.733 73,496.50 713.550 12.3104 97 ......... 8.132 27.81 6.313 2.4192

43 ......... 5,145.561 67,974.77 698.614 12.2104 95 ......... 5.997 19.67 4.710 2.2804

44 ......... 4,794.008 62,829.21 683.686 12.1058 99 ......... 4.341 13.68 3.446 2.1507

45 ......... 4,465.431 58,035.20 668.736 11.9965 100 ......... 3.087 9.34 2.476 2.0244

46 ......... 4,158.126 53,569.77 653.562 11.8832 101 ......... 2.154 6.25 1.745 1.9015

47 ......... 3,870.712 49,411.64 638.174 11.7655 102 ......... 1.472 4.10 1.204 1.7820

48 ......... 3,601.824 45,540.93 622.511 11.6439 103 ......... 0.984 2.62 0.812 1.6660

49 ......... 3,350.245 41,939.10 606.565 11.5182 104 ......... 0.642 1.64 0.535 1.5534

50 ......... 3,114.945 38,588.86 590.440 11.3883 105 ......... 0.408 1.00 0.343 1.4443

51 ......... 2,894.824 35,473.92 574.100 11.2543 106 ......... 0.252 0.59 0.213 1.3386

52 ......... 2,688.868 32,579.09 557.525 11.1163 107 ......... 0.151 0.34 0.129 1.2363

53 ......... 2,496.250 29,890.22 540.815 10.9740 108 ......... 0.087 0.19 0.075 1.1374

54 ......... 2,316.110 27,393.97 523.981 10.8276 109 ......... 0.049 0.10 0.042 1.0419

x x x x x x x x

106
Table 9.H. -- Actuarial Functions at 8.0 Percent Interest for 1989-91 United States 

Females Other than White

x D N M a x D N M a

0 ......... 100,000.000 1,318,452.91 2,336.821 12.1845 55 ......... 1,287.564 13,860.11 260.889 9.7646

1 ......... 91,270.370 1,218,452.91 1,014.599 12.3499 56 ......... 1,182.152 12,572.55 250.853 9.6353

2 ......... 84,423.011 1,127,182.54 928.008 12.3516 57 ......... 1,084.620 11,390.39 240.888 9.5017

3 ......... 78,121.031 1,042,759.53 879.584 12.3480 58 ......... 994.372 10,305.77 230.981 9.3641

4 ......... 72,300.476 964,638.50 845.773 12.3421 59 ......... 910.795 9,311.40 221.062 9.2234

5 ......... 66,921.746 892,338.03 822.633 12.3341 60 ......... 833.413 8,400.61 211.146 9.0798

6 ......... 61,943.154 825,416.28 801.207 12.3254 61 ......... 761.812 7,567.19 201.280 8.9331

7 ......... 57,338.434 763,473.13 784.869 12.3152 62 ......... 695.645 6,805.38 191.543 8.7828

8 ......... 53,077.636 706,134.69 771.363 12.3038 63 ......... 634.512 6,109.74 181.939 8.6290

9 ......... 49,135.454 653,057.06 760.857 12.2910 64 ......... 578.052 5,475.22 172.480 8.4718

10 ......... 45,486.527 603,921.60 751.593 12.2769 65 ......... 525.918 4,897.17 163.165 8.3117

11 ......... 42,109.006 558,435.08 743.445 12.2617 66 ......... 477.825 4,371.25 154.029 8.1482

12 ......... 38,981.878 516,326.07 735.502 12.2453 67 ......... 433.499 3,893.43 145.097 7.9814

13 ......... 36,086.610 477,344.19 727.781 12.2277 68 ......... 392.707 3,459.93 136.416 7.8105

14 ......... 33,405.016 441,257.58 719.269 12.2093 69 ......... 355.214 3,067.22 128.012 7.6349

15 ......... 30,920.798 407,852.57 709.497 12.1902 70 ......... 320.768 2,712.01 119.879 7.4547

16 ......... 28,619.860 376,931.77 698.989 12.1703 71 ......... 289.138 2,391.24 112.009 7.2702

17 ......... 26,488.519 348,311.91 687.637 12.1495 72 ......... 260.085 2,102.10 104.373 7.0824

18 ......... 24,514.145 321,823.39 675.375 12.1281 73 ......... 233.415 1,842.02 96.969 6.8916

19 ......... 22,686.001 297,309.24 663.094 12.1054 74 ......... 208.960 1,608.60 89.804 6.6982

20 ......... 20,993.113 274,623.24 650.651 12.0816 75 ......... 186.585 1,399.64 82.908 6.5014

21 ......... 19,425.354 253,630.13 637.937 12.0567 76 ......... 166.171 1,213.06 76.315 6.3000

22 ......... 17,973.931 234,204.78 625.429 12.0302 77 ......... 147.582 1,046.89 70.035 6.0936

23 ......... 16,629.755 216,230.85 612.655 12.0026 78 ......... 130.669 899.31 64.054 5.8823

24 ......... 15,385.147 199,601.09 599.881 11.9736 79 ......... 115.271 768.64 58.335 5.6681

25 ......... 14,232.949 184,215.94 587.324 11.9429 80 ......... 101.241 653.36 52.843 5.4536

26 ......... 13,166.353 169,982.99 575.020 11.9104 81 ......... 88.448 552.12 47.550 5.2424

27 ......... 12,178.800 156,816.64 562.752 11.8762 82 ......... 76.812 463.68 42.465 5.0365

28 ......... 11,264.611 144,637.84 550.697 11.8400 83 ......... 66.283 386.86 37.626 4.8366

29 ......... 10,418.175 133,373.23 538.676 11.8020 84 ......... 56.850 320.58 33.104 4.6390

30 ......... 9,634.334 122,955.05 526.552 11.7622 85 ......... 48.483 263.73 28.948 4.4396

31 ......... 8,908.442 113,320.72 514.314 11.7206 86 ......... 41.097 215.25 25.153 4.2375

32 ......... 8,236.459 104,412.28 502.216 11.6768 87 ......... 34.589 174.15 21.689 4.0349

33 ......... 7,614.360 96,175.82 490.225 11.6308 88 ......... 28.877 139.56 18.539 3.8329

34 ......... 7,038.500 88,561.46 478.391 11.5824 89 ......... 23.886 110.68 15.687 3.6339

35 ......... 6,505.564 81,522.96 466.826 11.5313 90 ......... 19.544 86.80 13.115 3.4411

36 ......... 6,012.335 75,017.40 455.491 11.4772 91 ......... 15.788 67.25 10.807 3.2597

37 ......... 5,555.786 69,005.06 444.300 11.4204 92 ......... 12.576 51.47 8.764 3.0924

38 ......... 5,133.293 63,449.28 433.347 11.3603 93 ......... 9.874 38.89 6.994 2.9385

39 ......... 4,742.361 58,315.98 422.658 11.2968 94 ......... 7.656 29.02 5.507 2.7899

40 ......... 4,380.534 53,573.62 412.117 11.2299 95 ......... 5.866 21.36 4.284 2.6413

41 ......... 4,045.735 49,193.09 401.803 11.1592 96 ......... 4.435 15.49 3.288 2.4932

42 ......... 3,735.909 45,147.35 391.661 11.0847 97 ......... 3.299 11.06 2.479 2.3525

43 ......... 3,449.163 41,411.44 381.648 11.0062 95 ......... 2.410 7.76 1.835 2.2197

44 ......... 3,183.756 37,962.28 371.735 10.9237 99 ......... 1.728 5.35 1.332 2.0955

45 ......... 2,938.085 34,778.53 361.898 10.8371 100 ......... 1.218 3.62 0.949 1.9744

46 ......... 2,710.558 31,840.44 352.007 10.7468 101 ......... 0.842 2.40 0.664 1.8563

47 ......... 2,499.838 29,129.88 342.069 10.6527 102 ......... 0.570 1.56 0.454 1.7412

48 ......... 2,304.643 26,630.04 332.047 10.5550 103 ......... 0.377 0.99 0.304 1.6293

49 ......... 2,123.820 24,325.40 321.938 10.4536 104 ......... 0.244 0.61 0.198 1.5206

50 ......... 1,956.372 22,201.58 311.810 10.3483 105 ......... 0.154 0.37 0.126 1.4149

51 ......... 1,801.288 20,245.21 301.643 10.2393 106 ......... 0.094 0.22 0.078 1.3125

52 ......... 1,657.641 18,443.92 291.425 10.1266 107 ......... 0.056 0.12 0.047 1.2131

53 ......... 1,524.647 16,786.28 281.219 10.0099 108 ......... 0.032 0.07 0.027 1.1170

54 ......... 1,401.524 15,261.63 271.032 9.8893 109 ......... 0.018 0.04 0.015 1.0239

x x x x x x x x

107
Table 9.I. -- Actuarial Functions at 9.0 Percent Interest for 1989-91 United States 

Females Other than White

x D N M a x D N M a

0 ......... 100,000.000 1,186,105.47 2,064.686 10.8611 55 ......... 775.565 7,741.52 136.357 8.9818

1 ......... 90,433.028 1,086,105.47 754.595 11.0101 56 ......... 705.537 6,965.95 130.367 8.8733

2 ......... 82,881.071 995,672.44 669.585 11.0133 57 ......... 641.389 6,260.42 124.474 8.7607

3 ......... 75,990.576 912,791.37 622.482 11.0119 58 ......... 582.626 5,619.03 118.669 8.6443

4 ......... 69,683.537 836,800.79 589.894 11.0086 59 ......... 528.760 5,036.40 112.911 8.5249

5 ......... 63,907.753 767,117.25 567.796 11.0035 60 ......... 479.398 4,507.64 107.207 8.4027

6 ......... 58,610.693 703,209.50 547.523 10.9980 61 ......... 434.191 4,028.24 101.584 8.2776

7 ......... 53,755.961 644,598.81 532.206 10.9912 62 ......... 392.842 3,594.05 96.085 8.1489

8 ......... 49,304.849 590,842.85 519.660 10.9835 63 ......... 355.032 3,201.21 90.711 8.0167

9 ......... 45,224.137 541,538.00 509.991 10.9745 64 ......... 320.473 2,846.18 85.468 7.8812

10 ......... 41,481.586 496,313.86 501.543 10.9647 65 ......... 288.895 2,525.71 80.350 7.7426

11 ......... 38,049.138 454,832.27 494.179 10.9538 66 ......... 260.069 2,236.81 75.378 7.6008

12 ......... 34,900.355 416,783.14 487.069 10.9421 67 ......... 233.778 1,976.74 70.561 7.4556

13 ......... 32,011.825 381,882.78 480.219 10.9294 68 ......... 209.837 1,742.96 65.922 7.3063

14 ......... 29,361.165 349,870.96 472.738 10.9161 69 ......... 188.062 1,533.13 61.473 7.1523

15 ......... 26,928.338 320,509.79 464.227 10.9023 70 ......... 168.267 1,345.07 57.207 6.9936

16 ......... 24,695.830 293,581.45 455.160 10.8879 71 ......... 150.283 1,176.80 53.116 6.8305

17 ......... 22,647.020 268,885.62 445.455 10.8729 72 ......... 133.942 1,026.52 49.184 6.6639

18 ......... 20,766.695 246,238.60 435.067 10.8574 73 ......... 119.104 892.57 45.406 6.4940

19 ......... 19,041.706 225,471.91 424.759 10.8410 74 ......... 105.648 773.47 41.783 6.3212

20 ......... 17,459.106 206,430.20 414.410 10.8236 75 ......... 93.470 667.82 38.329 6.1448

21 ......... 16,007.051 188,971.10 403.933 10.8055 76 ......... 82.480 574.35 35.056 5.9635

22 ......... 14,675.156 172,964.05 393.721 10.7862 77 ......... 72.581 491.87 31.968 5.7769

23 ......... 13,453.112 158,288.89 383.387 10.7660 78 ......... 63.674 419.29 29.053 5.5850

24 ......... 12,332.066 144,835.78 373.149 10.7446 79 ......... 55.655 355.62 26.292 5.3897

25 ......... 11,303.849 132,503.71 363.175 10.7220 80 ......... 48.432 299.96 23.665 5.1934

26 ......... 10,360.822 121,199.86 353.494 10.6979 81 ......... 41.924 251.53 21.156 4.9996

27 ......... 9,495.776 110,839.04 343.928 10.6725 82 ......... 36.075 209.61 18.768 4.8103

28 ......... 8,702.408 101,343.27 334.615 10.6454 83 ......... 30.844 173.53 16.516 4.6260

29 ......... 7,974.659 92,640.86 325.414 10.6169 84 ......... 26.212 142.69 14.431 4.4435

30 ......... 7,307.006 84,666.20 316.218 10.5870 85 ......... 22.149 116.47 12.532 4.2586

31 ......... 6,694.478 77,359.19 307.022 10.5557 86 ......... 18.603 94.32 10.814 4.0705

32 ......... 6,132.715 70,664.71 298.014 10.5226 87 ......... 15.513 75.72 9.261 3.8812

33 ......... 5,617.497 64,532.00 289.167 10.4877 88 ......... 12.833 60.21 7.861 3.6919

34 ......... 5,145.017 58,914.50 280.517 10.4508 89 ......... 10.517 47.38 6.605 3.5047

35 ......... 4,711.823 53,769.49 272.141 10.4116 90 ......... 8.527 36.86 5.483 3.3229

36 ......... 4,314.639 49,057.66 264.006 10.3701 91 ......... 6.825 28.33 4.485 3.1515

37 ......... 3,950.427 44,743.02 256.049 10.3261 92 ......... 5.386 21.51 3.610 2.9931

38 ......... 3,616.528 40,792.60 248.332 10.2795 93 ......... 4.190 16.12 2.859 2.8474

39 ......... 3,310.455 37,176.07 240.871 10.2299 94 ......... 3.219 11.93 2.234 2.7064

40 ......... 3,029.824 33,865.61 233.580 10.1774 95 ......... 2.444 8.71 1.724 2.5650

41 ......... 2,772.586 30,835.79 226.512 10.1217 96 ......... 1.831 6.27 1.313 2.4236

42 ......... 2,536.770 28,063.20 219.625 10.0626 97 ......... 1.349 4.44 0.983 2.2891

43 ......... 2,320.576 25,526.43 212.889 10.0000 95 ......... 0.977 3.09 0.722 2.1620

44 ......... 2,122.360 23,205.86 206.280 9.9340 99 ......... 0.694 2.11 0.520 2.0430

45 ......... 1,940.622 21,083.50 199.783 9.8643 100 ......... 0.484 1.42 0.367 1.9267

46 ......... 1,773.914 19,142.88 193.309 9.7913 101 ......... 0.332 0.93 0.255 1.8131

47 ......... 1,621.000 17,368.96 186.865 9.7150 102 ......... 0.223 0.60 0.173 1.7022

48 ......... 1,480.717 15,747.96 180.426 9.6354 103 ......... 0.146 0.38 0.115 1.5942

49 ......... 1,352.020 14,267.25 173.991 9.5525 104 ......... 0.094 0.23 0.074 1.4890

50 ......... 1,233.998 12,915.23 167.603 9.4662 105 ......... 0.058 0.14 0.047 1.3867

51 ......... 1,125.754 11,681.23 161.249 9.3764 106 ......... 0.035 0.08 0.029 1.2873

52 ......... 1,026.474 10,555.47 154.921 9.2832 107 ......... 0.021 0.05 0.017 1.1908

53 ......... 935.457 9,529.00 148.659 9.1865 108 ......... 0.012 0.02 0.010 1.0972

54 ......... 852.025 8,593.54 142.466 9.0860 109 ......... 0.006 0.01 0.005 1.0066

x x x x x x x x

108
Table 9.J. -- Actuarial Functions at 10.0 Percent Interest for 1989-91 United States 

Females Other than White

x D N M a x D N M a

0 ......... 100,000.000 1,079,207.67 1,890.211 9.7921 55 ......... 469.329 4,366.99 72.330 8.3047

1 ......... 89,610.909 979,207.67 592.030 9.9273 56 ......... 423.071 3,897.66 68.738 8.2128

2 ......... 81,380.992 889,596.76 508.559 9.9313 57 ......... 381.109 3,474.59 65.237 8.1171

3 ......... 73,936.890 808,215.77 462.728 9.9312 58 ......... 343.045 3,093.48 61.819 8.0177

4 ......... 67,183.936 734,278.88 431.310 9.9294 59 ......... 308.499 2,750.44 58.459 7.9155

5 ......... 61,055.194 667,094.95 410.198 9.9261 60 ......... 277.156 2,441.94 55.162 7.8107

6 ......... 55,485.529 606,039.75 391.006 9.9225 61 ......... 248.739 2,164.78 51.940 7.7030

7 ......... 50,427.022 550,554.22 376.638 9.9178 62 ......... 223.005 1,916.04 48.819 7.5919

8 ......... 45,831.085 500,127.20 364.975 9.9124 63 ......... 199.709 1,693.04 45.796 7.4775

9 ......... 41,655.716 454,296.12 356.069 9.9060 64 ......... 178.631 1,493.33 42.873 7.3599

10 ......... 37,861.122 412,640.40 348.358 9.8988 65 ......... 159.565 1,314.70 40.047 7.2393

11 ......... 34,412.543 374,779.28 341.699 9.8908 66 ......... 142.338 1,155.13 37.325 7.1154

12 ......... 31,277.757 340,366.74 335.326 9.8821 67 ......... 126.786 1,012.80 34.713 6.9883

13 ......... 28,428.242 309,088.98 329.243 9.8726 68 ......... 112.767 886.01 32.220 6.8570

14 ......... 25,837.273 280,660.74 322.660 9.8626 69 ......... 100.146 773.24 29.851 6.7212

15 ......... 23,481.009 254,823.47 315.239 9.8523 70 ......... 88.790 673.10 27.600 6.5807

16 ......... 21,338.537 231,342.46 307.404 9.8415 71 ......... 78.580 584.31 25.461 6.4358

17 ......... 19,390.360 210,003.92 299.095 9.8303 72 ......... 69.399 505.73 23.424 6.2873

18 ......... 17,618.787 190,613.56 290.282 9.8188 73 ......... 61.150 436.33 21.484 6.1354

19 ......... 16,008.413 172,994.77 281.616 9.8065 74 ......... 53.748 375.18 19.641 5.9803

20 ......... 14,544.482 156,986.36 272.994 9.7935 75 ......... 47.120 321.43 17.899 5.8215

21 ......... 13,213.608 142,441.88 264.346 9.7799 76 ......... 41.202 274.31 16.265 5.6577

22 ......... 12,004.017 129,228.27 255.993 9.7654 77 ......... 35.927 233.11 14.736 5.4883

23 ......... 10,904.367 117,224.25 247.617 9.7502 78 ......... 31.232 197.18 13.306 5.3135

24 ......... 9,904.837 106,319.89 239.393 9.7341 79 ......... 27.051 165.95 11.964 5.1348

25 ......... 8,996.460 96,415.05 231.456 9.7170 80 ......... 23.326 138.90 10.699 4.9547

26 ......... 8,170.965 87,418.59 223.820 9.6987 81 ......... 20.008 115.57 9.501 4.7763

27 ......... 7,420.675 79,247.62 216.345 9.6793 82 ......... 17.060 95.56 8.372 4.6017

28 ......... 6,738.856 71,826.95 209.133 9.6586 83 ......... 14.454 78.50 7.317 4.4314

29 ......... 6,119.172 65,088.09 202.073 9.6367 84 ......... 12.171 64.05 6.349 4.2624

30 ......... 5,555.892 58,968.92 195.081 9.6138 85 ......... 10.191 51.88 5.475 4.0905

31 ......... 5,043.882 53,413.03 188.152 9.5897 86 ......... 8.482 41.69 4.692 3.9151

32 ......... 4,578.622 48,369.15 181.427 9.5641 87 ......... 7.009 33.21 3.990 3.7379

33 ......... 4,155.839 43,790.53 174.882 9.5371 88 ......... 5.745 26.20 3.363 3.5601

34 ......... 3,771.694 39,634.69 168.541 9.5085 89 ......... 4.666 20.45 2.806 3.3837

35 ......... 3,422.728 35,862.99 162.456 9.4779 90 ......... 3.748 15.79 2.313 3.2120

36 ......... 3,105.716 32,440.26 156.601 9.4453 91 ......... 2.973 12.04 1.878 3.0497

37 ......... 2,817.702 29,334.55 150.925 9.4108 92 ......... 2.325 9.07 1.501 2.8996

38 ......... 2,556.094 26,516.85 145.471 9.3740 93 ......... 1.792 6.74 1.179 2.7614

39 ......... 2,318.496 23,960.75 140.246 9.3346 94 ......... 1.364 4.95 0.914 2.6274

40 ......... 2,102.664 21,642.26 135.186 9.2928 95 ......... 1.026 3.58 0.700 2.4927

41 ......... 1,906.652 19,539.59 130.325 9.2481 96 ......... 0.762 2.56 0.529 2.3576

42 ......... 1,728.627 17,632.94 125.632 9.2005 97 ......... 0.556 1.80 0.393 2.2289

43 ......... 1,566.930 15,904.31 121.084 9.1500 95 ......... 0.399 1.24 0.286 2.1071

44 ......... 1,420.061 14,337.38 116.662 9.0963 99 ......... 0.281 0.84 0.205 1.9929

45 ......... 1,286.656 12,917.32 112.354 9.0395 100 ......... 0.194 0.56 0.143 1.8811

46 ......... 1,165.435 11,630.67 108.101 8.9797 101 ......... 0.132 0.37 0.099 1.7717

47 ......... 1,055.291 10,465.23 103.906 8.9169 102 ......... 0.088 0.23 0.066 1.6648

48 ......... 955.201 9,409.94 99.752 8.8513 103 ......... 0.057 0.15 0.044 1.5604

49 ......... 864.251 8,454.74 95.639 8.7827 104 ......... 0.036 0.09 0.028 1.4586

50 ......... 781.637 7,590.49 91.592 8.7110 105 ......... 0.022 0.05 0.018 1.3595

51 ......... 706.591 6,808.85 87.604 8.6362 106 ......... 0.013 0.03 0.011 1.2630

52 ......... 638.420 6,102.26 83.669 8.5584 107 ......... 0.008 0.02 0.006 1.1692

53 ......... 576.522 5,463.84 79.809 8.4772 108 ......... 0.004 0.01 0.004 1.0782

54 ......... 520.329 4,887.32 76.027 8.3927 109 ......... 0.002 0.00 0.002 0.9898

x x x x x x x x

109
Table 9.K. -- Actuarial Functions at 11.0 Percent Interest for 1989-91 United States 

Females Other than White

x D N M a x D N M a

0 ......... 100,000.000 991,210.35 1,771.947 8.9121 55 ......... 285.306 2,486.43 38.904 7.7149

1 ......... 88,803.604 891,210.35 485.461 9.0357 56 ......... 254.869 2,201.12 36.740 7.6363

2 ......... 79,921.273 802,406.75 403.487 9.0400 57 ......... 227.521 1,946.25 34.650 7.5542

3 ......... 71,956.544 722,485.47 358.884 9.0406 58 ......... 202.952 1,718.73 32.628 7.4686

4 ......... 64,795.414 650,528.93 328.583 9.0397 59 ......... 180.870 1,515.78 30.658 7.3805

5 ......... 58,354.069 585,733.52 308.405 9.0376 60 ......... 161.030 1,334.91 28.742 7.2898

6 ......... 52,553.056 527,379.45 290.227 9.0352 61 ......... 143.217 1,173.88 26.887 7.1965

7 ......... 47,331.609 474,826.39 276.741 9.0319 62 ......... 127.244 1,030.66 25.106 7.0999

8 ......... 42,630.241 427,494.78 265.893 9.0280 63 ......... 112.925 903.42 23.397 7.0002

9 ......... 38,397.413 384,864.54 257.683 9.0232 64 ......... 100.096 790.49 21.759 6.8973

10 ......... 34,585.220 346,467.13 250.640 9.0178 65 ......... 88.607 690.40 20.189 6.7917

11 ......... 31,151.828 311,881.91 244.611 9.0117 66 ......... 78.329 601.79 18.692 6.6829

12 ......... 28,058.993 280,730.08 238.895 9.0050 67 ......... 69.142 523.46 17.267 6.5708

13 ......... 25,272.964 252,671.09 233.487 8.9977 68 ......... 60.943 454.32 15.920 6.4549

14 ......... 22,762.636 227,398.13 227.687 8.9900 69 ......... 53.634 393.38 14.651 6.3344

15 ......... 20,500.400 204,635.49 221.208 8.9820 70 ......... 47.124 339.74 13.456 6.2095

16 ......... 18,462.051 184,135.09 214.429 8.9737 71 ......... 41.330 292.62 12.331 6.0801

17 ......... 16,625.353 165,673.04 207.305 8.9651 72 ......... 36.172 251.29 11.269 5.9471

18 ......... 14,970.308 149,047.68 199.816 8.9562 73 ......... 31.585 215.12 10.267 5.8106

19 ......... 13,479.467 134,077.38 192.519 8.9468 74 ......... 27.512 183.53 9.324 5.6710

20 ......... 12,136.470 120,597.91 185.325 8.9368 75 ......... 23.902 156.02 8.441 5.5274

21 ......... 10,926.605 108,461.44 178.174 8.9264 76 ......... 20.712 132.12 7.619 5.3789

22 ......... 9,836.943 97,534.84 171.329 8.9152 77 ......... 17.898 111.41 6.857 5.2246

23 ......... 8,855.309 87,697.89 164.527 8.9034 78 ......... 15.418 93.51 6.152 5.0648

24 ......... 7,971.138 78,842.58 157.908 8.8910 79 ......... 13.234 78.09 5.495 4.9008

25 ......... 7,174.875 70,871.45 151.578 8.8777 80 ......... 11.309 64.86 4.882 4.7350

26 ......... 6,457.817 63,696.57 145.544 8.8635 81 ......... 9.613 53.55 4.306 4.5704

27 ......... 5,811.998 57,238.76 139.689 8.8484 82 ......... 8.123 43.93 3.769 4.4089

28 ......... 5,230.437 51,426.76 134.091 8.8322 83 ......... 6.820 35.81 3.271 4.2512

29 ......... 4,706.675 46,196.32 128.661 8.8151 84 ......... 5.691 28.99 2.818 4.0942

30 ......... 4,234.918 41,489.65 123.332 8.7970 85 ......... 4.722 23.30 2.413 3.9341

31 ......... 3,810.007 37,254.73 118.097 8.7781 86 ......... 3.895 18.58 2.054 3.7701

32 ......... 3,427.405 33,444.72 113.063 8.7580 87 ......... 3.189 14.68 1.734 3.6039

33 ......... 3,082.897 30,017.32 108.208 8.7367 88 ......... 2.591 11.49 1.452 3.4366

34 ......... 2,772.723 26,934.42 103.546 8.7141 89 ......... 2.085 8.90 1.203 3.2702

35 ......... 2,493.516 24,161.70 99.114 8.6898 90 ......... 1.660 6.82 0.984 3.1077

36 ......... 2,242.183 21,668.18 94.886 8.6639 91 ......... 1.305 5.16 0.793 2.9538

37 ......... 2,015.924 19,426.00 90.826 8.6363 92 ......... 1.011 3.85 0.629 2.8114

38 ......... 1,812.281 17,410.07 86.959 8.6067 93 ......... 0.772 2.84 0.491 2.6800

39 ......... 1,629.014 15,597.79 83.287 8.5750 94 ......... 0.583 2.07 0.378 2.5526

40 ......... 1,464.057 13,968.78 79.764 8.5411 95 ......... 0.434 1.49 0.287 2.4241

41 ......... 1,315.617 12,504.72 76.410 8.5048 96 ......... 0.320 1.05 0.215 2.2949

42 ......... 1,182.031 11,189.10 73.201 8.4660 97 ......... 0.231 0.73 0.159 2.1716

43 ......... 1,061.811 10,007.07 70.119 8.4245 95 ......... 0.164 0.50 0.115 2.0547

44 ......... 953.617 8,945.26 67.150 8.3804 99 ......... 0.115 0.34 0.081 1.9451

45 ......... 856.248 7,991.64 64.283 8.3333 100 ......... 0.079 0.22 0.057 1.8375

46 ......... 768.589 7,135.40 61.478 8.2838 101 ......... 0.053 0.14 0.039 1.7321

47 ......... 689.681 6,366.81 58.736 8.2315 102 ......... 0.035 0.09 0.026 1.6289

48 ......... 618.644 5,677.13 56.046 8.1767 103 ......... 0.022 0.06 0.017 1.5280

49 ......... 554.697 5,058.48 53.406 8.1194 104 ......... 0.014 0.03 0.011 1.4295

50 ......... 497.153 4,503.78 50.832 8.0591 105 ......... 0.009 0.02 0.007 1.3333

51 ......... 445.372 4,006.63 48.318 7.9961 106 ......... 0.005 0.01 0.004 1.2396

52 ......... 398.778 3,561.26 45.860 7.9304 107 ......... 0.003 0.01 0.002 1.1484

53 ......... 356.870 3,162.48 43.471 7.8617 108 ......... 0.002 0.00 0.001 1.0597

54 ......... 319.185 2,805.61 41.151 7.7899 109 ......... 0.001 0.00 0.001 0.9735

x x x x x x x x

110
Table 9.L. -- Actuarial Functions at 12.0 Percent Interest for 1989-91 United States 

Females Other than White

x D N M a x D N M a

0 ......... 100,000.000 917,584.79 1,687.344 8.1758 55 ......... 174.214 1,428.14 21.199 7.1976

1 ......... 88,010.714 817,584.79 412.344 8.2896 56 ......... 154.239 1,253.93 19.889 7.1298

2 ......... 78,500.478 729,574.07 331.828 8.2939 57 ......... 136.460 1,099.69 18.636 7.0587

3 ......... 70,046.294 651,073.59 288.409 8.2949 58 ......... 120.637 963.23 17.434 6.9845

4 ......... 62,512.100 581,027.30 259.175 8.2946 59 ......... 106.551 842.59 16.273 6.9079

5 ......... 55,795.083 518,515.20 239.883 8.2932 60 ......... 94.017 736.04 15.155 6.8289

6 ......... 49,799.813 462,720.12 222.657 8.2916 61 ......... 82.870 642.03 14.082 6.7474

7 ......... 44,451.453 412,920.30 209.992 8.2892 62 ......... 72.970 559.16 13.060 6.6628

8 ......... 39,678.700 368,468.85 199.894 8.2863 63 ......... 64.180 486.19 12.089 6.5753

9 ......... 35,419.838 328,790.15 192.322 8.2827 64 ......... 56.381 422.01 11.166 6.4849

10 ......... 31,618.416 293,370.31 185.882 8.2785 65 ......... 49.464 365.63 10.290 6.3917

11 ......... 28,225.266 261,751.90 180.420 8.2737 66 ......... 43.336 316.16 9.461 6.2956

12 ......... 25,195.997 233,526.63 175.287 8.2684 67 ......... 37.912 272.83 8.680 6.1964

13 ......... 22,491.613 208,330.63 170.474 8.2626 68 ......... 33.118 234.91 7.948 6.0933

14 ......... 20,076.682 185,839.02 165.358 8.2565 69 ......... 28.886 201.80 7.265 5.9860

15 ......... 17,919.945 165,762.34 159.695 8.2502 70 ......... 25.153 172.91 6.627 5.8743

16 ......... 15,994.079 147,842.39 153.823 8.2436 71 ......... 21.863 147.76 6.032 5.7583

17 ......... 14,274.311 131,848.31 147.705 8.2368 72 ......... 18.964 125.89 5.475 5.6386

18 ......... 12,738.548 117,574.00 141.334 8.2298 73 ......... 16.411 106.93 4.955 5.5156

19 ......... 11,367.550 104,835.46 135.180 8.2223 74 ......... 14.167 90.52 4.469 5.3893

20 ......... 10,143.586 93,467.91 129.167 8.2145 75 ......... 12.199 76.35 4.018 5.2591

21 ......... 9,050.849 83,324.32 123.243 8.2062 76 ......... 10.476 64.15 3.602 5.1238

22 ......... 8,075.496 74,273.47 117.624 8.1974 77 ......... 8.972 53.68 3.221 4.9829

23 ......... 7,204.730 66,197.98 112.090 8.1881 78 ......... 7.660 44.71 2.870 4.8363

24 ......... 6,427.458 58,993.25 106.753 8.1783 79 ......... 6.516 37.05 2.547 4.6854

25 ......... 5,733.743 52,565.79 101.694 8.1678 80 ......... 5.518 30.53 2.247 4.5323

26 ......... 5,114.634 46,832.04 96.915 8.1565 81 ......... 4.649 25.01 1.969 4.3800

27 ......... 4,562.042 41,717.41 92.319 8.1445 82 ......... 3.893 20.36 1.711 4.2303

28 ......... 4,068.897 37,155.37 87.965 8.1316 83 ......... 3.239 16.47 1.475 4.0838

29 ......... 3,628.757 33,086.47 83.778 8.1179 84 ......... 2.679 13.23 1.262 3.9378

30 ......... 3,235.890 29,457.71 79.706 8.1034 85 ......... 2.203 10.55 1.073 3.7883

31 ......... 2,885.224 26,221.82 75.742 8.0883 86 ......... 1.801 8.35 0.907 3.6347

32 ......... 2,572.314 23,336.60 71.964 8.0722 87 ......... 1.462 6.55 0.760 3.4786

33 ......... 2,293.098 20,764.29 68.353 8.0551 88 ......... 1.177 5.08 0.632 3.3209

34 ......... 2,043.972 18,471.19 64.916 8.0369 89 ......... 0.939 3.91 0.520 3.1635

35 ......... 1,821.737 16,427.22 61.678 8.0173 90 ......... 0.741 2.97 0.422 3.0095

36 ......... 1,623.490 14,605.48 58.617 7.9963 91 ......... 0.577 2.23 0.338 2.8634

37 ......... 1,446.630 12,981.99 55.703 7.9740 92 ......... 0.443 1.65 0.266 2.7280

38 ......... 1,288.884 11,535.36 52.953 7.9499 93 ......... 0.335 1.21 0.206 2.6031

39 ......... 1,148.202 10,246.48 50.365 7.9239 94 ......... 0.251 0.87 0.157 2.4817

40 ......... 1,022.719 9,098.27 47.904 7.8962 95 ......... 0.185 0.62 0.119 2.3590

41 ......... 910.820 8,075.56 45.582 7.8662 96 ......... 0.135 0.44 0.088 2.2353

42 ......... 811.030 7,164.74 43.380 7.8341 97 ......... 0.097 0.30 0.065 2.1171

43 ......... 722.038 6,353.71 41.284 7.7997 95 ......... 0.068 0.21 0.046 2.0048

44 ......... 642.676 5,631.67 39.283 7.7628 99 ......... 0.047 0.14 0.033 1.8994

45 ......... 571.903 4,988.99 37.368 7.7235 100 ......... 0.032 0.09 0.022 1.7958

46 ......... 508.771 4,417.09 35.512 7.6819 101 ......... 0.021 0.06 0.015 1.6941

47 ......... 452.461 3,908.32 33.713 7.6379 102 ......... 0.014 0.04 0.010 1.5945

48 ......... 402.234 3,455.86 31.964 7.5917 103 ......... 0.009 0.02 0.007 1.4969

49 ......... 357.436 3,053.62 30.262 7.5431 104 ......... 0.006 0.01 0.004 1.4014

50 ......... 317.496 2,696.19 28.619 7.4920 105 ......... 0.003 0.01 0.003 1.3081

51 ......... 281.887 2,378.69 27.028 7.4384 106 ......... 0.002 0.00 0.002 1.2171

52 ......... 250.143 2,096.80 25.486 7.3824 107 ......... 0.001 0.00 0.001 1.1283

53 ......... 221.857 1,846.66 24.001 7.3236 108 ......... 0.001 0.00 0.000 1.0419

54 ......... 196.657 1,624.80 22.571 7.2621 109 ......... 0.000 0.00 0.000 0.9578

x x x x x x x x

111
Table 10.A. -- Actuarial Functions at 1.0 Percent Interest for 1989-91 United States 

Total Black Population

x D N M a x D N M a

0 ......... 100,000.000 4,937,759.57 51,111.291 48.3776 55 ......... 46,649.612 918,547.32 37,555.084 18.6904

1 ......... 97,214.851 4,837,759.57 49,316.242 48.7636 56 ......... 45,548.489 871,897.71 36,915.839 18.1422

2 ......... 96,132.732 4,740,544.72 49,196.646 48.3125 57 ......... 44,426.601 826,349.22 36,244.925 17.6003

3 ......... 95,107.158 4,644,411.99 49,122.881 47.8335 58 ......... 43,281.472 781,922.62 35,539.664 17.0660

4 ......... 94,109.766 4,549,304.83 49,067.144 47.3404 59 ......... 42,111.856 738,641.15 34,798.577 16.5400

5 ......... 93,133.267 4,455,195.06 49,022.425 46.8368 60 ......... 40,917.672 696,529.29 34,021.343 16.0227

6 ......... 92,172.532 4,362,061.80 48,983.801 46.3250 61 ......... 39,701.587 655,611.62 33,210.383 15.5135

7 ......... 91,225.422 4,269,889.27 48,949.291 45.8059 62 ......... 38,467.260 615,910.03 32,369.141 15.0113

8 ......... 90,291.725 4,178,663.84 48,918.816 45.2796 63 ......... 37,214.482 577,442.77 31,497.227 14.5166

9 ......... 89,372.146 4,088,372.12 48,893.214 44.7455 64 ......... 35,940.423 540,228.29 30,591.628 14.0312

10 ......... 88,464.641 3,998,999.97 48,870.582 44.2045 65 ......... 34,647.094 504,287.86 29,654.145 13.5550

11 ......... 87,569.931 3,910,535.33 48,851.759 43.6561 66 ......... 33,335.405 469,640.77 28,685.496 13.0883

12 ......... 86,683.378 3,822,965.40 48,832.235 43.1026 67 ......... 32,010.868 436,305.37 27,691.013 12.6299

13 ......... 85,798.767 3,736,282.02 48,805.876 42.5470 68 ......... 30,678.792 404,294.50 26,675.876 12.1783

14 ......... 84,910.996 3,650,483.26 48,767.597 41.9919 69 ......... 29,341.770 373,615.71 25,642.605 11.7332

15 ......... 84,015.166 3,565,572.26 48,712.471 41.4396 70 ......... 28,001.308 344,273.94 24,592.656 11.2949

16 ......... 83,109.990 3,481,557.09 48,639.128 40.8910 71 ......... 26,655.898 316,272.63 23,524.486 10.8650

17 ......... 82,195.927 3,398,447.10 48,547.935 40.3457 72 ......... 25,305.563 289,616.73 22,438.070 10.4448

18 ......... 81,277.603 3,316,251.18 48,443.433 39.8015 73 ......... 23,953.236 264,311.17 21,336.294 10.0345

19 ......... 80,356.163 3,234,973.57 48,326.722 39.2579 74 ......... 22,607.011 240,357.93 20,227.229 9.6320

20 ......... 79,434.348 3,154,617.41 48,200.512 38.7135 75 ......... 21,275.138 217,750.92 19,119.189 9.2350

21 ......... 78,512.360 3,075,183.06 48,065.003 38.1681 76 ......... 19,965.546 196,475.78 18,020.241 8.8407

22 ......... 77,588.792 2,996,670.70 47,918.785 37.6225 77 ......... 18,681.659 176,510.24 16,934.033 8.4483

23 ......... 76,667.066 2,919,081.91 47,765.265 37.0748 78 ......... 17,421.699 157,828.58 15,859.040 8.0593

24 ......... 75,748.898 2,842,414.84 47,606.176 36.5242 79 ......... 16,180.757 140,406.88 14,790.590 7.6774

25 ......... 74,835.937 2,766,665.95 47,443.205 35.9698 80 ......... 14,954.109 124,226.12 13,724.147 7.3072

26 ......... 73,930.541 2,691,830.01 47,278.759 35.4103 81 ......... 13,737.211 109,272.01 12,655.310 6.9545

27 ......... 73,030.387 2,617,899.47 47,110.590 34.8467 82 ......... 12,535.427 95,534.80 11,589.538 6.6212

28 ......... 72,133.998 2,544,869.08 46,937.274 34.2797 83 ......... 11,360.035 82,999.37 10,538.259 6.3063

29 ......... 71,238.459 2,472,735.08 46,755.934 33.7107 84 ......... 10,230.532 71,639.34 9,521.231 6.0025

30 ......... 70,340.970 2,401,496.62 46,563.776 33.1408 85 ......... 9,164.775 61,408.81 8,556.767 5.7005

31 ......... 69,441.781 2,331,155.65 46,361.032 32.5699 86 ......... 8,165.441 52,244.03 7,648.173 5.3982

32 ......... 68,541.866 2,261,713.87 46,148.660 31.9976 87 ......... 7,227.916 44,078.59 6,791.494 5.0984

33 ......... 67,640.722 2,193,172.01 45,926.148 31.4238 88 ......... 6,349.398 36,850.68 5,984.540 4.8038

34 ......... 66,737.870 2,125,531.28 45,693.005 30.8490 89 ......... 5,526.341 30,501.28 5,224.349 4.5193

35 ......... 65,833.558 2,058,793.42 45,449.465 30.2727 90 ......... 4,756.124 24,974.94 4,508.847 4.2511

36 ......... 64,927.332 1,992,959.86 45,195.056 29.6952 91 ......... 4,040.242 20,218.81 3,840.056 4.0044

37 ......... 64,017.373 1,928,032.52 44,927.942 29.1173 92 ......... 3,382.509 16,178.57 3,222.325 3.7830

38 ......... 63,106.051 1,864,015.15 44,650.455 28.5378 93 ......... 2,791.708 12,796.06 2,665.014 3.5836

39 ......... 62,193.610 1,800,909.10 44,362.827 27.9565 94 ......... 2,276.244 10,004.35 2,177.191 3.3951

40 ......... 61,280.961 1,738,715.49 44,065.956 27.3728 95 ......... 1,837.548 7,728.11 1,761.033 3.2057

41 ......... 60,366.987 1,677,434.53 43,758.724 26.7873 96 ......... 1,466.655 5,890.56 1,408.332 3.0163

42 ......... 59,451.278 1,617,067.54 43,440.708 26.1999 97 ......... 1,153.139 4,423.91 1,109.338 2.8364

43 ......... 58,531.486 1,557,616.27 43,109.543 25.6116 95 ......... 892.587 3,270.77 860.203 2.6644

44 ......... 57,607.944 1,499,084.78 42,765.521 25.0222 99 ......... 679.718 2,378.18 656.172 2.4988

45 ......... 56,677.141 1,441,476.83 42,405.094 24.4331 100 ......... 508.604 1,698.46 491.788 2.3395

46 ......... 55,738.243 1,384,799.69 42,027.355 23.8447 101 ......... 373.431 1,189.86 361.650 2.1863

47 ......... 54,787.949 1,329,061.45 41,628.925 23.2583 102 ......... 268.641 816.43 260.558 2.0391

48 ......... 53,824.337 1,274,273.50 41,207.768 22.6747 103 ......... 189.041 547.79 183.617 1.8977

49 ......... 52,847.415 1,220,449.16 40,763.760 22.0938 104 ......... 129.886 358.74 126.334 1.7620

50 ......... 51,856.591 1,167,601.75 40,296.178 21.5160 105 ......... 86.959 228.86 84.693 1.6318

51 ......... 50,850.708 1,115,745.16 39,803.727 20.9416 106 ......... 56.603 141.90 55.198 1.5069

52 ......... 49,828.665 1,064,894.45 39,285.156 20.3711 107 ......... 35.730 85.30 34.885 1.3873

53 ......... 48,788.827 1,015,065.78 38,738.671 19.8053 108 ......... 21.810 49.57 21.319 1.2727

54 ......... 47,729.637 966,276.96 38,162.538 19.2448 109 ......... 12.833 27.76 12.558 1.1629

x x x x x x x x

112
Table 10.B. -- Actuarial Functions at 2.0 Percent Interest for 1989-91 United States 

Total Black Population

x D N M a x D N M a

0 ......... 100,000.000 3,688,994.32 27,666.778 35.8899 55 ......... 27,134.020 473,588.46 17,847.972 16.4537

1 ......... 96,261.765 3,588,994.32 25,889.327 36.2837 56 ......... 26,233.805 446,454.44 17,479.797 16.0183

2 ......... 94,257.017 3,492,732.56 25,772.064 36.0554 57 ......... 25,336.791 420,220.63 17,097.170 15.5854

3 ......... 92,337.223 3,398,475.54 25,700.448 35.8050 58 ......... 24,441.719 394,883.84 16,698.898 15.1561

4 ......... 90,473.106 3,306,138.32 25,646.865 35.5428 59 ......... 23,548.069 370,442.12 16,284.498 14.7313

5 ......... 88,656.555 3,215,665.21 25,604.296 35.2710 60 ......... 22,655.990 346,894.05 15,854.146 14.3114

6 ......... 86,881.784 3,127,008.65 25,567.889 34.9915 61 ......... 21,767.131 324,238.06 15,409.522 13.8958

7 ......... 85,146.009 3,040,126.87 25,535.678 34.7049 62 ......... 20,883.620 302,470.93 14,952.817 13.4836

8 ......... 83,448.314 2,954,980.86 25,507.513 34.4109 63 ......... 20,005.422 281,587.31 14,484.102 13.0755

9 ......... 81,788.643 2,871,532.55 25,484.084 34.1092 64 ......... 19,131.108 261,581.89 14,002.051 12.6731

10 ......... 80,164.436 2,789,743.90 25,463.575 33.8003 65 ......... 18,261.857 242,450.78 13,507.920 12.2763

11 ......... 78,575.695 2,709,579.47 25,446.685 33.4837 66 ......... 17,398.230 224,188.93 13,002.369 11.8857

12 ......... 77,017.648 2,631,003.77 25,429.339 33.1611 67 ......... 16,543.141 206,790.70 12,488.422 11.5001

13 ......... 75,484.307 2,553,986.13 25,406.148 32.8347 68 ......... 15,699.289 190,247.55 11,968.945 11.1182

14 ......... 73,970.876 2,478,501.82 25,372.801 32.5065 69 ......... 14,867.887 174,548.26 11,445.372 10.7400

15 ......... 72,472.914 2,404,530.94 25,325.248 32.1783 70 ......... 14,049.552 159,680.38 10,918.564 10.3655

16 ......... 70,989.230 2,332,058.03 25,262.602 31.8509 71 ......... 13,243.374 145,630.83 10,387.868 9.9965

17 ......... 69,520.155 2,261,068.80 25,185.472 31.5239 72 ......... 12,449.232 132,387.45 9,853.399 9.6342

18 ......... 68,069.494 2,191,548.64 25,097.952 31.1958 73 ......... 11,668.417 119,938.22 9,316.687 9.2789

19 ......... 66,638.012 2,123,479.15 25,001.166 30.8659 74 ......... 10,904.659 108,269.80 8,781.722 8.9288

20 ......... 65,227.746 2,056,841.14 24,897.528 30.5332 75 ......... 10,161.611 97,365.14 8,252.490 8.5817

21 ......... 63,838.588 1,991,613.39 24,787.345 30.1976 76 ......... 9,442.621 87,203.53 7,732.747 8.2351

22 ......... 62,469.127 1,927,774.80 24,669.621 29.8596 77 ......... 8,748.790 77,760.91 7,224.066 7.8882

23 ......... 61,121.850 1,865,305.68 24,547.229 29.5178 78 ......... 8,078.752 69,012.12 6,725.573 7.5424

24 ......... 59,797.794 1,804,183.83 24,421.641 29.1714 79 ......... 7,429.743 60,933.37 6,234.971 7.2013

25 ......... 58,497.897 1,744,386.03 24,294.249 28.8196 80 ......... 6,799.182 53,503.63 5,750.092 6.8691

26 ......... 57,223.595 1,685,888.14 24,166.965 28.4614 81 ......... 6,184.662 46,704.45 5,268.888 6.5517

27 ......... 55,972.674 1,628,664.54 24,038.075 28.0975 82 ......... 5,588.274 40,519.78 4,793.769 6.2509

28 ......... 54,743.639 1,572,691.87 23,906.543 27.7283 83 ......... 5,014.636 34,931.51 4,329.704 5.9659

29 ......... 53,533.961 1,517,948.23 23,770.270 27.3549 84 ......... 4,471.767 29,916.87 3,885.162 5.6902

30 ......... 52,341.289 1,464,414.27 23,627.284 26.9782 85 ......... 3,966.651 25,445.11 3,467.727 5.4148

31 ......... 51,165.605 1,412,072.98 23,477.900 26.5981 86 ......... 3,499.476 21,478.46 3,078.330 5.1376

32 ......... 50,007.413 1,360,907.37 23,322.955 26.2141 87 ......... 3,067.310 17,978.98 2,714.781 4.8615

33 ......... 48,866.125 1,310,899.96 23,162.204 25.8264 88 ......... 2,668.077 14,911.67 2,375.691 4.5889

34 ......... 47,741.186 1,262,033.84 22,995.425 25.4349 89 ......... 2,299.454 12,243.59 2,059.383 4.3246

35 ......... 46,632.575 1,214,292.65 22,822.915 25.0396 90 ......... 1,959.572 9,944.14 1,764.589 4.0746

36 ......... 45,539.770 1,167,660.07 22,644.474 24.6404 91 ......... 1,648.302 7,984.57 1,491.742 3.8441

37 ......... 44,461.317 1,122,120.30 22,458.958 24.2381 92 ......... 1,366.437 6,336.26 1,242.196 3.6371

38 ......... 43,398.696 1,077,658.99 22,268.128 23.8316 93 ......... 1,116.713 4,969.83 1,019.266 3.4504

39 ......... 42,351.875 1,034,260.29 22,072.262 23.4206 94 ......... 901.596 3,853.11 826.044 3.2737

40 ......... 41,321.269 991,908.42 21,872.084 23.0048 95 ......... 720.697 2,951.52 662.825 3.0954

41 ......... 40,305.915 950,587.15 21,666.951 22.5843 96 ......... 569.591 2,230.82 525.850 2.9165

42 ......... 39,305.351 910,281.23 21,456.699 22.1592 97 ......... 443.444 1,661.23 410.870 2.7462

43 ......... 38,317.859 870,975.88 21,239.901 21.7303 95 ......... 339.882 1,217.79 316.004 2.5830

44 ......... 37,343.521 832,658.02 21,016.893 21.2973 99 ......... 256.288 877.90 239.074 2.4255

45 ......... 36,379.944 795,314.50 20,785.542 20.8613 100 ......... 189.889 621.62 177.701 2.2736

46 ......... 35,426.526 758,934.56 20,545.456 20.4228 101 ......... 138.055 431.73 129.590 2.1272

47 ......... 34,481.134 723,508.03 20,294.702 19.9827 102 ......... 98.341 293.67 92.583 1.9863

48 ......... 33,542.574 689,026.90 20,032.243 19.5419 103 ......... 68.524 195.33 64.694 1.8506

49 ......... 32,610.890 655,484.32 19,758.256 19.1002 104 ......... 46.620 126.81 44.133 1.7201

50 ......... 31,685.755 622,873.43 19,472.551 18.6578 105 ......... 30.906 80.19 29.334 1.5946

51 ......... 30,766.515 591,187.68 19,174.600 18.2153 106 ......... 19.920 49.28 18.953 1.4741

52 ......... 29,852.572 560,421.16 18,863.922 17.7730 107 ......... 12.451 29.36 11.875 1.3583

53 ......... 28,943.036 530,568.59 18,539.730 17.3315 108 ......... 7.526 16.91 7.194 1.2472

54 ......... 28,037.097 501,625.55 18,201.301 16.8915 109 ......... 4.385 9.39 4.201 1.1407

x x x x x x x x

113
Table 10.C. -- Actuarial Functions at 3.0 Percent Interest for 1989-91 United States 

Total Black Population

x D N M a x D N M a

0 ......... 100,000.000 2,883,119.27 16,025.652 27.8312 55 ......... 15,866.321 247,822.61 8,648.186 14.6194

1 ......... 95,327.184 2,783,119.27 14,265.458 28.1954 56 ......... 15,190.999 231,956.29 8,434.990 14.2693

2 ......... 92,435.668 2,687,792.09 14,150.461 28.0774 57 ......... 14,529.129 216,765.29 8,215.577 13.9194

3 ......... 89,673.816 2,595,356.42 14,080.911 27.9422 58 ......... 13,879.783 202,236.16 7,989.409 13.5706

4 ......... 87,010.425 2,505,682.60 14,029.378 27.7975 59 ......... 13,242.476 188,356.38 7,756.367 13.2237

5 ......... 84,435.598 2,418,672.18 13,988.836 27.6452 60 ......... 12,617.109 175,113.90 7,516.704 12.8791

6 ......... 81,941.972 2,334,236.58 13,954.499 27.4865 61 ......... 12,004.414 162,496.80 7,271.498 12.5364

7 ......... 79,525.228 2,252,294.61 13,924.415 27.3218 62 ......... 11,405.347 150,492.38 7,022.074 12.1949

8 ......... 77,182.909 2,172,769.38 13,898.364 27.1509 63 ......... 10,819.654 139,087.03 6,768.575 11.8550

9 ......... 74,913.404 2,095,586.47 13,876.904 26.9735 64 ......... 10,246.339 128,267.38 6,510.396 11.5184

10 ......... 72,712.857 2,020,673.07 13,858.302 26.7898 65 ......... 9,685.822 118,021.04 6,248.316 11.1849

11 ......... 70,579.836 1,947,960.21 13,843.131 26.5994 66 ......... 9,138.177 108,335.22 5,982.782 10.8552

12 ......... 68,508.683 1,877,380.37 13,827.701 26.4035 67 ......... 8,604.694 99,197.04 5,715.460 10.5282

13 ......... 66,492.855 1,808,871.69 13,807.272 26.2040 68 ......... 8,086.496 90,592.35 5,447.884 10.2029

14 ......... 64,527.081 1,742,378.84 13,778.183 26.0023 69 ......... 7,583.900 82,505.85 5,180.817 9.8791

15 ......... 62,606.572 1,677,851.75 13,737.104 25.7999 70 ......... 7,096.901 74,921.95 4,914.708 9.5570

16 ......... 60,729.488 1,615,245.18 13,683.512 25.5974 71 ......... 6,624.726 67,825.05 4,649.239 9.2382

17 ......... 58,895.326 1,554,515.69 13,618.170 25.3946 72 ......... 6,167.011 61,200.32 4,384.477 8.9238

18 ......... 57,106.504 1,495,620.37 13,544.745 25.1900 73 ......... 5,724.098 55,033.31 4,121.186 8.6143

19 ......... 55,362.797 1,438,513.87 13,464.335 24.9834 74 ......... 5,297.490 49,309.21 3,861.300 8.3080

20 ......... 53,665.022 1,383,151.07 13,379.069 24.7738 75 ......... 4,888.590 44,011.72 3,606.695 8.0029

21 ......... 52,012.193 1,329,486.05 13,289.298 24.5610 76 ......... 4,498.591 39,123.14 3,359.082 7.6968

22 ......... 50,402.290 1,277,473.85 13,194.314 24.3456 77 ......... 4,127.575 34,624.54 3,119.093 7.3886

23 ......... 48,836.471 1,227,071.56 13,096.522 24.1261 78 ......... 3,774.454 30,496.97 2,886.193 7.0798

24 ......... 47,314.679 1,178,235.09 12,997.152 23.9021 79 ......... 3,437.531 26,722.52 2,659.205 6.7738

25 ......... 45,836.762 1,130,920.41 12,897.332 23.6728 80 ......... 3,115.247 23,284.98 2,437.043 6.4745

26 ......... 44,402.943 1,085,083.65 12,798.565 23.4372 81 ......... 2,806.174 20,169.74 2,218.706 6.1876

27 ......... 43,010.612 1,040,680.71 12,699.524 23.1959 82 ......... 2,510.957 17,363.56 2,005.223 5.9151

28 ......... 41,657.785 997,670.10 12,599.433 22.9492 83 ......... 2,231.331 14,852.61 1,798.731 5.6564

29 ......... 40,341.760 956,012.31 12,496.741 22.6978 84 ......... 1,970.456 12,621.27 1,602.846 5.4053

30 ......... 39,060.053 915,670.55 12,390.037 22.4426 85 ......... 1,730.910 10,650.82 1,420.692 5.1533

31 ......... 37,811.985 876,610.50 12,279.640 22.1834 86 ......... 1,512.225 8,919.91 1,252.422 4.8985

32 ......... 36,597.270 838,798.51 12,166.246 21.9197 87 ......... 1,312.605 7,407.68 1,096.847 4.6435

33 ......... 35,414.829 802,201.24 12,049.745 21.6516 88 ......... 1,130.675 6,095.08 953.148 4.3907

34 ......... 34,263.633 766,786.41 11,930.048 21.3790 89 ......... 964.999 4,964.40 820.405 4.1445

35 ......... 33,143.056 732,522.78 11,807.441 21.1018 90 ......... 814.379 3,999.40 697.891 3.9110

36 ......... 32,052.132 699,379.72 11,681.849 20.8201 91 ......... 678.367 3,185.03 585.600 3.6951

37 ......... 30,989.271 667,327.59 11,552.546 20.5341 92 ......... 556.904 2,506.66 483.895 3.5011

38 ......... 29,954.955 636,338.32 11,420.829 20.2432 93 ......... 450.709 1,949.75 393.920 3.3260

39 ......... 28,948.601 606,383.37 11,286.949 19.9469 94 ......... 360.354 1,499.05 316.692 3.1599

40 ......... 27,969.940 577,434.77 11,151.451 19.6448 95 ......... 285.255 1,138.69 252.089 2.9918

41 ......... 27,017.777 549,464.83 11,013.947 19.3372 96 ......... 223.258 853.44 198.400 2.8227

42 ......... 26,091.284 522,447.05 10,874.380 19.0238 97 ......... 172.125 630.18 153.770 2.6612

43 ......... 25,188.828 496,355.76 10,731.864 18.7054 95 ......... 130.646 458.05 117.305 2.5061

44 ......... 24,309.999 471,166.94 10,586.690 18.3816 99 ......... 97.557 327.41 88.021 2.3561

45 ......... 23,452.797 446,856.94 10,437.546 18.0535 100 ......... 71.581 229.85 64.886 2.2111

46 ......... 22,616.434 423,404.14 10,284.275 17.7211 101 ......... 51.536 158.27 46.926 2.0711

47 ......... 21,799.175 400,787.71 10,125.746 17.3855 102 ......... 36.354 106.73 33.246 1.9360

48 ......... 20,999.930 378,988.53 9,961.429 17.0471 103 ......... 25.086 70.38 23.036 1.8056

49 ......... 20,218.412 357,988.60 9,791.560 16.7061 104 ......... 16.901 45.29 15.582 1.6800

50 ......... 19,454.112 337,770.19 9,616.146 16.3624 105 ......... 11.096 28.39 10.269 1.5590

51 ......... 18,706.331 318,316.08 9,434.989 16.0165 106 ......... 7.082 17.30 6.578 1.4425

52 ......... 17,974.425 299,609.75 9,247.928 15.6687 107 ......... 4.384 10.22 4.086 1.3305

53 ......... 17,257.595 281,635.32 9,054.625 15.3195 108 ......... 2.624 5.83 2.454 1.2228

54 ......... 16,555.114 264,377.73 8,854.792 14.9696 109 ......... 1.514 3.21 1.420 1.1193

x x x x x x x x

114
Table 10.D. -- Actuarial Functions at 4.0 Percent Interest for 1989-91 United States 

Total Black Population

x D N M a x D N M a

0 ......... 100,000.000 2,339,335.38 10,025.562 22.3934 55 ......... 9,325.882 131,488.36 4,268.638 13.0993

1 ......... 94,410.577 2,239,335.38 8,282.293 22.7191 56 ......... 8,843.087 122,162.48 4,144.530 12.8145

2 ......... 90,666.605 2,144,924.80 8,169.497 22.6573 57 ......... 8,376.470 113,319.39 4,018.032 12.5283

3 ......... 87,111.864 2,054,258.20 8,101.933 22.5818 58 ......... 7,925.160 104,942.92 3,888.894 12.2417

4 ......... 83,711.829 1,967,146.33 8,052.355 22.4990 59 ......... 7,488.562 97,017.76 3,757.109 11.9555

5 ......... 80,453.513 1,883,434.51 8,013.724 22.4102 60 ......... 7,066.315 89,529.20 3,622.884 11.6699

6 ......... 77,326.744 1,802,980.99 7,981.321 22.3164 61 ......... 6,658.524 82,462.89 3,486.875 11.3846

7 ......... 74,324.522 1,725,654.25 7,953.204 22.2178 62 ......... 6,265.409 75,804.36 3,349.856 11.0989

8 ......... 71,441.773 1,651,329.73 7,929.092 22.1143 63 ......... 5,886.514 69,538.95 3,211.939 10.8133

9 ......... 68,674.340 1,579,887.95 7,909.419 22.0055 64 ......... 5,520.996 63,652.44 3,072.825 10.5292

10 ......... 66,016.131 1,511,213.61 7,892.530 21.8916 65 ......... 5,168.792 58,131.44 2,932.967 10.2466

11 ......... 63,463.407 1,445,197.48 7,878.889 21.7721 66 ......... 4,829.654 52,962.65 2,792.629 9.9661

12 ......... 61,008.766 1,381,734.07 7,865.148 21.6481 67 ......... 4,503.973 48,133.00 2,652.704 9.6868

13 ......... 58,644.258 1,320,725.31 7,847.131 21.5210 68 ......... 4,192.032 43,629.03 2,513.993 9.4076

14 ......... 56,363.301 1,262,081.05 7,821.722 21.3919 69 ......... 3,893.684 39,436.99 2,376.876 9.1285

15 ......... 54,159.944 1,205,717.75 7,786.185 21.2622 70 ......... 3,608.617 35,543.31 2,241.566 8.8496

16 ......... 52,030.953 1,151,557.81 7,740.269 21.1322 71 ......... 3,336.136 31,934.69 2,107.879 8.5724

17 ......... 49,974.319 1,099,526.85 7,684.824 21.0018 72 ......... 3,075.774 28,598.56 1,975.830 8.2980

18 ......... 47,990.526 1,049,552.53 7,623.121 20.8700 73 ......... 2,827.423 25,522.78 1,845.777 8.0269

19 ......... 46,077.812 1,001,562.01 7,556.196 20.7363 74 ......... 2,591.539 22,695.36 1,718.640 7.7575

20 ......... 44,235.305 955,484.20 7,485.913 20.6000 75 ......... 2,368.509 20,103.82 1,595.285 7.4880

21 ......... 42,460.662 911,248.89 7,412.627 20.4610 76 ......... 2,158.598 17,735.31 1,476.471 7.2161

22 ......... 40,750.763 868,788.23 7,335.832 20.3196 77 ......... 1,961.526 15,576.71 1,362.422 6.9411

23 ......... 39,105.121 828,037.47 7,257.526 20.1747 78 ......... 1,776.467 13,615.19 1,252.806 6.6642

24 ......... 37,522.274 788,932.34 7,178.722 20.0257 79 ......... 1,602.336 11,838.72 1,147.000 6.3884

25 ......... 36,000.710 751,410.07 7,100.322 19.8721 80 ......... 1,438.147 10,236.39 1,044.440 6.1178

26 ......... 34,539.240 715,409.36 7,023.496 19.7129 81 ......... 1,283.008 8,798.24 944.614 5.8575

27 ......... 33,134.508 680,870.12 6,947.196 19.5487 82 ......... 1,136.993 7,515.23 847.946 5.6097

28 ......... 31,783.738 647,735.61 6,870.830 19.3795 83 ......... 1,000.660 6,378.24 755.343 5.3740

29 ......... 30,483.689 615,951.88 6,793.232 19.2059 84 ......... 875.171 5,377.58 668.341 5.1446

30 ......... 29,231.385 585,468.19 6,713.377 19.0288 85 ......... 761.386 4,502.41 588.216 4.9134

31 ......... 28,025.278 556,236.80 6,631.554 18.8477 86 ......... 658.795 3,741.02 514.910 4.6786

32 ......... 26,864.145 528,211.52 6,548.317 18.6623 87 ......... 566.333 3,082.22 447.786 4.4424

33 ......... 25,746.214 501,347.38 6,463.622 18.4727 88 ......... 483.147 2,515.89 386.382 4.2073

34 ......... 24,669.793 475,601.17 6,377.441 18.2787 89 ......... 408.388 2,032.74 330.205 3.9775

35 ......... 23,633.527 450,931.37 6,290.012 18.0802 90 ......... 341.331 1,624.36 278.856 3.7589

36 ......... 22,635.850 427,297.85 6,201.317 17.8770 91 ......... 281.591 1,283.02 232.244 3.5563

37 ......... 21,674.801 404,662.00 6,110.878 17.6697 92 ......... 228.949 1,001.43 190.432 3.3741

38 ......... 20,749.915 382,987.19 6,019.638 17.4573 93 ......... 183.509 772.48 153.798 3.2095

39 ......... 19,859.994 362,237.28 5,927.791 17.2395 94 ......... 145.310 588.98 122.657 3.0533

40 ......... 19,004.084 342,377.29 5,835.727 17.0160 95 ......... 113.921 443.67 96.856 2.8945

41 ......... 18,180.629 323,373.20 5,743.199 16.7867 96 ......... 88.304 329.75 75.621 2.7342

42 ......... 17,388.361 305,192.57 5,650.185 16.5515 97 ......... 67.425 241.44 58.139 2.5809

43 ......... 16,625.512 287,804.21 5,556.119 16.3110 95 ......... 50.685 174.02 43.992 2.4333

44 ......... 15,891.171 271,178.70 5,461.221 16.0647 99 ......... 37.484 123.33 32.740 2.2903

45 ......... 15,183.416 255,287.53 5,364.665 15.8136 100 ......... 27.239 85.85 23.937 2.1517

46 ......... 14,501.164 240,104.11 5,266.390 15.5576 101 ......... 19.422 58.61 17.168 2.0176

47 ......... 13,842.759 225,602.95 5,165.723 15.2975 102 ......... 13.569 39.19 12.062 1.8880

48 ......... 13,207.005 211,760.19 5,062.382 15.0339 103 ......... 9.273 25.62 8.288 1.7627

49 ......... 12,593.239 198,553.18 4,956.578 14.7666 104 ......... 6.188 16.35 5.559 1.6416

50 ......... 12,000.675 185,959.95 4,848.370 14.4958 105 ......... 4.023 10.16 3.632 1.5249

51 ......... 11,428.435 173,959.27 4,737.694 14.2216 106 ......... 2.543 6.13 2.307 1.4122

52 ......... 10,875.696 162,530.84 4,624.510 13.9444 107 ......... 1.559 3.59 1.421 1.3037

53 ......... 10,341.564 151,655.14 4,508.674 13.6646 108 ......... 0.924 2.03 0.846 1.1992

54 ......... 9,825.213 141,313.58 4,390.076 13.3827 109 ......... 0.528 1.11 0.485 1.0987

x x x x x x x x

115
Table 10.E. -- Actuarial Functions at 5.0 Percent Interest for 1989-91 United States 

Total Black Population

x D N M a x D N M a

0 ......... 100,000.000 1,957,053.07 6,806.997 18.5705 55 ......... 5,509.499 70,670.33 2,144.246 11.8270

1 ......... 93,511.429 1,857,053.07 5,080.330 18.8591 56 ......... 5,174.521 65,160.83 2,071.624 11.5926

2 ......... 88,947.846 1,763,541.64 4,969.672 18.8267 57 ......... 4,854.800 59,986.31 1,998.309 11.3561

3 ......... 84,646.582 1,674,593.80 4,904.021 18.7834 58 ......... 4,549.486 55,131.51 1,924.176 11.1182

4 ......... 80,568.076 1,589,947.21 4,856.304 18.7342 59 ......... 4,257.913 50,582.02 1,849.245 10.8795

5 ......... 76,694.675 1,509,379.14 4,819.478 18.6804 60 ......... 3,979.563 46,324.11 1,773.653 10.6405

6 ......... 73,011.953 1,432,684.46 4,788.883 18.6226 61 ......... 3,714.193 42,344.55 1,697.786 10.4007

7 ......... 69,508.898 1,359,672.51 4,762.588 18.5611 62 ......... 3,461.624 38,630.35 1,622.083 10.1596

8 ......... 66,176.615 1,290,163.61 4,740.253 18.4958 63 ......... 3,221.311 35,168.73 1,546.610 9.9175

9 ......... 63,007.299 1,223,987.00 4,722.203 18.4261 64 ......... 2,992.512 31,947.42 1,471.207 9.6758

10 ......... 59,991.603 1,160,979.70 4,706.856 18.3524 65 ......... 2,774.928 28,954.91 1,396.123 9.4345

11 ......... 57,122.582 1,100,988.09 4,694.577 18.2741 66 ......... 2,568.163 26,179.98 1,321.498 9.1940

12 ......... 54,390.208 1,043,865.51 4,682.327 18.1922 67 ......... 2,372.174 23,611.82 1,247.801 8.9537

13 ......... 51,784.289 989,475.30 4,666.417 18.1076 68 ......... 2,186.852 21,239.64 1,175.440 8.7124

14 ......... 49,296.147 937,691.01 4,644.194 18.0216 69 ......... 2,011.868 19,052.79 1,104.592 8.4702

15 ......... 46,917.927 888,394.87 4,613.409 17.9351 70 ......... 1,846.816 17,040.92 1,035.343 8.2272

16 ......... 44,644.342 841,476.94 4,574.012 17.8485 71 ......... 1,691.105 15,194.11 967.576 7.9847

17 ......... 42,471.301 796,832.60 4,526.892 17.7617 72 ......... 1,544.278 13,503.00 901.278 7.7439

18 ......... 40,396.918 754,361.30 4,474.952 17.6737 73 ......... 1,406.066 11,958.72 836.603 7.5051

19 ......... 38,417.457 713,964.38 4,419.153 17.5844 74 ......... 1,276.488 10,552.66 773.980 7.2669

20 ......... 36,530.013 675,546.92 4,361.112 17.4929 75 ......... 1,155.521 9,276.17 713.799 7.0277

21 ......... 34,730.545 639,016.91 4,301.169 17.3993 76 ......... 1,043.083 8,120.65 656.385 6.7852

22 ......... 33,014.493 604,286.36 4,238.952 17.3037 77 ......... 938.826 7,077.57 601.799 6.5387

23 ......... 31,379.539 571,271.87 4,176.117 17.2052 78 ......... 842.156 6,138.74 549.835 6.2893

24 ......... 29,822.642 539,892.33 4,113.483 17.1034 79 ......... 752.372 5,296.58 500.154 6.0398

25 ......... 28,340.798 510,069.69 4,051.765 16.9977 80 ......... 668.847 4,544.21 452.456 5.7941

26 ......... 26,931.332 481,728.89 3,991.860 16.8873 81 ......... 591.012 3,875.37 406.471 5.5572

27 ......... 25,589.961 454,797.56 3,932.934 16.7725 82 ......... 518.763 3,284.35 362.366 5.3311

28 ......... 24,312.975 429,207.60 3,874.517 16.6534 83 ......... 452.212 2,765.59 320.517 5.1157

29 ......... 23,096.421 404,894.63 3,815.724 16.5306 84 ......... 391.735 2,313.38 281.574 4.9055

30 ......... 21,936.665 381,798.21 3,755.798 16.4046 85 ......... 337.558 1,921.64 246.051 4.6928

31 ......... 20,831.242 359,861.54 3,694.978 16.2751 86 ......... 289.293 1,584.09 213.860 4.4757

32 ......... 19,777.997 339,030.30 3,633.697 16.1418 87 ......... 246.322 1,294.79 184.665 4.2565

33 ......... 18,774.427 319,252.30 3,571.937 16.0046 88 ......... 208.140 1,048.47 158.213 4.0373

34 ......... 17,818.161 300,477.87 3,509.691 15.8636 89 ......... 174.258 840.33 134.242 3.8223

35 ......... 16,907.132 282,659.71 3,447.146 15.7184 90 ......... 144.258 666.07 112.540 3.6172

36 ......... 16,039.183 265,752.58 3,384.298 15.5690 91 ......... 117.876 521.81 93.028 3.4268

37 ......... 15,211.940 249,713.40 3,320.826 15.4156 92 ......... 94.927 403.94 75.692 3.2552

38 ......... 14,424.137 234,501.46 3,257.401 15.2576 93 ......... 75.362 309.01 60.647 3.1004

39 ......... 13,674.035 220,077.32 3,194.162 15.0945 94 ......... 59.106 233.65 47.980 2.9530

40 ......... 12,960.106 206,403.29 3,131.378 14.9260 95 ......... 45.897 174.54 37.586 2.8029

41 ......... 12,280.458 193,443.18 3,068.878 14.7521 96 ......... 35.238 128.65 29.112 2.6508

42 ......... 11,633.445 181,162.72 3,006.649 14.5726 97 ......... 26.650 93.41 22.202 2.5050

43 ......... 11,017.137 169,529.28 2,944.315 14.3878 95 ......... 19.842 66.76 16.663 2.3644

44 ......... 10,430.225 158,512.14 2,882.028 14.1974 99 ......... 14.535 46.92 12.301 2.2278

45 ......... 9,870.776 148,081.91 2,819.256 14.0021 100 ......... 10.461 32.38 8.919 2.0953

46 ......... 9,337.459 138,211.14 2,755.976 13.8018 101 ......... 7.388 21.92 6.345 1.9668

47 ......... 8,828.614 128,873.68 2,691.773 13.5973 102 ......... 5.113 14.53 4.421 1.8422

48 ......... 8,342.924 120,045.06 2,626.492 13.3888 103 ......... 3.461 9.42 3.012 1.7216

49 ......... 7,879.441 111,702.14 2,560.291 13.1764 104 ......... 2.287 5.96 2.003 1.6049

50 ......... 7,437.170 103,822.70 2,493.232 12.9600 105 ......... 1.473 3.67 1.298 1.4921

51 ......... 7,015.083 96,385.53 2,425.296 12.7398 106 ......... 0.922 2.20 0.818 1.3832

52 ......... 6,612.218 89,370.45 2,356.482 12.5160 107 ......... 0.560 1.28 0.499 1.2780

53 ......... 6,227.595 82,758.23 2,286.727 12.2890 108 ......... 0.329 0.72 0.295 1.1765

54 ......... 5,860.304 76,530.63 2,215.988 12.0592 109 ......... 0.186 0.39 0.168 1.0788

x x x x x x x x

116
Table 10.F. -- Actuarial Functions at 6.0 Percent Interest for 1989-91 United States 

Total Black Population

x D N M a x D N M a

0 ......... 100,000.000 1,678,233.22 5,005.667 15.7823 55 ......... 3,271.154 38,443.14 1,095.127 10.7522

1 ......... 92,629.245 1,578,233.22 3,295.290 16.0382 56 ......... 3,043.284 35,171.99 1,052.417 10.5572

2 ......... 87,277.501 1,485,603.97 3,186.710 16.0216 57 ......... 2,828.310 32,128.70 1,009.705 10.3597

3 ......... 82,273.454 1,398,326.47 3,122.899 15.9961 58 ......... 2,625.437 29,300.39 966.924 10.1602

4 ......... 77,570.525 1,316,053.02 3,076.958 15.9659 59 ......... 2,433.993 26,674.96 924.090 9.9593

5 ......... 73,144.619 1,238,482.49 3,041.836 15.9320 60 ......... 2,253.416 24,240.96 881.286 9.7574

6 ......... 68,975.454 1,165,337.87 3,012.933 15.8950 61 ......... 2,083.310 21,987.55 838.732 9.5541

7 ......... 65,046.576 1,096,362.42 2,988.326 15.8550 62 ......... 1,923.325 19,904.24 796.671 9.3489

8 ......... 61,343.990 1,031,315.84 2,967.621 15.8120 63 ......... 1,772.920 17,980.91 755.132 9.1420

9 ......... 57,855.115 969,971.85 2,951.048 15.7655 64 ......... 1,631.457 16,207.99 714.024 8.9347

10 ......... 54,566.338 912,116.74 2,937.088 15.7157 65 ......... 1,498.563 14,576.54 673.476 8.7270

11 ......... 51,466.614 857,550.40 2,926.026 15.6623 66 ......... 1,373.818 13,077.97 633.556 8.5194

12 ......... 48,542.477 806,083.78 2,915.092 15.6057 67 ......... 1,257.004 11,704.15 594.504 8.3112

13 ......... 45,780.724 757,541.31 2,901.027 15.5472 68 ......... 1,147.870 10,447.15 556.522 8.1013

14 ......... 43,169.901 711,760.58 2,881.566 15.4874 69 ......... 1,046.060 9,299.28 519.685 7.8898

15 ......... 40,699.617 668,590.68 2,854.861 15.4274 70 ......... 951.183 8,253.22 484.019 7.6768

16 ......... 38,362.011 627,891.07 2,821.008 15.3675 71 ......... 862.769 7,302.04 449.446 7.4635

17 ......... 36,150.469 589,529.05 2,780.900 15.3076 72 ......... 780.428 6,439.27 415.941 7.2510

18 ......... 34,060.423 553,378.59 2,737.107 15.2470 73 ......... 703.876 5,658.84 383.564 7.0395

19 ......... 32,085.873 519,318.16 2,690.505 15.1853 74 ......... 632.981 4,954.97 352.511 6.8280

20 ......... 30,221.673 487,232.29 2,642.487 15.1219 75 ......... 567.591 4,321.98 322.950 6.6146

21 ......... 28,461.888 457,010.62 2,593.363 15.0569 76 ......... 507.528 3,754.39 295.015 6.3974

22 ......... 26,800.332 428,548.73 2,542.857 14.9904 77 ......... 452.491 3,246.87 268.706 6.1755

23 ......... 25,232.805 401,748.40 2,492.330 14.9217 78 ......... 402.069 2,794.38 243.896 5.9500

24 ......... 23,754.644 376,515.59 2,442.441 14.8502 79 ......... 355.815 2,392.31 220.401 5.7235

25 ......... 22,361.345 352,760.95 2,393.744 14.7755 80 ......... 313.329 2,036.49 198.056 5.4995

26 ......... 21,048.789 330,399.60 2,346.924 14.6968 81 ......... 274.255 1,723.16 176.718 5.2831

27 ......... 19,811.727 309,350.81 2,301.303 14.6145 82 ......... 238.457 1,448.91 156.444 5.0762

28 ......... 18,645.509 289,539.09 2,256.504 14.5286 83 ......... 205.905 1,210.45 137.389 4.8787

29 ......... 17,545.440 270,893.58 2,211.841 14.4395 84 ......... 176.686 1,004.54 119.824 4.6855

30 ......... 16,507.207 253,348.14 2,166.747 14.3477 85 ......... 150.813 827.86 103.953 4.4893

31 ......... 15,527.503 236,840.93 2,121.412 14.2530 86 ......... 128.030 677.05 89.707 4.2882

32 ......... 14,603.340 221,313.43 2,076.165 14.1550 87 ......... 107.985 549.02 76.908 4.0842

33 ......... 13,731.564 206,710.09 2,030.993 14.0536 88 ......... 90.385 441.03 65.421 3.8795

34 ......... 12,909.209 192,978.52 1,985.896 13.9489 89 ......... 74.958 350.65 55.110 3.6779

35 ......... 12,133.613 180,069.31 1,941.010 13.8405 90 ......... 61.468 275.69 45.863 3.4851

36 ......... 11,402.127 167,935.70 1,896.332 13.7285 91 ......... 49.753 214.22 37.627 3.3057

37 ......... 10,712.027 156,533.57 1,851.636 13.6129 92 ......... 39.689 164.47 30.379 3.1439

38 ......... 10,061.444 145,821.55 1,807.394 13.4931 93 ......... 31.211 124.78 24.148 2.9978

39 ......... 9,448.233 135,760.10 1,763.699 13.3688 94 ......... 24.248 93.57 18.952 2.8587

40 ......... 8,870.455 126,311.87 1,720.727 13.2396 95 ......... 18.651 69.32 14.728 2.7165

41 ......... 8,325.980 117,441.42 1,678.352 13.1054 96 ......... 14.185 50.67 11.317 2.5720

42 ......... 7,812.905 109,115.44 1,636.560 12.9661 97 ......... 10.626 36.48 8.561 2.4332

43 ......... 7,329.197 101,302.53 1,595.092 12.8218 95 ......... 7.837 25.86 6.374 2.2991

44 ......... 6,873.291 93,973.33 1,554.046 12.6722 99 ......... 5.687 18.02 4.667 2.1685

45 ......... 6,443.262 87,100.04 1,513.071 12.5180 100 ......... 4.054 12.33 3.356 2.0416

46 ......... 6,037.632 80,656.78 1,472.154 12.3590 101 ......... 2.836 8.28 2.368 1.9182

47 ......... 5,654.757 74,619.15 1,431.032 12.1958 102 ......... 1.944 5.44 1.636 1.7985

48 ......... 5,293.258 68,964.39 1,389.614 12.0287 103 ......... 1.304 3.50 1.106 1.6823

49 ......... 4,952.035 63,671.13 1,348.008 11.8576 104 ......... 0.853 2.19 0.729 1.5698

50 ......... 4,629.983 58,719.10 1,306.260 11.6824 105 ......... 0.544 1.34 0.469 1.4607

51 ......... 4,326.014 54,089.11 1,264.366 11.5032 106 ......... 0.338 0.80 0.293 1.3552

52 ......... 4,039.110 49,763.10 1,222.331 11.3203 107 ......... 0.203 0.46 0.177 1.2532

53 ......... 3,768.273 45,723.99 1,180.122 11.1339 108 ......... 0.118 0.25 0.104 1.1547

54 ......... 3,512.575 41,955.72 1,137.723 10.9444 109 ......... 0.066 0.14 0.059 1.0595

x x x x x x x x

117
Table 10.G. -- Actuarial Functions at 7.0 Percent Interest for 1989-91 United States 

Total Black Population

x D N M a x D N M a

0 ......... 100,000.000 1,468,168.13 3,951.618 13.6817 55 ......... 1,951.712 21,149.14 568.124 9.8362

1 ......... 91,763.551 1,368,168.13 2,257.225 13.9097 56 ......... 1,798.785 19,197.42 542.879 9.6724

2 ......... 85,653.769 1,276,404.58 2,150.666 13.9019 57 ......... 1,656.098 17,398.64 517.869 9.5058

3 ......... 79,988.213 1,190,750.81 2,088.627 13.8866 58 ......... 1,522.939 15,742.54 493.054 9.3369

4 ......... 74,711.091 1,110,762.60 2,044.379 13.8674 59 ......... 1,398.693 14,219.60 468.439 9.1663

5 ......... 69,789.939 1,036,051.51 2,010.869 13.8453 60 ......... 1,282.823 12,820.91 444.072 8.9943

6 ......... 65,196.922 966,261.57 1,983.549 13.8207 61 ......... 1,174.901 11,538.08 420.073 8.8205

7 ......... 60,908.661 901,064.64 1,960.507 13.7937 62 ......... 1,074.539 10,363.18 396.574 8.6443

8 ......... 56,904.776 840,155.98 1,941.301 13.7642 63 ......... 981.252 9,288.64 373.584 8.4661

9 ......... 53,166.804 783,251.21 1,926.070 13.7320 64 ......... 894.519 8,307.39 351.044 8.2870

10 ......... 49,675.893 730,084.40 1,913.362 13.6970 65 ......... 813.974 7,412.87 329.020 8.1070

11 ......... 46,416.091 680,408.51 1,903.385 13.6589 66 ......... 739.243 6,598.90 307.539 7.9266

12 ......... 43,369.756 633,992.42 1,893.617 13.6183 67 ......... 670.064 5,859.66 286.722 7.7449

13 ......... 40,520.033 590,622.66 1,881.168 13.5761 68 ......... 606.170 5,189.59 266.664 7.5613

14 ......... 37,852.126 550,102.63 1,864.104 13.5329 69 ......... 547.243 4,583.42 247.393 7.3755

15 ......... 35,352.622 512,250.50 1,840.907 13.4897 70 ......... 492.958 4,036.18 228.909 7.1877

16 ......... 33,010.703 476,897.88 1,811.776 13.4468 71 ......... 442.958 3,543.22 211.159 6.9990

17 ......... 30,816.934 443,887.18 1,777.586 13.4040 72 ......... 396.938 3,100.26 194.117 6.8104

18 ......... 28,763.890 413,070.24 1,740.603 13.3607 73 ......... 354.657 2,703.32 177.804 6.6224

19 ......... 26,843.152 384,306.36 1,701.615 13.3167 74 ......... 315.955 2,348.67 162.304 6.4336

20 ......... 25,047.262 357,463.20 1,661.819 13.2715 75 ......... 280.667 2,032.71 147.686 6.2424

21 ......... 23,368.323 332,415.94 1,621.486 13.2251 76 ......... 248.621 1,752.04 134.002 6.0470

22 ......... 21,798.475 309,047.62 1,580.406 13.1775 77 ......... 219.589 1,503.42 121.234 5.8465

23 ......... 20,331.693 287,249.14 1,539.693 13.1281 78 ......... 193.296 1,283.83 109.307 5.6418

24 ......... 18,961.759 266,917.45 1,499.870 13.0766 79 ......... 169.461 1,090.54 98.117 5.4353

25 ......... 17,682.762 247,955.69 1,461.362 13.0225 80 ......... 147.832 921.08 87.574 5.2306

26 ......... 16,489.268 230,272.93 1,424.684 12.9650 81 ......... 128.187 773.25 77.601 5.0322

27 ......... 15,375.126 213,783.66 1,389.279 12.9045 82 ......... 110.413 645.06 68.213 4.8422

28 ......... 14,334.835 198,408.53 1,354.837 12.8410 83 ......... 94.450 534.65 59.473 4.6606

29 ......... 13,363.026 184,073.70 1,320.821 12.7749 84 ......... 80.289 440.20 51.491 4.4826

30 ......... 12,454.785 170,710.67 1,286.797 12.7064 85 ......... 67.892 359.91 44.347 4.3012

31 ......... 11,606.101 158,255.89 1,252.912 12.6356 86 ......... 57.097 292.02 37.993 4.1144

32 ......... 10,813.319 146,649.79 1,219.407 12.5620 87 ......... 47.707 234.92 32.339 3.9242

33 ......... 10,072.770 135,836.47 1,186.272 12.4855 88 ......... 39.559 187.21 27.311 3.7325

34 ......... 9,381.032 125,763.70 1,153.500 12.4062 89 ......... 32.500 147.65 22.841 3.5431

35 ......... 8,735.006 116,382.67 1,121.186 12.3237 90 ......... 26.402 115.15 18.869 3.3615

36 ......... 8,131.694 107,647.66 1,089.323 12.2380 91 ......... 21.170 88.75 15.364 3.1922

37 ......... 7,568.136 99,515.97 1,057.745 12.1493 92 ......... 16.730 67.58 12.309 3.0394

38 ......... 7,042.059 91,947.83 1,026.780 12.0570 93 ......... 13.034 50.85 9.707 2.9014

39 ......... 6,551.067 84,905.77 996.483 11.9606 94 ......... 10.031 37.82 7.557 2.7699

40 ......... 6,092.975 78,354.71 966.966 11.8598 95 ......... 7.644 27.79 5.826 2.6350

41 ......... 5,665.535 72,261.73 938.132 11.7546 96 ......... 5.759 20.14 4.441 2.4974

42 ......... 5,266.720 66,596.20 909.959 11.6447 97 ......... 4.274 14.38 3.333 2.3651

43 ......... 4,894.476 61,329.48 882.267 11.5303 95 ......... 3.123 10.11 2.461 2.2370

44 ......... 4,547.122 56,435.00 855.113 11.4111 99 ......... 2.245 6.99 1.788 2.1121

45 ......... 4,222.793 51,887.88 828.259 11.2876 100 ......... 1.585 4.74 1.275 1.9904

46 ......... 3,919.970 47,665.09 801.693 11.1596 101 ......... 1.099 3.16 0.892 1.8719

47 ......... 3,637.073 43,745.12 775.243 11.0276 102 ......... 0.746 2.06 0.612 1.7567

48 ......... 3,372.743 40,108.04 748.853 10.8918 103 ......... 0.496 1.31 0.410 1.6447

49 ......... 3,125.834 36,735.30 722.590 10.7522 104 ......... 0.321 0.82 0.268 1.5360

50 ......... 2,895.235 33,609.47 696.485 10.6085 105 ......... 0.203 0.49 0.171 1.4305

51 ......... 2,679.874 30,714.23 670.532 10.4611 106 ......... 0.125 0.29 0.106 1.3283

52 ......... 2,478.759 28,034.36 644.735 10.3098 107 ......... 0.074 0.17 0.064 1.2293

53 ......... 2,290.936 25,555.60 619.075 10.1551 108 ......... 0.043 0.09 0.037 1.1335

54 ......... 2,115.526 23,264.66 593.539 9.9971 109 ......... 0.024 0.05 0.021 1.0409

x x x x x x x x

118
Table 10.H. -- Actuarial Functions at 8.0 Percent Interest for 1989-91 United States 

Total Black Population

x D N M a x D N M a

0 ......... 100,000.000 1,305,370.80 3,305.867 12.0537 55 ......... 1,170.084 11,758.42 299.090 9.0492

1 ......... 90,913.889 1,205,370.80 1,627.163 12.2584 56 ......... 1,068.417 10,588.33 284.096 8.9103

2 ......... 84,074.931 1,114,456.91 1,522.568 12.2555 57 ......... 974.557 9,519.92 269.378 8.7685

3 ......... 77,786.827 1,030,381.98 1,462.236 12.2462 58 ......... 887.900 8,545.36 254.910 8.6242

4 ......... 71,982.209 952,595.15 1,419.605 12.2338 59 ......... 807.912 7,657.46 240.692 8.4781

5 ......... 66,618.206 880,612.94 1,387.617 12.2188 60 ......... 734.122 6,849.55 226.748 8.3303

6 ......... 61,657.687 813,994.74 1,361.780 12.2018 61 ......... 666.136 6,115.43 213.141 8.1805

7 ......... 57,068.862 752,337.05 1,340.191 12.1830 62 ......... 603.592 5,449.29 199.941 8.0281

8 ......... 52,823.710 695,268.19 1,322.362 12.1620 63 ......... 546.087 4,845.70 187.147 7.8735

9 ......... 48,896.835 642,444.48 1,308.355 12.1388 64 ......... 493.209 4,299.61 174.719 7.7176

10 ......... 45,263.268 593,547.64 1,296.775 12.1132 65 ......... 444.644 3,806.40 162.688 7.5606

11 ......... 41,901.426 548,284.38 1,287.769 12.0851 66 ......... 400.082 3,361.76 151.062 7.4027

12 ......... 38,788.881 506,382.95 1,279.032 12.0548 67 ......... 359.284 2,961.68 139.901 7.2433

13 ......... 35,904.599 467,594.07 1,268.001 12.0232 68 ......... 322.015 2,602.39 129.245 7.0816

14 ......... 33,230.019 431,689.47 1,253.021 11.9909 69 ......... 288.020 2,280.38 119.103 6.9174

15 ......... 30,748.361 398,459.45 1,232.846 11.9587 70 ......... 257.046 1,992.36 109.464 6.7510

16 ......... 28,445.602 367,711.09 1,207.743 11.9268 71 ......... 228.836 1,735.31 100.294 6.5832

17 ......... 26,309.331 339,265.49 1,178.554 11.8953 72 ......... 203.163 1,506.48 91.572 6.4151

18 ......... 24,329.211 312,956.16 1,147.273 11.8634 73 ......... 179.842 1,303.31 83.300 6.2470

19 ......... 22,494.375 288,626.95 1,114.602 11.8311 74 ......... 158.733 1,123.47 75.513 6.0777

20 ......... 20,795.085 266,132.57 1,081.561 11.7979 75 ......... 139.699 964.74 68.237 5.9058

21 ......... 19,221.533 245,337.49 1,048.386 11.7637 76 ......... 122.603 825.04 61.489 5.7294

22 ......... 17,764.238 226,115.95 1,014.908 11.7287 77 ......... 107.283 702.44 55.251 5.5475

23 ......... 16,415.498 208,351.72 982.038 11.6924 78 ......... 93.563 595.15 49.478 5.3610

24 ......... 15,167.680 191,936.22 950.182 11.6543 79 ......... 81.266 501.59 44.112 5.1722

25 ......... 14,013.630 176,768.54 919.665 11.6140 80 ......... 70.238 420.32 39.103 4.9843

26 ......... 12,946.786 162,754.91 890.867 11.5711 81 ......... 60.340 350.09 34.408 4.8019

27 ......... 11,960.223 149,808.12 863.326 11.5255 82 ......... 51.492 289.75 30.030 4.6270

28 ......... 11,047.737 137,847.90 836.781 11.4775 83 ......... 43.640 238.25 25.991 4.4596

29 ......... 10,203.413 126,800.16 810.808 11.4272 84 ......... 36.753 194.61 22.338 4.2951

30 ......... 9,421.866 116,596.75 785.069 11.3751 85 ......... 30.791 157.86 19.097 4.1269

31 ......... 8,698.553 107,174.88 759.673 11.3210 86 ......... 25.655 127.07 16.243 3.9530

32 ......... 8,029.337 98,476.33 734.794 11.2646 87 ......... 21.238 101.41 13.725 3.7752

33 ......... 7,410.195 90,446.99 710.418 11.2058 88 ......... 17.447 80.18 11.508 3.5954

34 ......... 6,837.406 83,036.80 686.532 11.1445 89 ......... 14.201 62.73 9.555 3.4172

35 ......... 6,307.597 76,199.39 663.198 11.0806 90 ......... 11.430 48.53 7.835 3.2458

36 ......... 5,817.573 69,891.79 640.403 11.0139 91 ......... 9.080 37.10 6.332 3.0857

37 ......... 5,364.259 64,074.22 618.020 10.9447 92 ......... 7.109 28.02 5.034 2.9412

38 ......... 4,945.162 58,709.96 596.276 10.8722 93 ......... 5.487 20.91 3.938 2.8106

39 ......... 4,557.775 53,764.80 575.197 10.7963 94 ......... 4.184 15.42 3.042 2.6860

40 ......... 4,199.816 49,207.03 554.851 10.7165 95 ......... 3.159 11.24 2.326 2.5579

41 ......... 3,869.028 45,007.21 535.160 10.6327 96 ......... 2.358 8.08 1.759 2.4268

42 ......... 3,563.372 41,138.18 516.099 10.5447 97 ......... 1.734 5.72 1.310 2.3005

43 ......... 3,280.856 37,574.81 497.537 10.4527 95 ......... 1.255 3.99 0.959 2.1781

44 ......... 3,019.796 34,293.95 479.503 10.3564 99 ......... 0.894 2.73 0.691 2.0584

45 ......... 2,778.438 31,274.16 461.834 10.2560 100 ......... 0.625 1.84 0.489 1.9416

46 ......... 2,555.311 28,495.72 444.517 10.1516 101 ......... 0.429 1.21 0.339 1.8277

47 ......... 2,348.946 25,940.41 427.435 10.0434 102 ......... 0.289 0.78 0.231 1.7167

48 ......... 2,158.064 23,591.46 410.548 9.9318 103 ......... 0.190 0.50 0.153 1.6087

49 ......... 1,981.559 21,433.40 393.900 9.8164 104 ......... 0.122 0.31 0.100 1.5036

50 ......... 1,818.381 19,451.84 377.504 9.6973 105 ......... 0.076 0.18 0.063 1.4015

51 ......... 1,667.537 17,633.46 361.355 9.5746 106 ......... 0.047 0.11 0.039 1.3024

52 ......... 1,528.113 15,965.92 345.452 9.4481 107 ......... 0.027 0.06 0.023 1.2063

53 ......... 1,399.246 14,437.81 329.779 9.3183 108 ......... 0.016 0.03 0.013 1.1132

54 ......... 1,280.146 13,038.56 314.327 9.1852 109 ......... 0.009 0.02 0.007 1.0230

x x x x x x x x

119
Table 10.I. -- Actuarial Functions at 9.0 Percent Interest for 1989-91 United States 

Total Black Population

x D N M a x D N M a

0 ......... 100,000.000 1,176,091.73 2,891.509 10.7609 55 ......... 704.801 6,602.47 159.642 8.3679

1 ......... 90,079.817 1,076,091.73 1,228.206 10.9460 56 ......... 637.657 5,897.67 150.693 8.2490

2 ......... 82,539.349 986,011.91 1,125.521 10.9460 57 ......... 576.303 5,260.02 141.990 8.1272

3 ......... 75,665.487 903,472.56 1,066.835 10.9404 58 ......... 520.241 4,683.71 133.513 8.0030

4 ......... 69,376.789 827,807.07 1,025.747 10.9320 59 ......... 469.032 4,163.47 125.259 7.8767

5 ......... 63,617.884 758,430.28 995.200 10.9217 60 ......... 422.283 3,694.44 117.237 7.7487

6 ......... 58,340.584 694,812.40 970.753 10.9096 61 ......... 379.660 3,272.16 109.482 7.6186

7 ......... 53,503.231 636,471.82 950.513 10.8960 62 ......... 340.858 2,892.50 102.028 7.4859

8 ......... 49,068.972 582,968.58 933.951 10.8806 63 ......... 305.555 2,551.64 94.869 7.3508

9 ......... 45,004.513 533,899.61 921.059 10.8632 64 ......... 273.436 2,246.08 87.979 7.2143

10 ......... 41,277.984 488,895.10 910.499 10.8440 65 ......... 244.250 1,972.65 81.370 7.0764

11 ......... 37,861.572 447,617.12 902.361 10.8225 66 ......... 217.755 1,728.40 75.043 6.9374

12 ......... 34,727.565 409,755.54 894.539 10.7991 67 ......... 193.756 1,510.64 69.024 6.7966

13 ......... 31,850.366 375,027.98 884.753 10.7747 68 ......... 172.064 1,316.89 63.330 6.6535

14 ......... 29,207.353 343,177.61 871.587 10.7497 69 ......... 152.487 1,144.82 57.960 6.5077

15 ......... 26,778.166 313,970.26 854.016 10.7249 70 ......... 134.840 992.34 52.904 6.3594

16 ......... 24,545.464 287,192.09 832.355 10.7004 71 ......... 118.940 857.50 48.138 6.2095

17 ......... 22,493.818 262,646.63 807.399 10.6764 72 ......... 104.628 738.56 43.646 6.0589

18 ......... 20,610.031 240,152.81 780.900 10.6522 73 ......... 91.768 633.93 39.425 5.9080

19 ......... 18,880.863 219,542.78 753.477 10.6278 74 ......... 80.253 542.16 35.488 5.7556

20 ......... 17,294.414 200,661.92 725.999 10.6027 75 ......... 69.982 461.91 31.843 5.6003

21 ......... 15,839.097 183,367.50 698.661 10.5769 76 ......... 60.854 391.93 28.494 5.4404

22 ......... 14,503.949 167,528.41 671.328 10.5505 77 ......... 52.762 331.07 25.426 5.2748

23 ......... 13,279.783 153,024.46 644.736 10.5231 78 ......... 45.592 278.31 22.613 5.1043

24 ......... 12,157.754 139,744.67 619.203 10.4943 79 ......... 39.237 232.72 20.022 4.9311

25 ......... 11,129.665 127,586.92 594.965 10.4637 80 ......... 33.601 193.48 17.625 4.7582

26 ......... 10,188.040 116,457.25 572.304 10.4308 81 ......... 28.601 159.88 15.400 4.5899

27 ......... 9,325.352 106,269.21 550.830 10.3957 82 ......... 24.183 131.28 13.344 4.4284

28 ......... 8,534.862 96,943.86 530.323 10.3586 83 ......... 20.307 107.09 11.465 4.2737

29 ......... 7,810.268 88,409.00 510.442 10.3196 84 ......... 16.946 86.79 9.780 4.1214

30 ......... 7,145.862 80,598.73 490.921 10.2791 85 ......... 14.067 69.84 8.300 3.9650

31 ......... 6,536.752 73,452.87 471.836 10.2369 86 ......... 11.613 55.77 7.008 3.8028

32 ......... 5,978.496 66,916.12 453.312 10.1928 87 ......... 9.525 44.16 5.879 3.6363

33 ......... 5,466.875 60,937.62 435.328 10.1467 88 ......... 7.753 34.64 4.893 3.4674

34 ......... 4,998.021 55,470.75 417.868 10.0985 89 ......... 6.253 26.88 4.033 3.2993

35 ......... 4,568.441 50,472.73 400.968 10.0481 90 ......... 4.986 20.63 3.283 3.1373

36 ......... 4,174.871 45,904.29 384.609 9.9954 91 ......... 3.925 15.64 2.633 2.9857

37 ......... 3,814.242 41,729.41 368.694 9.9404 92 ......... 3.045 11.72 2.077 2.8487

38 ......... 3,483.985 37,915.17 353.375 9.8827 93 ......... 2.329 8.67 1.612 2.7250

39 ......... 3,181.603 34,431.19 338.661 9.8220 94 ......... 1.759 6.35 1.235 2.6068

40 ......... 2,904.829 31,249.58 324.588 9.7578 95 ......... 1.316 4.59 0.937 2.4849

41 ......... 2,651.486 28,344.75 311.094 9.6901 96 ......... 0.973 3.27 0.703 2.3599

42 ......... 2,419.613 25,693.27 298.151 9.6187 97 ......... 0.709 2.30 0.519 2.2392

43 ......... 2,207.340 23,273.66 285.662 9.5438 95 ......... 0.509 1.59 0.377 2.1220

44 ......... 2,013.061 21,066.32 273.640 9.4648 99 ......... 0.359 1.08 0.270 2.0072

45 ......... 1,835.174 19,053.25 261.970 9.3823 100 ......... 0.249 0.72 0.189 1.8950

46 ......... 1,672.313 17,218.08 250.637 9.2960 101 ......... 0.169 0.47 0.130 1.7854

47 ......... 1,523.155 15,545.77 239.560 9.2063 102 ......... 0.113 0.30 0.088 1.6785

48 ......... 1,386.541 14,022.61 228.711 9.1134 103 ......... 0.074 0.19 0.058 1.5741

49 ......... 1,261.458 12,636.07 218.112 9.0170 104 ......... 0.047 0.12 0.037 1.4725

50 ......... 1,146.959 11,374.61 207.770 8.9172 105 ......... 0.029 0.07 0.023 1.3736

51 ......... 1,042.163 10,227.65 197.678 8.8139 106 ......... 0.018 0.04 0.014 1.2775

52 ......... 946.265 9,185.49 187.830 8.7071 107 ......... 0.010 0.02 0.008 1.1841

53 ......... 858.517 8,239.23 178.214 8.5970 108 ......... 0.006 0.01 0.005 1.0935

54 ......... 778.236 7,380.71 168.820 8.4839 109 ......... 0.003 0.01 0.003 1.0056

x x x x x x x x

120
Table 10.J. -- Actuarial Functions at 10.0 Percent Interest for 1989-91 United States 

Total Black Population

x D N M a x D N M a

0 ......... 100,000.000 1,071,254.39 2,613.237 9.7125 55 ......... 426.507 3,742.07 86.319 7.7738

1 ......... 89,260.909 971,254.39 965.055 9.8811 56 ......... 382.367 3,315.56 80.952 7.6711

2 ......... 81,045.455 881,993.48 864.229 9.8827 57 ......... 342.435 2,933.20 75.781 7.5657

3 ......... 73,620.586 800,948.03 807.129 9.8794 58 ......... 306.313 2,590.76 70.790 7.4579

4 ......... 66,888.191 727,327.44 767.514 9.8738 59 ......... 273.651 2,284.45 65.974 7.3480

5 ......... 60,778.263 660,439.25 738.331 9.8664 60 ......... 244.136 2,010.80 61.337 7.2364

6 ......... 55,229.823 599,660.99 715.187 9.8576 61 ......... 217.499 1,766.66 56.894 7.1226

7 ......... 50,189.943 544,431.17 696.201 9.8474 62 ......... 193.495 1,549.16 52.662 7.0062

8 ......... 45,611.826 494,241.22 680.806 9.8358 63 ......... 171.878 1,355.67 48.635 6.8874

9 ......... 41,453.422 448,629.40 668.931 9.8225 64 ......... 152.412 1,183.79 44.795 6.7670

10 ......... 37,675.290 407,175.98 659.292 9.8075 65 ......... 134.906 1,031.38 41.145 6.6451

11 ......... 34,242.903 369,500.69 651.932 9.7906 66 ......... 119.179 896.47 37.682 6.5220

12 ......... 31,122.902 335,257.78 644.922 9.7721 67 ......... 105.080 777.29 34.417 6.3971

13 ......... 28,284.858 304,134.88 636.232 9.7526 68 ......... 92.467 672.21 31.357 6.2697

14 ......... 25,701.920 275,850.02 624.646 9.7327 69 ......... 81.202 579.74 28.498 6.1395

15 ......... 23,350.061 250,148.10 609.325 9.7130 70 ......... 71.152 498.54 25.830 6.0067

16 ......... 21,208.612 226,798.04 590.608 9.6937 71 ......... 62.191 427.39 23.338 5.8722

17 ......... 19,259.189 205,589.43 569.241 9.6749 72 ......... 54.210 365.20 21.010 5.7367

18 ......... 17,485.872 186,330.24 546.759 9.6560 73 ......... 47.115 310.99 18.843 5.6006

19 ......... 15,873.192 168,844.37 523.704 9.6371 74 ......... 40.829 263.87 16.840 5.4629

20 ......... 14,407.284 152,971.18 500.813 9.6176 75 ......... 35.280 223.04 15.003 5.3222

21 ......... 13,074.964 138,563.89 478.246 9.5977 76 ......... 30.399 187.76 13.330 5.1766

22 ......... 11,863.973 125,488.93 455.888 9.5773 77 ......... 26.117 157.37 11.811 5.0254

23 ......... 10,763.876 113,624.96 434.335 9.5561 78 ......... 22.363 131.25 10.431 4.8690

24 ......... 9,764.834 102,861.08 413.826 9.5338 79 ......... 19.071 108.89 9.172 4.7096

25 ......... 8,857.832 93,096.25 394.536 9.5100 80 ......... 16.183 89.81 8.018 4.5500

26 ......... 8,034.702 84,238.41 376.665 9.4843 81 ......... 13.650 73.63 6.956 4.3944

27 ......... 7,287.494 76,203.71 359.884 9.4568 82 ......... 11.436 59.98 5.984 4.2448

28 ......... 6,609.115 68,916.22 344.004 9.4275 83 ......... 9.516 48.55 5.103 4.1014

29 ......... 5,993.030 62,307.10 328.748 9.3966 84 ......... 7.869 39.03 4.321 3.9600

30 ......... 5,433.367 56,314.07 313.905 9.3645 85 ......... 6.472 31.16 3.640 3.8144

31 ......... 4,925.045 50,880.71 299.526 9.3310 86 ......... 5.295 24.69 3.050 3.6628

32 ......... 4,463.484 45,955.66 285.696 9.2959 87 ......... 4.303 19.39 2.540 3.5066

33 ......... 4,044.408 41,492.18 272.392 9.2591 88 ......... 3.471 15.09 2.099 3.3475

34 ......... 3,663.935 37,447.77 259.592 9.2206 89 ......... 2.774 11.62 1.718 3.1887

35 ......... 3,318.573 33,783.83 247.316 9.1802 90 ......... 2.192 8.85 1.388 3.0353

36 ......... 3,005.110 30,465.26 235.541 9.1378 91 ......... 1.710 6.65 1.105 2.8915

37 ......... 2,720.566 27,460.15 224.189 9.0935 92 ......... 1.314 4.94 0.865 2.7615

38 ......... 2,462.415 24,739.59 213.361 9.0469 93 ......... 0.996 3.63 0.666 2.6441

39 ......... 2,228.254 22,277.17 203.056 8.9976 94 ......... 0.746 2.63 0.506 2.5318

40 ......... 2,015.919 20,048.92 193.290 8.9453 95 ......... 0.553 1.89 0.381 2.4157

41 ......... 1,823.374 18,033.00 184.010 8.8899 96 ......... 0.405 1.34 0.284 2.2963

42 ......... 1,648.793 16,209.62 175.191 8.8312 97 ......... 0.292 0.93 0.208 2.1809

43 ......... 1,490.470 14,560.83 166.758 8.7693 95 ......... 0.208 0.64 0.150 2.0686

44 ......... 1,346.929 13,070.36 158.714 8.7038 99 ......... 0.145 0.43 0.106 1.9584

45 ......... 1,216.743 11,723.43 150.977 8.6351 100 ......... 0.100 0.28 0.074 1.8505

46 ......... 1,098.684 10,506.69 143.531 8.5630 101 ......... 0.067 0.18 0.051 1.7450

47 ......... 991.593 9,408.00 136.320 8.4878 102 ......... 0.044 0.12 0.034 1.6418

48 ......... 894.449 8,416.41 129.321 8.4096 103 ......... 0.029 0.07 0.022 1.5410

49 ......... 806.361 7,521.96 122.546 8.3283 104 ......... 0.018 0.04 0.014 1.4426

50 ......... 726.505 6,715.60 115.995 8.2437 105 ......... 0.011 0.03 0.009 1.3468

51 ......... 654.124 5,989.10 109.661 8.1559 106 ......... 0.007 0.02 0.005 1.2535

52 ......... 588.533 5,334.97 103.536 8.0649 107 ......... 0.004 0.01 0.003 1.1627

53 ......... 529.104 4,746.44 97.609 7.9707 108 ......... 0.002 0.00 0.002 1.0745

54 ......... 475.267 4,217.34 91.872 7.8736 109 ......... 0.001 0.00 0.001 0.9888

x x x x x x x x

121
Table 10.K. -- Actuarial Functions at 11.0 Percent Interest for 1989-91 United States 

Total Black Population

x D N M a x D N M a

0 ......... 100,000.000 984,690.99 2,418.010 8.8469 55 ......... 259.274 2,139.61 47.241 7.2523

1 ......... 88,456.757 884,690.99 784.676 9.0014 56 ......... 230.348 1,880.33 44.008 7.1630

2 ......... 79,591.754 796,234.24 685.658 9.0040 57 ......... 204.433 1,649.99 40.921 7.0710

3 ......... 71,648.712 716,642.48 630.088 9.0022 58 ......... 181.221 1,445.55 37.968 6.9767

4 ......... 64,510.183 644,993.77 591.881 8.9983 59 ......... 160.439 1,264.33 35.145 6.8805

5 ......... 58,089.390 580,483.59 563.989 8.9929 60 ......... 141.845 1,103.89 32.450 6.7824

6 ......... 52,310.863 522,394.20 542.069 8.9863 61 ......... 125.230 962.05 29.892 6.6822

7 ......... 47,109.083 470,083.33 524.248 8.9786 62 ......... 110.406 836.82 27.478 6.5795

8 ......... 42,426.295 422,974.25 509.928 8.9696 63 ......... 97.188 726.41 25.201 6.4743

9 ......... 38,210.942 380,547.96 498.982 8.9591 64 ......... 85.404 629.22 23.049 6.3676

10 ......... 34,415.467 342,337.01 490.178 8.9472 65 ......... 74.914 543.82 21.022 6.2593

11 ......... 30,998.263 307,921.55 483.515 8.9335 66 ......... 65.584 468.91 19.116 6.1497

12 ......... 27,920.074 276,923.29 477.226 8.9184 67 ......... 57.305 403.32 17.336 6.0382

13 ......... 25,145.495 249,003.21 469.501 8.9025 68 ......... 49.972 346.02 15.682 5.9242

14 ......... 22,643.391 223,857.72 459.293 8.8862 69 ......... 43.489 296.04 14.151 5.8074

15 ......... 20,386.075 201,214.33 445.917 8.8702 70 ......... 37.763 252.56 12.735 5.6879

16 ......... 18,349.640 180,828.25 429.723 8.8546 71 ......... 32.710 214.79 11.424 5.5666

17 ......... 16,512.887 162,478.61 411.403 8.8395 72 ......... 28.255 182.08 10.211 5.4442

18 ......... 14,857.372 145,965.72 392.300 8.8245 73 ......... 24.336 153.83 9.092 5.3210

19 ......... 13,365.607 131,108.35 372.888 8.8094 74 ......... 20.899 129.49 8.066 5.1961

20 ......... 12,021.986 117,742.74 353.787 8.7940 75 ......... 17.896 108.59 7.134 5.0681

21 ......... 10,811.957 105,720.76 335.126 8.7781 76 ......... 15.281 90.70 6.293 4.9352

22 ......... 9,722.181 94,908.80 316.804 8.7621 77 ......... 13.010 75.42 5.537 4.7966

23 ......... 8,741.218 85,186.62 299.300 8.7454 78 ......... 11.040 62.41 4.856 4.6527

24 ......... 7,858.466 76,445.40 282.796 8.7278 79 ......... 9.330 51.37 4.240 4.5055

25 ......... 7,064.315 68,586.94 267.412 8.7089 80 ......... 7.846 42.04 3.680 4.3578

26 ......... 6,350.123 61,522.62 253.287 8.6884 81 ......... 6.558 34.19 3.170 4.2135

27 ......... 5,707.689 55,172.50 240.144 8.6663 82 ......... 5.445 27.63 2.707 4.0747

28 ......... 5,129.737 49,464.81 227.819 8.6428 83 ......... 4.490 22.19 2.291 3.9414

29 ......... 4,609.650 44,335.07 216.085 8.6179 84 ......... 3.679 17.70 1.926 3.8099

30 ......... 4,141.524 39,725.42 204.771 8.5920 85 ......... 2.999 14.02 1.610 3.6740

31 ......... 3,720.241 35,583.90 193.909 8.5649 86 ......... 2.431 11.02 1.339 3.5320

32 ......... 3,341.216 31,863.66 183.556 8.5365 87 ......... 1.958 8.59 1.107 3.3851

33 ......... 3,000.235 28,522.44 173.687 8.5067 88 ......... 1.565 6.63 0.908 3.2350

34 ......... 2,693.505 25,522.21 164.277 8.4755 89 ......... 1.240 5.06 0.738 3.0849

35 ......... 2,417.637 22,828.70 155.334 8.4426 90 ......... 0.971 3.82 0.592 2.9393

36 ......... 2,169.551 20,411.06 146.833 8.4080 91 ......... 0.750 2.85 0.468 2.8027

37 ......... 1,946.429 18,241.51 138.711 8.3718 92 ......... 0.572 2.10 0.363 2.6792

38 ......... 1,745.862 16,295.08 131.034 8.3335 93 ......... 0.429 1.53 0.277 2.5676

39 ......... 1,565.608 14,549.22 123.794 8.2930 94 ......... 0.318 1.10 0.209 2.4608

40 ......... 1,403.658 12,983.61 116.994 8.2498 95 ......... 0.234 0.78 0.156 2.3501

41 ......... 1,258.154 11,579.95 110.591 8.2039 96 ......... 0.170 0.55 0.115 2.2359

42 ......... 1,127.441 10,321.80 104.560 8.1551 97 ......... 0.122 0.38 0.084 2.1253

43 ......... 1,009.998 9,194.36 98.845 8.1033 95 ......... 0.086 0.26 0.060 2.0176

44 ......... 904.507 8,184.36 93.444 8.0484 99 ......... 0.059 0.17 0.042 1.9118

45 ......... 809.722 7,279.86 88.294 7.9906 100 ......... 0.040 0.11 0.029 1.8080

46 ......... 724.568 6,470.13 83.384 7.9296 101 ......... 0.027 0.07 0.020 1.7062

47 ......... 648.052 5,745.57 78.671 7.8659 102 ......... 0.018 0.05 0.013 1.6066

48 ......... 579.297 5,097.51 74.138 7.7995 103 ......... 0.011 0.03 0.008 1.5091

49 ......... 517.541 4,518.22 69.790 7.7302 104 ......... 0.007 0.02 0.005 1.4139

50 ......... 462.087 4,000.68 65.624 7.6578 105 ......... 0.004 0.01 0.003 1.3209

51 ......... 412.302 3,538.59 61.631 7.5825 106 ......... 0.003 0.01 0.002 1.2303

52 ......... 367.617 3,126.29 57.805 7.5042 107 ......... 0.001 0.00 0.001 1.1420

53 ......... 327.518 2,758.67 54.136 7.4230 108 ......... 0.001 0.00 0.001 1.0561

54 ......... 291.542 2,431.15 50.617 7.3389 109 ......... 0.000 0.00 0.000 0.9725

x x x x x x x x

122
Table 10.L. -- Actuarial Functions at 12.0 Percent Interest for 1989-91 United States 

Total Black Population

x D N M a x D N M a

0 ......... 100,000.000 912,096.98 2,275.323 8.1210 55 ......... 158.319 1,233.58 26.150 6.7917

1 ......... 87,666.964 812,096.98 656.573 8.2634 56 ......... 139.400 1,075.26 24.193 6.7135

2 ......... 78,176.818 724,430.02 559.315 8.2666 57 ......... 122.612 935.86 22.342 6.6327

3 ......... 69,746.635 646,253.20 505.220 8.2657 58 ......... 107.720 813.25 20.586 6.5496

4 ......... 62,236.921 576,506.57 468.360 8.2631 59 ......... 94.515 705.53 18.923 6.4647

5 ......... 55,542.010 514,269.65 441.691 8.2591 60 ......... 82.816 611.01 17.350 6.3780

6 ......... 49,570.309 458,727.64 420.919 8.2541 61 ......... 72.462 528.20 15.870 6.2893

7 ......... 44,242.467 409,157.33 404.182 8.2481 62 ......... 63.314 455.73 14.485 6.1980

8 ......... 39,488.875 364,914.86 390.854 8.2410 63 ......... 55.236 392.42 13.191 6.1044

9 ......... 35,247.827 325,425.99 380.757 8.2325 64 ......... 48.106 337.18 11.979 6.0092

10 ......... 31,463.225 290,178.16 372.708 8.2228 65 ......... 41.820 289.08 10.847 5.9124

11 ......... 28,086.128 258,714.93 366.671 8.2115 66 ......... 36.285 247.26 9.793 5.8143

12 ......... 25,071.253 230,628.81 361.024 8.1989 67 ......... 31.421 210.97 8.817 5.7144

13 ......... 22,378.172 205,557.55 354.149 8.1856 68 ......... 27.156 179.55 7.918 5.6119

14 ......... 19,971.508 183,179.38 345.145 8.1720 69 ......... 23.422 152.40 7.094 5.5066

15 ......... 17,820.011 163,207.87 333.453 8.1587 70 ......... 20.156 128.97 6.338 5.3987

16 ......... 15,896.695 145,387.86 319.424 8.1458 71 ......... 17.303 108.82 5.644 5.2888

17 ......... 14,177.748 129,491.17 303.695 8.1334 72 ......... 14.813 91.51 5.008 5.1778

18 ......... 12,642.449 115,313.42 287.440 8.1211 73 ......... 12.645 76.70 4.427 5.0659

19 ......... 11,271.530 102,670.97 271.069 8.1089 74 ......... 10.762 64.06 3.899 4.9521

20 ......... 10,047.901 91,399.44 255.104 8.0964 75 ......... 9.133 53.29 3.423 4.8352

21 ......... 8,955.883 81,351.54 239.647 8.0836 76 ......... 7.729 44.16 2.998 4.7135

22 ......... 7,981.283 72,395.66 224.606 8.0707 77 ......... 6.522 36.43 2.618 4.5861

23 ......... 7,111.905 64,414.37 210.365 8.0573 78 ......... 5.485 29.91 2.280 4.4534

24 ......... 6,336.607 57,302.47 197.056 8.0431 79 ......... 4.594 24.43 1.977 4.3171

25 ......... 5,645.390 50,965.86 184.762 8.0279 80 ......... 3.828 19.83 1.704 4.1800

26 ......... 5,029.340 45,320.47 173.575 8.0112 81 ......... 3.172 16.00 1.457 4.0458

27 ......... 4,480.166 40,291.13 163.259 7.9932 82 ......... 2.610 12.83 1.235 3.9166

28 ......... 3,990.560 35,810.97 153.671 7.9739 83 ......... 2.133 10.22 1.038 3.7925

29 ......... 3,553.953 31,820.41 144.624 7.9535 84 ......... 1.732 8.09 0.865 3.6699

30 ......... 3,164.528 28,266.45 135.979 7.9323 85 ......... 1.399 6.36 0.718 3.5428

31 ......... 2,817.246 25,101.92 127.754 7.9101 86 ......... 1.124 4.96 0.593 3.4095

32 ......... 2,507.628 22,284.68 119.984 7.8868 87 ......... 0.897 3.83 0.487 3.2713

33 ......... 2,231.613 19,777.05 112.643 7.8622 88 ......... 0.711 2.94 0.396 3.1295

34 ......... 1,985.575 17,545.44 105.707 7.8365 89 ......... 0.558 2.22 0.320 2.9871

35 ......... 1,766.301 15,559.86 99.172 7.8093 90 ......... 0.433 1.67 0.254 2.8489

36 ......... 1,570.899 13,793.56 93.017 7.7807 91 ......... 0.332 1.23 0.200 2.7189

37 ......... 1,396.760 12,222.66 87.189 7.7507 92 ......... 0.250 0.90 0.154 2.6013

38 ......... 1,241.648 10,825.90 81.729 7.7190 93 ......... 0.186 0.65 0.117 2.4951

39 ......... 1,103.510 9,584.26 76.626 7.6852 94 ......... 0.137 0.47 0.087 2.3934

40 ......... 980.527 8,480.75 71.876 7.6492 95 ......... 0.100 0.33 0.065 2.2877

41 ......... 871.038 7,500.22 67.443 7.6107 96 ......... 0.072 0.23 0.047 2.1784

42 ......... 773.574 6,629.18 63.305 7.5695 97 ......... 0.051 0.16 0.034 2.0724

43 ......... 686.805 5,855.61 59.419 7.5259 95 ......... 0.036 0.11 0.024 1.9690

44 ......... 609.579 5,168.80 55.779 7.4793 99 ......... 0.024 0.07 0.017 1.8672

45 ......... 540.827 4,559.22 52.339 7.4301 100 ......... 0.016 0.05 0.012 1.7672

46 ......... 479.631 4,018.40 49.089 7.3781 101 ......... 0.011 0.03 0.008 1.6691

47 ......... 425.150 3,538.76 45.997 7.3236 102 ......... 0.007 0.02 0.005 1.5728

48 ......... 376.651 3,113.61 43.050 7.2666 103 ......... 0.004 0.01 0.003 1.4785

49 ......... 333.494 2,736.96 40.248 7.2069 104 ......... 0.003 0.01 0.002 1.3862

50 ......... 295.102 2,403.47 37.587 7.1445 105 ......... 0.002 0.00 0.001 1.2960

51 ......... 260.956 2,108.37 35.060 7.0794 106 ......... 0.001 0.00 0.001 1.2079

52 ......... 230.597 1,847.41 32.660 7.0114 107 ......... 0.001 0.00 0.000 1.1220

53 ......... 203.609 1,616.81 30.379 6.9408 108 ......... 0.000 0.00 0.000 1.0383

54 ......... 179.626 1,413.20 28.211 6.8675 109 ......... 0.000 0.00 0.000 0.9568

x x x x x x x x

123
Table 11.A. -- Actuarial Functions at 1.0 Percent Interest for 1989-91 United States 

Black Males

x D N M a x D N M a

0 ......... 100,000.000 4,692,163.70 53,542.934 45.9216 55 ......... 42,866.038 746,482.20 35,475.125 16.4143

1 ......... 97,052.475 4,592,163.70 51,585.508 46.3163 56 ......... 41,641.420 703,616.16 34,674.923 15.8970

2 ......... 95,962.161 4,495,111.22 51,456.109 45.8425 57 ......... 40,392.614 661,974.74 33,838.408 15.3885

3 ......... 94,931.481 4,399,149.06 51,375.550 45.3403 58 ......... 39,120.656 621,582.13 32,966.378 14.8888

4 ......... 93,927.180 4,304,217.58 51,311.164 44.8250 59 ......... 37,827.118 582,461.47 32,060.173 14.3980

5 ......... 92,946.780 4,210,290.40 51,260.737 44.2979 60 ......... 36,513.525 544,634.35 31,121.106 13.9160

6 ......... 91,982.239 4,117,343.62 51,216.460 43.7624 61 ......... 35,186.265 508,120.83 30,155.366 13.4409

7 ......... 91,032.349 4,025,361.38 51,177.286 43.2190 62 ......... 33,847.714 472,934.56 29,165.194 12.9724

8 ......... 90,095.947 3,934,329.03 51,142.194 42.6682 63 ......... 32,496.424 439,086.85 28,149.029 12.5119

9 ......... 89,173.734 3,844,233.08 51,112.021 42.1095 64 ......... 31,128.901 406,590.42 27,103.253 12.0615

10 ......... 88,266.383 3,755,059.35 51,087.578 41.5423 65 ......... 29,745.468 375,461.52 26,028.027 11.6225

11 ......... 87,373.636 3,666,792.97 51,068.755 40.9668 66 ......... 28,349.562 345,716.05 24,926.630 11.1948

12 ......... 86,488.139 3,579,419.33 51,048.344 40.3862 67 ......... 26,949.116 317,366.49 23,806.874 10.7765

13 ......... 85,601.946 3,492,931.19 51,018.469 39.8043 68 ......... 25,549.732 290,417.38 22,674.312 10.3667

14 ......... 84,702.205 3,407,329.25 50,966.271 39.2272 69 ......... 24,155.788 264,867.64 21,533.336 9.9650

15 ......... 83,781.741 3,322,627.04 50,884.443 38.6581 70 ......... 22,768.006 240,711.86 20,384.720 9.5724

16 ......... 82,838.793 3,238,845.30 50,771.018 38.0982 71 ......... 21,386.095 217,943.85 19,228.235 9.1909

17 ......... 81,876.752 3,156,006.51 50,629.163 37.5458 72 ......... 20,009.777 196,557.76 18,063.660 8.8231

18 ......... 80,899.723 3,074,129.75 50,462.795 36.9993 73 ......... 18,645.557 176,547.98 16,897.557 8.4686

19 ......... 79,913.322 2,993,230.03 50,277.381 36.4560 74 ......... 17,306.390 157,902.42 15,743.000 8.1239

20 ......... 78,922.952 2,913,316.71 50,078.232 35.9134 75 ......... 16,004.241 140,596.03 14,612.201 7.7849

21 ......... 77,927.319 2,834,393.76 49,864.015 35.3723 76 ......... 14,747.774 124,591.79 13,514.192 7.4482

22 ......... 76,925.187 2,756,466.44 49,633.440 34.8331 77 ......... 13,537.859 109,844.02 12,450.294 7.1138

23 ......... 75,921.737 2,679,541.25 49,391.626 34.2935 78 ......... 12,375.306 96,306.16 11,421.780 6.7821

24 ......... 74,921.953 2,603,619.51 49,143.542 33.7511 79 ......... 11,254.495 83,930.85 10,423.496 6.4575

25 ......... 73,929.066 2,528,697.56 48,892.457 33.2044 80 ......... 10,172.258 72,676.36 9,452.691 6.1446

26 ......... 72,945.408 2,454,768.49 48,640.769 32.6521 81 ......... 9,124.642 62,504.10 8,505.789 5.8500

27 ......... 71,969.394 2,381,823.09 48,386.987 32.0949 82 ......... 8,115.347 53,379.46 7,586.837 5.5776

28 ......... 70,997.988 2,309,853.69 48,128.149 31.5341 83 ......... 7,156.231 45,264.11 6,708.071 5.3251

29 ......... 70,026.024 2,238,855.70 47,859.135 30.9718 84 ......... 6,265.166 38,107.88 5,887.860 5.0825

30 ......... 69,050.766 2,168,829.68 47,577.205 30.4092 85 ......... 5,454.998 31,842.71 5,139.724 4.8373

31 ......... 68,071.060 2,099,778.92 47,281.170 29.8469 86 ......... 4,724.855 26,387.72 4,463.591 4.5849

32 ......... 67,087.985 2,031,707.85 46,972.066 29.2842 87 ......... 4,065.860 21,662.86 3,851.377 4.3280

33 ......... 66,101.862 1,964,619.87 46,650.180 28.7211 88 ......... 3,470.277 17,597.00 3,296.049 4.0708

34 ......... 65,110.864 1,898,518.01 46,313.656 28.1582 89 ......... 2,929.398 14,126.72 2,789.530 3.8224

35 ......... 64,116.069 1,833,407.14 45,963.523 27.5951 90 ......... 2,438.912 11,197.33 2,328.048 3.5911

36 ......... 63,115.020 1,769,291.07 45,597.286 27.0328 91 ......... 1,997.478 8,758.41 1,910.761 3.3847

37 ......... 62,107.440 1,706,176.05 45,214.608 26.4714 92 ......... 1,606.982 6,760.94 1,540.042 3.2072

38 ......... 61,095.811 1,644,068.62 44,817.904 25.9097 93 ......... 1,270.003 5,153.95 1,218.974 3.0582

39 ......... 60,082.523 1,582,972.80 44,409.525 25.3466 94 ......... 990.559 3,883.95 952.104 2.9210

40 ......... 59,070.550 1,522,890.28 43,992.429 24.7809 95 ......... 765.872 2,893.39 737.224 2.7779

41 ......... 58,058.761 1,463,819.73 43,565.497 24.2127 96 ......... 586.468 2,127.52 565.404 2.6277

42 ......... 57,045.415 1,405,760.97 43,126.990 23.6428 97 ......... 442.511 1,541.05 427.253 2.4825

43 ......... 56,029.494 1,348,715.55 42,675.875 23.0715 95 ......... 328.676 1,098.54 317.799 2.3423

44 ......... 55,008.735 1,292,686.06 42,209.863 22.4997 99 ......... 240.060 769.87 232.438 2.2070

45 ......... 53,979.052 1,237,677.32 41,724.821 21.9288 100 ......... 172.221 529.80 166.975 2.0763

46 ......... 52,939.056 1,183,698.27 41,219.271 21.3596 101 ......... 121.202 357.58 117.662 1.9503

47 ......... 51,885.546 1,130,759.22 40,689.910 20.7933 102 ......... 83.564 236.38 81.223 1.8288

48 ......... 50,816.074 1,078,873.67 40,134.157 20.2310 103 ......... 56.357 152.82 54.844 1.7116

49 ......... 49,731.988 1,028,057.60 39,553.200 19.6720 104 ......... 37.118 96.46 36.163 1.5987

50 ......... 48,633.377 978,325.61 38,946.985 19.1163 105 ......... 23.832 59.34 23.245 1.4900

51 ......... 47,519.137 929,692.23 38,314.264 18.5646 106 ......... 14.887 35.51 14.536 1.3853

52 ......... 46,388.218 882,173.09 37,653.831 18.0172 107 ......... 9.027 20.62 8.823 1.2846

53 ......... 45,237.856 835,784.88 36,962.758 17.4753 108 ......... 5.301 11.60 5.186 1.1876

54 ......... 44,064.823 790,547.02 36,237.625 16.9405 109 ......... 3.006 6.30 2.944 1.0944

x x x x x x x x

124
Table 11.B. -- Actuarial Functions at 2.0 Percent Interest for 1989-91 United States 

Black Males

x D N M a x D N M a

0 ......... 100,000.000 3,555,040.64 30,293.321 34.5504 55 ......... 24,933.282 389,540.39 17,295.235 14.6233

1 ......... 96,100.980 3,455,040.64 28,355.086 34.9522 56 ......... 23,983.516 364,607.11 16,834.357 14.2024

2 ......... 94,089.773 3,358,939.66 28,228.211 34.6993 57 ......... 23,036.180 340,623.59 16,357.286 13.7865

3 ......... 92,166.663 3,264,849.88 28,149.999 34.4233 58 ......... 22,092.041 317,587.41 15,864.837 13.3756

4 ......... 90,297.576 3,172,683.22 28,088.101 34.1359 59 ......... 21,152.133 295,495.37 15,358.106 12.9700

5 ......... 88,479.031 3,082,385.64 28,040.097 33.8375 60 ......... 20,217.427 274,343.24 14,838.148 12.5696

6 ......... 86,702.414 2,993,906.61 27,998.363 33.5308 61 ......... 19,291.522 254,125.81 14,308.663 12.1729

7 ......... 84,965.803 2,907,204.20 27,961.799 33.2162 62 ......... 18,375.699 234,834.29 13,771.105 11.7796

8 ......... 83,267.374 2,822,238.40 27,929.366 32.8937 63 ......... 17,469.131 216,458.59 13,224.845 11.3909

9 ......... 81,607.068 2,738,971.02 27,901.753 32.5629 64 ......... 16,569.932 198,989.46 12,668.177 11.0091

10 ......... 79,984.780 2,657,363.95 27,879.604 32.2234 65 ......... 15,678.299 182,419.53 12,101.445 10.6352

11 ......... 78,399.561 2,577,379.17 27,862.714 31.8749 66 ......... 14,796.046 166,741.23 11,526.610 10.2693

12 ......... 76,844.179 2,498,979.61 27,844.579 31.5201 67 ......... 13,927.240 151,945.18 10,947.923 9.9099

13 ......... 75,311.148 2,422,135.43 27,818.296 31.1617 68 ......... 13,074.590 138,017.94 10,368.356 9.5562

14 ......... 73,788.986 2,346,824.29 27,772.824 30.8045 69 ......... 12,240.077 124,943.35 9,790.207 9.2077

15 ......... 72,271.557 2,273,035.30 27,702.237 30.4513 70 ......... 11,423.762 112,703.28 9,213.894 8.8657

16 ......... 70,757.584 2,200,763.74 27,605.354 30.1029 71 ......... 10,625.193 101,279.51 8,639.320 8.5320

17 ......... 69,250.201 2,130,006.16 27,485.375 29.7581 72 ......... 9,843.936 90,654.32 8,066.400 8.2092

18 ......... 67,753.022 2,060,755.96 27,346.043 29.4157 73 ......... 9,082.870 80,810.39 7,498.353 7.8970

19 ......... 66,270.771 1,993,002.94 27,192.282 29.0736 74 ......... 8,347.865 71,727.51 6,941.444 7.5923

20 ......... 64,807.812 1,926,732.16 27,028.750 28.7299 75 ......... 7,644.080 63,379.65 6,401.342 7.2913

21 ......... 63,362.890 1,861,924.35 26,854.569 28.3851 76 ......... 6,974.898 55,735.57 5,882.043 6.9909

22 ......... 61,934.838 1,798,561.46 26,668.927 28.0396 77 ......... 6,339.902 48,760.67 5,383.810 6.6911

23 ......... 60,527.646 1,736,626.62 26,476.143 27.6915 78 ......... 5,738.650 42,420.77 4,906.870 6.3921

24 ......... 59,144.987 1,676,098.98 26,280.301 27.3388 79 ......... 5,167.744 36,682.12 4,448.486 6.0983

25 ......... 57,789.012 1,616,953.99 26,084.032 26.9803 80 ......... 4,625.019 31,514.38 4,007.090 5.8139

26 ......... 56,461.084 1,559,164.98 25,889.221 26.6149 81 ......... 4,108.026 26,889.36 3,580.784 5.5456

27 ......... 55,159.497 1,502,703.90 25,694.715 26.2429 82 ......... 3,617.809 22,781.33 3,171.116 5.2970

28 ......... 53,881.502 1,447,544.40 25,498.279 25.8653 83 ......... 3,158.960 19,163.52 2,783.204 5.0664

29 ......... 52,622.845 1,393,662.90 25,296.122 25.4840 84 ......... 2,738.505 16,004.56 2,424.690 4.8443

30 ......... 51,381.238 1,341,040.05 25,086.335 25.0998 85 ......... 2,361.004 13,266.06 2,100.886 4.6188

31 ......... 50,155.640 1,289,658.81 24,868.213 24.7131 86 ......... 2,024.939 10,905.05 1,811.114 4.3854

32 ......... 48,946.677 1,239,503.17 24,642.693 24.3235 87 ......... 1,725.429 8,880.11 1,551.309 4.1466

33 ......... 47,754.396 1,190,556.50 24,410.151 23.9308 88 ......... 1,458.243 7,154.69 1,317.955 3.9064

34 ......... 46,577.302 1,142,802.10 24,169.418 23.5356 89 ......... 1,218.892 5,696.44 1,107.197 3.6735

35 ......... 45,416.008 1,096,224.80 23,921.404 23.1374 90 ......... 1,004.857 4,477.55 917.062 3.4559

36 ......... 44,268.621 1,050,808.79 23,664.527 22.7371 91 ......... 814.913 3,472.69 746.821 3.2614

37 ......... 43,134.831 1,006,540.17 23,398.749 22.3347 92 ......... 649.175 2,657.78 597.061 3.0941

38 ......... 42,016.233 963,405.34 23,125.932 21.9294 93 ......... 508.015 2,008.61 468.631 2.9538

39 ......... 40,914.292 921,389.10 22,847.839 21.5200 94 ......... 392.350 1,500.59 362.926 2.8246

40 ......... 39,830.806 880,474.81 22,566.594 21.1054 95 ......... 300.380 1,108.24 278.649 2.6895

41 ......... 38,764.755 840,644.01 22,281.540 20.6858 96 ......... 227.761 807.86 211.921 2.5470

42 ......... 37,714.750 801,879.25 21,991.627 20.2617 97 ......... 170.169 580.10 158.794 2.4090

43 ......... 36,679.921 764,164.50 21,696.303 19.8333 95 ......... 125.154 409.93 117.116 2.2754

44 ......... 35,658.621 727,484.58 21,394.218 19.4014 99 ......... 90.515 284.78 84.931 2.1462

45 ......... 34,648.093 691,825.96 21,082.878 18.9672 100 ......... 64.299 194.26 60.490 2.0212

46 ......... 33,647.398 657,177.87 20,761.558 18.5313 101 ......... 44.808 129.96 42.259 1.9005

47 ......... 32,654.488 623,530.47 20,428.401 18.0948 102 ......... 30.590 85.16 28.920 1.7837

48 ......... 31,667.867 590,875.98 20,082.063 17.6585 103 ......... 20.428 54.56 19.358 1.6711

49 ......... 30,688.433 559,208.11 19,723.568 17.2221 104 ......... 13.323 34.14 12.653 1.5623

50 ......... 29,716.286 528,519.68 19,353.155 16.7855 105 ......... 8.470 20.81 8.062 1.4573

51 ......... 28,750.794 498,803.39 18,970.336 16.3492 106 ......... 5.239 12.34 4.997 1.3561

52 ......... 27,791.385 470,052.60 18,574.668 15.9136 107 ......... 3.146 7.10 3.006 1.2585

53 ......... 26,836.490 442,261.21 18,164.702 15.4798 108 ......... 1.829 3.96 1.751 1.1645

54 ......... 25,884.331 415,424.72 17,738.748 15.0493 109 ......... 1.027 2.13 0.985 1.0739

x x x x x x x x

125
Table 11.C. -- Actuarial Functions at 3.0 Percent Interest for 1989-91 United States 

Black Males

x D N M a x D N M a

0 ......... 100,000.000 2,806,844.95 18,247.235 27.0684 55 ......... 14,579.464 206,022.27 8,578.815 13.1310

1 ......... 95,167.961 2,706,844.95 16,327.817 27.4428 56 ......... 13,887.942 191,442.80 8,311.938 12.7848

2 ......... 92,271.656 2,611,676.98 16,203.394 27.3042 57 ......... 13,209.867 177,554.86 8,038.366 12.4411

3 ......... 89,508.175 2,519,405.33 16,127.438 27.1472 58 ......... 12,545.465 164,344.99 7,758.718 12.1000

4 ......... 86,841.613 2,429,897.15 16,067.909 26.9808 59 ......... 11,895.099 151,799.53 7,473.753 11.7615

5 ......... 84,266.527 2,343,055.54 16,022.191 26.8053 60 ......... 11,259.075 139,904.43 7,184.188 11.4259

6 ......... 81,772.800 2,258,789.01 15,982.829 26.6227 61 ......... 10,639.134 128,645.36 6,892.182 11.0917

7 ......... 79,356.918 2,177,016.21 15,948.679 26.4332 62 ......... 10,035.675 118,006.22 6,598.601 10.7587

8 ......... 77,015.554 2,097,659.29 15,918.682 26.2368 63 ......... 9,447.936 107,970.55 6,303.163 10.4280

9 ......... 74,747.091 2,020,643.74 15,893.390 26.0331 64 ......... 8,874.611 98,522.61 6,005.020 10.1016

10 ......... 72,549.901 1,945,896.65 15,873.299 25.8215 65 ......... 8,315.541 89,648.00 5,704.434 9.7808

11 ......... 70,421.626 1,873,346.75 15,858.129 25.6019 66 ......... 7,771.417 81,332.46 5,402.510 9.4656

12 ......... 68,354.379 1,802,925.12 15,841.997 25.3761 67 ......... 7,244.068 73,561.04 5,101.513 9.1547

13 ......... 66,340.322 1,734,570.74 15,818.844 25.1466 68 ......... 6,734.549 66,316.97 4,802.986 8.8473

14 ......... 64,368.413 1,668,230.42 15,779.177 24.9169 69 ......... 6,243.491 59,582.43 4,508.081 8.5431

15 ......... 62,432.628 1,603,862.01 15,718.200 24.6895 70 ......... 5,770.526 53,338.93 4,216.965 8.2433

16 ......... 60,531.321 1,541,429.38 15,635.319 24.4650 71 ......... 5,315.034 47,568.41 3,929.547 7.9498

17 ......... 58,666.630 1,480,898.06 15,533.677 24.2426 72 ......... 4,876.419 42,253.37 3,645.738 7.6648

18 ......... 56,841.001 1,422,231.43 15,416.785 24.0212 73 ......... 4,455.724 37,376.96 3,367.074 7.3885

19 ......... 55,057.694 1,365,390.43 15,289.041 23.7993 74 ......... 4,055.398 32,921.23 3,096.528 7.1179

20 ......... 53,319.529 1,310,332.73 15,154.498 23.5751 75 ......... 3,677.446 28,865.83 2,836.693 6.8494

21 ......... 51,624.620 1,257,013.21 15,012.585 23.3491 76 ......... 3,322.935 25,188.39 2,589.292 6.5802

22 ......... 49,971.207 1,205,388.59 14,862.802 23.1217 77 ......... 2,991.090 21,865.45 2,354.232 6.3102

23 ......... 48,361.701 1,155,417.38 14,708.767 22.8912 78 ......... 2,681.141 18,874.36 2,131.402 6.0397

24 ......... 46,798.148 1,107,055.68 14,553.808 22.6560 79 ......... 2,390.968 16,193.22 1,919.321 5.7727

25 ......... 45,281.306 1,060,257.53 14,400.019 22.4149 80 ......... 2,119.090 13,802.25 1,717.082 5.5133

26 ......... 43,811.269 1,014,976.22 14,248.855 22.1670 81 ......... 1,863.940 11,683.17 1,523.654 5.2680

27 ......... 42,385.750 971,164.95 14,099.392 21.9125 82 ......... 1,625.576 9,819.23 1,339.579 5.0405

28 ......... 41,001.733 928,779.20 13,949.912 21.6522 83 ......... 1,405.623 8,193.65 1,166.973 4.8292

29 ......... 39,655.168 887,777.47 13,797.571 21.3874 84 ......... 1,206.705 6,788.03 1,008.995 4.6253

30 ......... 38,343.608 848,122.30 13,641.016 21.1190 85 ......... 1,030.261 5,581.32 867.698 4.4174

31 ......... 37,065.609 809,778.70 13,479.822 20.8472 86 ......... 875.035 4,551.06 742.480 4.2010

32 ......... 35,820.985 772,713.09 13,314.778 20.5715 87 ......... 738.369 3,676.03 631.300 3.9786

33 ......... 34,609.124 736,892.10 13,146.248 20.2918 88 ......... 617.973 2,937.66 532.410 3.7537

34 ......... 33,428.318 702,282.98 12,973.474 20.0086 89 ......... 511.526 2,319.68 443.962 3.5348

35 ......... 32,278.408 668,854.66 12,797.204 19.7214 90 ......... 417.609 1,808.16 364.944 3.3298

36 ......... 31,157.463 636,576.25 12,616.407 19.4309 91 ......... 335.382 1,390.55 294.880 3.1462

37 ......... 30,064.719 605,418.79 12,431.162 19.1372 92 ......... 264.577 1,055.17 233.844 2.9881

38 ......... 29,000.741 575,354.07 12,242.856 18.8393 93 ......... 205.036 790.59 182.009 2.8559

39 ......... 27,965.976 546,353.33 12,052.772 18.5364 94 ......... 156.816 585.55 139.761 2.7340

40 ......... 26,961.061 518,387.35 11,862.400 18.2273 95 ......... 118.891 428.74 106.404 2.6061

41 ......... 25,984.710 491,426.29 11,671.323 17.9121 96 ......... 89.274 309.85 80.249 2.4708

42 ......... 25,035.427 465,441.58 11,478.876 17.5913 97 ......... 66.052 220.57 59.628 2.3394

43 ......... 24,112.104 440,406.15 11,284.741 17.2649 95 ......... 48.108 154.52 43.607 2.2120

44 ......... 23,213.158 416,294.05 11,088.088 16.9335 99 ......... 34.455 106.41 31.355 2.0885

45 ......... 22,336.337 393,080.89 10,887.379 16.5983 100 ......... 24.238 71.96 22.142 1.9688

46 ......... 21,480.632 370,744.56 10,682.247 16.2595 101 ......... 16.727 47.72 15.337 1.8530

47 ......... 20,644.359 349,263.92 10,471.623 15.9181 102 ......... 11.308 30.99 10.406 1.7408

48 ......... 19,826.236 328,619.57 10,254.792 15.5750 103 ......... 7.478 19.69 6.905 1.6323

49 ......... 19,026.510 308,793.33 10,032.529 15.2296 104 ......... 4.830 12.21 4.474 1.5274

50 ......... 18,244.917 289,766.82 9,805.106 14.8821 105 ......... 3.041 7.38 2.826 1.4260

51 ......... 17,480.754 271,521.90 9,572.349 14.5326 106 ......... 1.863 4.34 1.736 1.3280

52 ......... 16,733.371 254,041.15 9,334.114 14.1817 107 ......... 1.108 2.47 1.036 1.2335

53 ......... 16,001.545 237,307.78 9,089.668 13.8303 108 ......... 0.638 1.37 0.598 1.1422

54 ......... 15,283.967 221,306.23 8,838.154 13.4796 109 ......... 0.355 0.73 0.333 1.0541

x x x x x x x x

126
Table 11.D. -- Actuarial Functions at 4.0 Percent Interest for 1989-91 United States 

Black Males

x D N M a x D N M a

0 ......... 100,000.000 2,293,925.28 11,772.104 21.9393 55 ......... 8,569.495 110,340.52 4,325.629 11.8760

1 ......... 94,252.885 2,193,925.28 9,871.143 22.2770 56 ......... 8,084.543 101,771.03 4,170.273 11.5883

2 ......... 90,505.732 2,099,672.40 9,749.101 22.1993 57 ......... 7,615.877 93,686.48 4,012.551 11.3015

3 ......... 86,950.956 2,009,166.67 9,675.315 22.1069 58 ......... 7,163.283 86,070.61 3,852.875 11.0155

4 ......... 83,549.416 1,922,215.71 9,618.043 22.0069 59 ......... 6,726.626 78,907.32 3,691.729 10.7306

5 ......... 80,292.415 1,838,666.30 9,574.481 21.8996 60 ......... 6,305.737 72,180.70 3,529.556 10.4468

6 ......... 77,167.101 1,758,373.88 9,537.336 21.7866 61 ......... 5,901.240 65,874.96 3,367.588 10.1629

7 ......... 74,167.219 1,681,206.78 9,505.419 21.6678 62 ......... 5,512.994 59,973.72 3,206.312 9.8786

8 ......... 71,286.867 1,607,039.56 9,477.653 21.5433 63 ......... 5,140.220 54,460.73 3,045.577 9.5950

9 ......... 68,521.879 1,535,752.69 9,454.468 21.4126 64 ......... 4,781.873 49,320.51 2,884.930 9.3141

10 ......... 65,868.182 1,467,230.82 9,436.228 21.2753 65 ......... 4,437.548 44,538.63 2,724.523 9.0368

11 ......... 63,321.149 1,401,362.63 9,422.586 21.1310 66 ......... 4,107.302 40,101.09 2,564.952 8.7634

12 ......... 60,871.355 1,338,041.48 9,408.221 20.9815 67 ......... 3,791.777 35,993.78 2,407.401 8.4926

13 ......... 58,509.729 1,277,170.13 9,387.801 20.8283 68 ......... 3,491.184 32,202.01 2,252.645 8.2238

14 ......... 56,224.706 1,218,660.40 9,353.153 20.6748 69 ......... 3,205.499 28,710.82 2,101.236 7.9567

15 ......... 54,009.468 1,162,435.69 9,300.403 20.5228 70 ......... 2,934.184 25,505.32 1,953.210 7.6925

16 ......... 51,861.171 1,108,426.23 9,229.393 20.3730 71 ......... 2,676.591 22,571.14 1,808.470 7.4328

17 ......... 49,780.264 1,056,565.06 9,143.146 20.2246 72 ......... 2,432.096 19,894.55 1,666.921 7.1800

18 ......... 47,767.406 1,006,784.79 9,044.914 20.0768 73 ......... 2,200.908 17,462.45 1,529.275 6.9342

19 ......... 45,823.878 959,017.39 8,938.594 19.9283 74 ......... 1,983.906 15,261.55 1,396.923 6.6927

20 ......... 43,950.519 913,193.51 8,827.692 19.7778 75 ......... 1,781.713 13,277.64 1,271.034 6.4522

21 ......... 42,144.263 869,242.99 8,711.840 19.6254 76 ......... 1,594.473 11,495.93 1,152.322 6.2099

22 ......... 40,402.228 827,098.73 8,590.739 19.4716 77 ......... 1,421.440 9,901.45 1,040.615 5.9658

23 ......... 38,724.956 786,696.50 8,467.398 19.3150 78 ......... 1,261.893 8,480.01 935.739 5.7201

24 ......... 37,112.646 747,971.54 8,344.510 19.1541 79 ......... 1,114.502 7,218.12 836.882 5.4765

25 ......... 35,564.449 710,858.90 8,223.722 18.9879 80 ......... 978.273 6,103.62 743.519 5.2392

26 ......... 34,079.001 675,294.45 8,106.137 18.8156 81 ......... 852.210 5,125.35 655.081 5.0142

27 ......... 32,653.127 641,215.45 7,990.994 18.6372 82 ......... 736.082 4,273.14 571.730 4.8052

28 ......... 31,283.188 608,562.32 7,876.945 18.4533 83 ......... 630.364 3,537.05 494.323 4.6111

29 ......... 29,964.875 577,279.13 7,761.831 18.2652 84 ......... 535.954 2,906.69 424.158 4.4234

30 ......... 28,695.218 547,314.26 7,644.670 18.0734 85 ......... 453.187 2,370.74 362.005 4.2313

31 ......... 27,472.083 518,619.04 7,525.197 17.8780 86 ......... 381.206 1,917.55 307.454 4.0302

32 ......... 26,294.315 491,146.96 7,404.047 17.6788 87 ......... 318.575 1,536.34 259.485 3.8226

33 ......... 25,160.475 464,852.64 7,281.527 17.4755 88 ......... 264.065 1,217.77 217.228 3.6116

34 ......... 24,068.367 439,692.17 7,157.130 17.2685 89 ......... 216.478 953.70 179.797 3.4055

35 ......... 23,016.967 415,623.80 7,031.436 17.0573 90 ......... 175.033 737.23 146.678 3.2119

36 ......... 22,004.017 392,606.83 6,903.754 16.8425 91 ......... 139.217 562.19 117.594 3.0382

37 ......... 21,028.142 370,602.81 6,774.188 16.6241 92 ......... 108.770 422.98 92.502 2.8887

38 ......... 20,088.927 349,574.67 6,643.747 16.4014 93 ......... 83.482 314.21 71.397 2.7638

39 ......... 19,185.870 329,485.75 6,513.342 16.1734 94 ......... 63.235 230.72 54.361 2.6487

40 ......... 18,318.605 310,299.88 6,383.994 15.9391 95 ......... 47.481 167.49 41.039 2.5275

41 ......... 17,485.465 291,981.27 6,255.416 15.6985 96 ......... 35.310 120.01 30.694 2.3987

42 ......... 16,684.692 274,495.81 6,127.161 15.4520 97 ......... 25.874 84.70 22.616 2.2735

43 ......... 15,914.837 257,811.11 5,999.025 15.1994 95 ......... 18.664 58.82 16.401 2.1518

44 ......... 15,174.178 241,896.28 5,870.475 14.9413 99 ......... 13.238 40.16 11.694 2.0337

45 ......... 14,460.616 226,722.10 5,740.536 14.6786 100 ......... 9.223 26.92 8.188 1.9189

46 ......... 13,772.912 212,261.48 5,609.009 14.4115 101 ......... 6.304 17.70 5.623 1.8077

47 ......... 13,109.436 198,488.57 5,475.260 14.1409 102 ......... 4.221 11.40 3.783 1.6998

48 ......... 12,468.860 185,379.13 5,338.894 13.8674 103 ......... 2.764 7.17 2.489 1.5952

49 ......... 11,850.850 172,910.27 5,200.455 13.5905 104 ......... 1.768 4.41 1.599 1.4940

50 ......... 11,254.758 161,059.42 5,060.165 13.3103 105 ......... 1.103 2.64 1.001 1.3959

51 ......... 10,679.682 149,804.67 4,917.964 13.0271 106 ......... 0.669 1.54 0.610 1.3011

52 ......... 10,124.777 139,124.98 4,773.817 12.7410 107 ......... 0.394 0.87 0.360 1.2093

53 ......... 9,588.879 129,000.21 4,627.333 12.4531 108 ......... 0.225 0.48 0.206 1.1207

54 ......... 9,070.806 119,411.33 4,478.063 12.1644 109 ......... 0.124 0.25 0.114 1.0350

x x x x x x x x

127
Table 11.E. -- Actuarial Functions at 5.0 Percent Interest for 1989-91 United States 

Black Males

x D N M a x D N M a

0 ......... 100,000.000 1,928,765.78 8,154.011 18.2877 55 ......... 5,062.645 59,796.19 2,215.207 10.8113

1 ......... 93,355.238 1,828,765.78 6,271.154 18.5893 56 ......... 4,730.660 54,733.55 2,124.300 10.5700

2 ......... 88,790.023 1,735,410.54 6,151.426 18.5451 57 ......... 4,413.979 50,002.89 2,032.889 10.3283

3 ......... 84,490.228 1,646,620.52 6,079.727 18.4889 58 ......... 4,112.126 45,588.91 1,941.226 10.0865

4 ......... 80,411.763 1,562,130.29 6,024.606 18.4266 59 ......... 3,824.685 41,476.78 1,849.600 9.8445

5 ......... 76,541.104 1,481,718.52 5,983.079 18.3585 60 ......... 3,551.225 37,652.10 1,758.268 9.6026

6 ......... 72,861.218 1,405,177.42 5,948.007 18.2857 61 ......... 3,291.772 34,100.87 1,667.921 9.3594

7 ......... 69,361.787 1,332,316.20 5,918.158 18.2082 62 ......... 3,045.916 30,809.10 1,578.816 9.1149

8 ......... 66,033.125 1,262,954.42 5,892.439 18.1261 63 ......... 2,812.913 27,763.18 1,490.856 8.8699

9 ......... 62,867.418 1,196,921.29 5,871.166 18.0388 64 ......... 2,591.890 24,950.27 1,403.782 8.6263

10 ......... 59,857.156 1,134,053.87 5,854.591 17.9460 65 ......... 2,382.351 22,358.38 1,317.666 8.3850

11 ......... 56,994.537 1,074,196.72 5,842.313 17.8474 66 ......... 2,184.054 19,976.03 1,232.814 8.1463

12 ......... 54,267.704 1,017,202.18 5,829.505 17.7442 67 ......... 1,997.071 17,791.98 1,149.834 7.9090

13 ......... 51,665.497 962,934.48 5,811.474 17.6379 68 ......... 1,821.241 15,794.91 1,069.103 7.6726

14 ......... 49,174.931 911,268.98 5,781.170 17.5312 69 ......... 1,656.282 13,973.67 990.870 7.4368

15 ......... 46,787.571 862,094.05 5,735.474 17.4257 70 ......... 1,501.655 12,317.38 915.113 7.2025

16 ......... 44,498.663 815,306.48 5,674.545 17.3220 71 ......... 1,356.778 10,815.73 841.743 6.9716

17 ......... 42,306.381 770,807.81 5,601.247 17.2197 72 ......... 1,221.101 9,458.95 770.675 6.7462

18 ......... 40,209.103 728,501.43 5,518.558 17.1178 73 ......... 1,094.503 8,237.85 702.224 6.5266

19 ......... 38,205.739 688,292.33 5,429.914 17.0154 74 ......... 977.192 7,143.35 637.033 6.3101

20 ......... 36,294.834 650,086.59 5,338.330 16.9113 75 ......... 869.242 6,166.15 575.616 6.0937

21 ......... 34,471.748 613,791.76 5,243.569 16.8056 76 ......... 770.485 5,296.91 518.251 5.8748

22 ......... 32,732.125 579,320.01 5,145.458 16.6988 77 ......... 680.330 4,526.43 464.786 5.6533

23 ......... 31,074.479 546,587.88 5,046.484 16.5896 78 ......... 598.216 3,846.10 415.068 5.4293

24 ......... 29,497.070 515,513.40 4,948.813 16.4768 79 ......... 523.311 3,247.88 368.650 5.2064

25 ......... 27,997.360 486,016.33 4,853.726 16.3594 80 ......... 454.971 2,724.57 325.229 4.9885

26 ......... 26,572.468 458,018.97 4,762.041 16.2366 81 ......... 392.567 2,269.60 284.491 4.7814

27 ......... 25,218.187 431,446.51 4,673.115 16.1085 82 ......... 335.844 1,877.03 246.461 4.5890

28 ......... 23,930.079 406,228.32 4,585.873 15.9756 83 ......... 284.870 1,541.19 211.480 4.4101

29 ......... 22,703.334 382,298.24 4,498.656 15.8389 84 ......... 239.898 1,256.32 180.073 4.2369

30 ......... 21,534.299 359,594.91 4,410.732 15.6987 85 ......... 200.919 1,016.42 152.518 4.0589

31 ......... 20,420.051 338,060.61 4,321.927 15.5553 86 ......... 167.397 815.50 128.563 3.8717

32 ......... 19,358.475 317,640.55 4,232.734 15.4083 87 ......... 138.562 648.10 107.699 3.6774

33 ......... 18,347.300 298,282.08 4,143.391 15.2575 88 ......... 113.759 509.54 89.495 3.4791

34 ......... 17,383.771 279,934.78 4,053.544 15.1032 89 ......... 92.370 395.78 73.524 3.2847

35 ......... 16,466.053 262,551.01 3,963.624 14.9450 90 ......... 73.975 303.41 59.526 3.1016

36 ......... 15,591.483 246,084.96 3,873.151 14.7833 91 ......... 58.277 229.44 47.352 2.9370

37 ......... 14,758.098 230,493.47 3,782.218 14.6181 92 ......... 45.098 171.16 36.948 2.7953

38 ......... 13,964.657 215,735.38 3,691.544 14.4487 93 ......... 34.284 126.06 28.281 2.6771

39 ......... 13,209.886 201,770.72 3,601.757 14.2742 94 ......... 25.721 91.78 21.351 2.5682

40 ......... 12,492.634 188,560.83 3,513.546 14.0938 95 ......... 19.129 66.06 15.984 2.4532

41 ......... 11,810.896 176,068.20 3,426.696 13.9073 96 ......... 14.090 46.93 11.856 2.3305

42 ......... 11,162.665 164,257.30 3,340.888 13.7149 97 ......... 10.227 32.84 8.663 2.2110

43 ......... 10,546.198 153,094.64 3,255.977 13.5166 95 ......... 7.307 22.61 6.230 2.0947

44 ......... 9,959.624 142,548.44 3,171.603 13.3126 99 ......... 5.133 15.30 4.404 1.9815

45 ......... 9,400.882 132,588.82 3,087.129 13.1039 100 ......... 3.542 10.17 3.058 1.8714

46 ......... 8,868.530 123,187.93 3,002.438 12.8905 101 ......... 2.398 6.63 2.082 1.7644

47 ......... 8,360.917 114,319.40 2,917.136 12.6731 102 ......... 1.590 4.23 1.389 1.6605

48 ......... 7,876.635 105,958.49 2,830.992 12.4523 103 ......... 1.032 2.64 0.906 1.5597

49 ......... 7,414.937 98,081.85 2,744.373 12.2276 104 ......... 0.654 1.61 0.577 1.4619

50 ......... 6,974.903 90,666.92 2,657.431 11.9990 105 ......... 0.404 0.96 0.358 1.3671

51 ......... 6,555.478 83,692.01 2,570.144 11.7667 106 ......... 0.243 0.55 0.216 1.2751

52 ......... 6,155.674 77,136.53 2,482.505 11.5310 107 ......... 0.141 0.31 0.127 1.1861

53 ......... 5,774.335 70,980.86 2,394.294 11.2925 108 ......... 0.080 0.17 0.072 1.1000

54 ......... 5,410.334 65,206.53 2,305.261 11.0522 109 ......... 0.044 0.09 0.039 1.0166

x x x x x x x x

128
Table 11.F. -- Actuarial Functions at 6.0 Percent Interest for 1989-91 United States 

Black Males

x D N M a x D N M a

0 ......... 100,000.000 1,659,800.45 6,049.031 15.5980 55 ......... 3,005.843 32,765.42 1,151.197 9.9006

1 ......... 92,474.528 1,559,800.45 4,183.937 15.8674 56 ......... 2,782.236 29,759.57 1,097.732 9.6963

2 ......... 87,122.642 1,467,325.92 4,066.457 15.8421 57 ......... 2,571.497 26,977.34 1,044.477 9.4909

3 ......... 82,121.483 1,380,203.28 3,996.769 15.8068 58 ......... 2,373.043 24,405.84 991.580 9.2846

4 ......... 77,420.027 1,298,081.80 3,943.699 15.7667 59 ......... 2,186.343 22,032.80 939.203 9.0775

5 ......... 72,998.156 1,220,661.77 3,904.094 15.7218 60 ......... 2,010.871 19,846.45 887.487 8.8696

6 ......... 68,833.052 1,147,663.61 3,870.961 15.6731 61 ......... 1,846.372 17,835.58 836.811 8.6598

7 ......... 64,908.909 1,078,830.56 3,843.028 15.6207 62 ......... 1,692.353 15,989.21 787.303 8.4479

8 ......... 61,210.978 1,013,921.65 3,819.187 15.5644 63 ......... 1,548.148 14,296.86 738.892 8.2348

9 ......... 57,726.673 952,710.67 3,799.654 15.5038 64 ......... 1,413.046 12,748.71 691.421 8.0221

10 ......... 54,444.049 894,984.00 3,784.578 15.4386 65 ......... 1,286.556 11,335.66 644.915 7.8109

11 ......... 51,351.248 840,539.95 3,773.515 15.3684 66 ......... 1,168.342 10,049.11 599.524 7.6012

12 ......... 48,433.143 789,188.70 3,762.085 15.2944 67 ......... 1,058.239 8,880.77 555.554 7.3920

13 ......... 45,675.704 740,755.56 3,746.144 15.2177 68 ......... 955.963 7,822.53 513.178 7.1829

14 ......... 43,063.749 695,079.85 3,719.606 15.1407 69 ......... 861.175 6,866.56 472.501 6.9735

15 ......... 40,586.538 652,016.11 3,679.966 15.0648 70 ......... 773.411 6,005.39 433.484 6.7648

16 ......... 38,236.832 611,429.57 3,627.611 14.9906 71 ......... 692.202 5,231.98 396.052 6.5585

17 ......... 36,010.094 573,192.74 3,565.222 14.9176 72 ......... 617.105 4,539.78 360.136 6.3566

18 ......... 33,902.068 537,182.64 3,495.503 14.8451 73 ......... 547.908 3,922.67 325.870 6.1594

19 ......... 31,909.048 503,280.57 3,421.468 14.7723 74 ......... 484.567 3,374.76 293.543 5.9645

20 ......... 30,027.107 471,371.53 3,345.700 14.6982 75 ......... 426.971 2,890.20 263.375 5.7691

21 ......... 28,249.802 441,344.42 3,268.043 14.6229 76 ......... 374.891 2,463.23 235.463 5.5705

22 ......... 26,571.113 413,094.62 3,188.399 14.5468 77 ......... 327.902 2,088.33 209.694 5.3688

23 ......... 24,987.501 386,523.50 3,108.812 14.4687 78 ......... 285.605 1,760.43 185.958 5.1639

24 ......... 23,495.316 361,536.00 3,031.014 14.3876 79 ......... 247.486 1,474.83 164.006 4.9592

25 ......... 22,090.367 338,040.69 2,955.989 14.3026 80 ......... 213.137 1,227.34 143.664 4.7585

26 ......... 20,768.311 315,950.32 2,884.331 14.2131 81 ......... 182.168 1,014.20 124.760 4.5674

27 ......... 19,523.900 295,182.01 2,815.484 14.1190 82 ......... 154.376 832.04 107.279 4.3897

28 ......... 18,351.868 275,658.11 2,748.579 14.0207 83 ......... 129.709 677.66 91.351 4.2245

29 ......... 17,246.827 257,306.24 2,682.323 13.9190 84 ......... 108.202 547.95 77.186 4.0642

30 ......... 16,204.430 240,059.41 2,616.161 13.8144 85 ......... 89.766 439.75 64.875 3.8988

31 ......... 15,221.003 223,854.98 2,549.967 13.7070 86 ......... 74.084 349.98 54.273 3.7242

32 ......... 14,293.580 208,633.98 2,484.110 13.5963 87 ......... 60.744 275.90 45.127 3.5420

33 ......... 13,419.164 194,340.40 2,418.764 13.4823 88 ......... 49.400 215.16 37.222 3.3554

34 ......... 12,594.495 180,921.24 2,353.670 13.3651 89 ......... 39.734 165.76 30.351 3.1717

35 ......... 11,817.067 168,326.74 2,289.138 13.2444 90 ......... 31.520 126.02 24.387 2.9981

36 ......... 11,083.860 156,509.67 2,224.822 13.1205 91 ......... 24.598 94.50 19.248 2.8419

37 ......... 10,392.438 145,425.81 2,160.788 12.9934 92 ......... 18.855 69.90 14.899 2.7074

38 ......... 9,740.938 135,033.38 2,097.539 12.8625 93 ......... 14.199 51.05 11.309 2.5953

39 ......... 9,127.524 125,292.44 2,035.499 12.7269 94 ......... 10.552 36.85 8.466 2.4922

40 ......... 8,550.497 116,164.91 1,975.124 12.5857 95 ......... 7.774 26.30 6.285 2.3829

41 ......... 8,007.623 107,614.42 1,916.241 12.4390 96 ......... 5.672 18.52 4.623 2.2659

42 ......... 7,496.734 99,606.79 1,858.614 12.2867 97 ......... 4.078 12.85 3.350 2.1517

43 ......... 7,015.903 92,110.06 1,802.126 12.1288 95 ......... 2.886 8.77 2.389 2.0403

44 ......... 6,563.176 85,094.16 1,746.525 11.9654 99 ......... 2.008 5.89 1.675 1.9318

45 ......... 6,136.534 78,530.98 1,691.384 11.7973 100 ......... 1.373 3.88 1.153 1.8261

46 ......... 5,734.421 72,394.45 1,636.622 11.6245 101 ......... 0.921 2.51 0.779 1.7231

47 ......... 5,355.195 66,660.03 1,581.986 11.4477 102 ......... 0.605 1.59 0.515 1.6230

48 ......... 4,997.416 61,304.83 1,527.331 11.2673 103 ......... 0.389 0.98 0.333 1.5257

49 ......... 4,660.105 56,307.42 1,472.893 11.0829 104 ......... 0.244 0.59 0.210 1.4311

50 ......... 4,342.200 51,647.31 1,418.768 10.8943 105 ......... 0.149 0.35 0.129 1.3393

51 ......... 4,042.588 47,305.11 1,364.940 10.7017 106 ......... 0.089 0.20 0.077 1.2502

52 ......... 3,760.228 43,262.52 1,311.406 10.5053 107 ......... 0.051 0.11 0.045 1.1637

53 ......... 3,494.009 39,502.29 1,258.030 10.3057 108 ......... 0.029 0.06 0.025 1.0800

54 ......... 3,242.870 36,008.29 1,204.665 10.1038 109 ......... 0.016 0.03 0.014 0.9988

x x x x x x x x

129
Table 11.G. -- Actuarial Functions at 7.0 Percent Interest for 1989-91 United States 

Black Males

x D N M a x D N M a

0 ......... 100,000.000 1,455,619.28 4,772.570 13.5562 55 ......... 1,793.416 18,141.54 606.587 9.1156

1 ......... 91,610.280 1,355,619.28 2,924.907 13.7977 56 ......... 1,644.489 16,348.12 574.985 8.9412

2 ......... 85,501.791 1,264,009.00 2,809.613 13.7834 57 ......... 1,505.722 14,703.63 543.802 8.7652

3 ......... 79,840.463 1,178,507.21 2,741.860 13.7608 58 ......... 1,376.533 13,197.91 513.118 8.5878

4 ......... 74,566.141 1,098,666.75 2,690.746 13.7341 59 ......... 1,256.381 11,821.38 483.020 8.4091

5 ......... 69,650.194 1,024,100.61 2,652.958 13.7035 60 ......... 1,144.747 10,565.00 453.579 8.2291

6 ......... 65,062.321 954,450.42 2,621.640 13.6698 61 ......... 1,041.278 9,420.25 425.000 8.0468

7 ......... 60,779.752 889,388.09 2,595.484 13.6330 62 ......... 945.497 8,378.97 397.340 7.8620

8 ......... 56,781.390 828,608.34 2,573.368 13.5930 63 ......... 856.849 7,433.48 370.547 7.6754

9 ......... 53,048.770 771,826.95 2,555.418 13.5494 64 ......... 774.765 6,576.63 344.518 7.4885

10 ......... 49,564.564 718,778.18 2,541.693 13.5019 65 ......... 698.819 5,801.86 319.258 7.3024

11 ......... 46,312.046 669,213.62 2,531.716 13.4501 66 ......... 628.677 5,103.04 294.833 7.1171

12 ......... 43,272.074 622,901.57 2,521.503 13.3950 67 ......... 564.110 4,474.37 271.394 6.9317

13 ......... 40,427.081 579,629.50 2,507.395 13.3377 68 ......... 504.827 3,910.26 249.016 6.7457

14 ......... 37,759.050 539,202.42 2,484.126 13.2801 69 ......... 450.521 3,405.43 227.736 6.5589

15 ......... 35,254.399 501,443.37 2,449.693 13.2236 70 ......... 400.827 2,954.91 207.515 6.3720

16 ......... 32,902.985 466,188.97 2,404.641 13.1686 71 ......... 355.386 2,554.08 188.297 6.1868

17 ......... 30,697.269 433,285.98 2,351.457 13.1148 72 ......... 313.870 2,198.69 170.030 6.0051

18 ......... 28,630.159 402,588.71 2,292.580 13.0617 73 ......... 276.070 1,884.82 152.764 5.8273

19 ......... 26,695.221 373,958.55 2,230.642 13.0084 74 ......... 241.874 1,608.75 136.628 5.6512

20 ......... 24,886.008 347,263.33 2,167.846 12.9542 75 ......... 211.132 1,366.88 121.710 5.4740

21 ......... 23,194.192 322,377.33 2,104.087 12.8991 76 ......... 183.647 1,155.75 108.037 5.2933

22 ......... 21,612.036 299,183.13 2,039.307 12.8434 77 ......... 159.127 972.10 95.532 5.1090

23 ......... 20,134.036 277,571.10 1,975.179 12.7862 78 ......... 137.306 812.97 84.120 4.9209

24 ......... 18,754.755 257,437.06 1,913.078 12.7265 79 ......... 117.868 675.67 73.665 4.7324

25 ......... 17,468.480 238,682.31 1,853.750 12.6636 80 ......... 100.560 557.80 64.068 4.5469

26 ......... 16,269.547 221,213.83 1,797.614 12.5968 81 ......... 85.145 457.24 55.232 4.3701

27 ......... 15,151.755 204,944.28 1,744.185 12.5261 82 ......... 71.481 372.10 47.138 4.2055

28 ......... 14,109.081 189,792.52 1,692.748 12.4518 83 ......... 59.498 300.61 39.832 4.0525

29 ......... 13,135.595 175,683.44 1,642.286 12.3746 84 ......... 49.169 241.12 33.395 3.9038

30 ......... 12,226.338 162,547.85 1,592.366 12.2949 85 ......... 40.410 191.95 27.853 3.7500

31 ......... 11,377.006 150,321.51 1,542.889 12.2127 86 ......... 33.039 151.54 23.125 3.5867

32 ......... 10,583.951 138,944.50 1,494.124 12.1278 87 ......... 26.836 118.50 19.084 3.4156

33 ......... 9,843.609 128,360.55 1,446.190 12.0400 88 ......... 21.621 91.66 15.624 3.2395

34 ......... 9,152.331 118,516.94 1,398.886 11.9494 89 ......... 17.228 70.04 12.645 3.0656

35 ......... 8,507.124 109,364.61 1,352.429 11.8557 90 ......... 13.539 52.81 10.084 2.9009

36 ......... 7,904.714 100,857.49 1,306.561 11.7592 91 ......... 10.467 39.27 7.897 2.7524

37 ......... 7,342.343 92,952.77 1,261.321 11.6598 92 ......... 7.948 28.81 6.064 2.6245

38 ......... 6,817.735 85,610.43 1,217.052 11.5570 93 ......... 5.929 20.86 4.565 2.5181

39 ......... 6,328.699 78,792.70 1,174.036 11.4501 94 ......... 4.365 14.93 3.389 2.4203

40 ......... 5,873.201 72,464.00 1,132.566 11.3381 95 ......... 3.186 10.57 2.495 2.3163

41 ......... 5,448.905 66,590.80 1,092.497 11.2210 96 ......... 2.303 7.38 1.820 2.2046

42 ......... 5,053.587 61,141.89 1,053.650 11.0987 97 ......... 1.640 5.08 1.308 2.0953

43 ......... 4,685.256 56,088.31 1,015.928 10.9712 95 ......... 1.150 3.44 0.925 1.9886

44 ......... 4,341.961 51,403.05 979.144 10.8387 99 ......... 0.793 2.29 0.643 1.8844

45 ......... 4,021.769 47,061.09 943.006 10.7016 100 ......... 0.537 1.49 0.439 1.7827

46 ......... 3,723.108 43,039.32 907.451 10.5601 101 ......... 0.357 0.96 0.294 1.6837

47 ......... 3,444.399 39,316.21 872.310 10.4145 102 ......... 0.232 0.60 0.193 1.5871

48 ......... 3,184.239 35,871.81 837.485 10.2654 103 ......... 0.148 0.37 0.124 1.4931

49 ......... 2,941.562 32,687.57 803.123 10.1123 104 ......... 0.092 0.22 0.077 1.4016

50 ......... 2,715.278 29,746.01 769.277 9.9551 105 ......... 0.056 0.13 0.047 1.3126

51 ......... 2,504.298 27,030.73 735.932 9.7937 106 ......... 0.033 0.07 0.028 1.2261

52 ......... 2,307.611 24,526.44 703.078 9.6285 107 ......... 0.019 0.04 0.016 1.1422

53 ......... 2,124.196 22,218.83 670.628 9.4599 108 ......... 0.010 0.02 0.009 1.0607

54 ......... 1,953.090 20,094.63 638.488 9.2886 109 ......... 0.006 0.01 0.005 0.9816

x x x x x x x x

130
Table 11.H. -- Actuarial Functions at 8.0 Percent Interest for 1989-91 United States 

Black Males

x D N M a x D N M a

0 ......... 100,000.000 1,296,464.85 3,965.567 11.9646 55 ......... 1,075.183 10,143.47 323.814 8.4342

1 ......... 90,762.037 1,196,464.85 2,135.011 12.1824 56 ......... 976.770 9,068.29 305.044 8.2840

2 ......... 83,925.754 1,105,702.81 2,021.842 12.1748 57 ......... 886.066 8,091.52 286.694 8.1320

3 ......... 77,643.144 1,021,777.06 1,955.954 12.1599 58 ......... 802.542 7,205.46 268.805 7.9783

4 ......... 71,842.553 944,133.92 1,906.707 12.1417 59 ......... 725.709 6,402.91 251.420 7.8230

5 ......... 66,484.811 872,291.36 1,870.636 12.1202 60 ......... 655.105 5,677.20 234.571 7.6661

6 ......... 61,530.393 805,806.55 1,841.018 12.0961 61 ......... 590.375 5,022.10 218.368 7.5066

7 ......... 56,948.079 744,276.16 1,816.512 12.0694 62 ......... 531.107 4,431.72 202.831 7.3443

8 ......... 52,709.173 687,328.08 1,795.981 12.0400 63 ......... 476.854 3,900.62 187.919 7.1799

9 ......... 48,788.281 634,618.91 1,779.473 12.0076 64 ......... 427.180 3,423.76 173.568 7.0148

10 ......... 45,161.828 585,830.63 1,766.967 11.9718 65 ......... 381.739 2,996.58 159.769 6.8498

11 ......... 41,807.501 540,668.80 1,757.960 11.9323 66 ......... 340.243 2,614.84 146.551 6.6852

12 ......... 38,701.516 498,861.30 1,748.827 11.8900 67 ......... 302.472 2,274.60 133.983 6.5200

13 ......... 35,822.235 460,159.78 1,736.325 11.8456 68 ......... 268.179 1,972.13 122.095 6.3538

14 ......... 33,148.308 424,337.55 1,715.897 11.8012 69 ......... 237.114 1,703.95 110.895 6.1862

15 ......... 30,662.930 391,189.24 1,685.950 11.7577 70 ......... 209.006 1,466.84 100.351 6.0182

16 ......... 28,352.781 360,526.31 1,647.128 11.7157 71 ......... 183.596 1,257.83 90.423 5.8511

17 ......... 26,207.169 332,173.53 1,601.723 11.6749 72 ......... 160.646 1,074.24 81.073 5.6870

18 ......... 24,216.098 305,966.36 1,551.923 11.6348 73 ......... 139.991 913.59 72.318 5.5260

19 ......... 22,370.410 281,750.26 1,500.020 11.5948 74 ......... 121.515 773.60 64.212 5.3663

20 ......... 20,661.207 259,379.85 1,447.885 11.5540 75 ......... 105.089 652.08 56.786 5.2051

21 ......... 19,078.302 238,718.64 1,395.440 11.5126 76 ......... 90.562 546.99 50.044 5.0400

22 ......... 17,612.304 219,640.34 1,342.649 11.4708 77 ......... 77.744 456.43 43.934 4.8710

23 ......... 16,255.913 202,028.04 1,290.873 11.4280 78 ......... 66.462 378.69 38.411 4.6979

24 ......... 15,002.096 185,772.13 1,241.197 11.3831 79 ......... 56.525 312.23 33.397 4.5237

25 ......... 13,843.812 170,770.03 1,194.180 11.3355 80 ......... 47.778 255.70 28.837 4.3519

26 ......... 12,774.268 156,926.22 1,150.104 11.2846 81 ......... 40.080 207.92 24.678 4.1878

27 ......... 11,786.464 144,151.95 1,108.542 11.2303 82 ......... 33.336 167.84 20.903 4.0349

28 ......... 10,873.750 132,365.49 1,068.899 11.1729 83 ......... 27.491 134.51 17.527 3.8929

29 ......... 10,029.757 121,491.74 1,030.369 11.1131 84 ......... 22.508 107.02 14.581 3.7547

30 ......... 9,249.048 111,461.98 992.605 11.0512 85 ......... 18.327 84.51 12.067 3.6112

31 ......... 8,526.851 102,212.93 955.523 10.9872 86 ......... 14.845 66.18 9.943 3.4582

32 ......... 7,859.023 93,686.08 919.313 10.9208 87 ......... 11.947 51.34 8.144 3.2973

33 ......... 7,241.609 85,827.06 884.050 10.8519 88 ......... 9.536 39.39 6.618 3.1309

34 ......... 6,670.716 78,585.45 849.572 10.7807 89 ......... 7.528 29.86 5.316 2.9660

35 ......... 6,143.043 71,914.73 816.025 10.7067 90 ......... 5.861 22.33 4.207 2.8094

36 ......... 5,655.187 65,771.69 783.210 10.6303 91 ......... 4.489 16.47 3.269 2.6680

37 ......... 5,204.218 60,116.50 751.144 10.5515 92 ......... 3.377 11.98 2.490 2.5462

38 ......... 4,787.634 54,912.28 720.057 10.4696 93 ......... 2.496 8.60 1.859 2.4451

39 ......... 4,403.067 50,124.65 690.130 10.3840 94 ......... 1.821 6.10 1.369 2.3522

40 ......... 4,048.329 45,721.58 661.545 10.2939 95 ......... 1.317 4.28 0.999 2.2531

41 ......... 3,721.090 41,673.25 634.182 10.1992 96 ......... 0.943 2.97 0.723 2.1463

42 ......... 3,419.170 37,952.16 607.899 10.0998 97 ......... 0.665 2.02 0.515 2.0417

43 ......... 3,140.612 34,532.99 582.612 9.9956 95 ......... 0.462 1.36 0.361 1.9393

44 ......... 2,883.546 31,392.38 558.184 9.8867 99 ......... 0.316 0.90 0.249 1.8392

45 ......... 2,646.172 28,508.84 534.406 9.7736 100 ......... 0.212 0.58 0.169 1.7414

46 ......... 2,426.982 25,862.66 511.230 9.6563 101 ......... 0.139 0.37 0.112 1.6459

47 ......... 2,224.510 23,435.68 488.534 9.5352 102 ......... 0.090 0.23 0.073 1.5526

48 ......... 2,037.449 21,211.17 466.251 9.4107 103 ......... 0.057 0.14 0.046 1.4617

49 ......... 1,864.744 19,173.72 444.468 9.2822 104 ......... 0.035 0.08 0.029 1.3732

50 ......... 1,705.357 17,308.98 423.211 9.1498 105 ......... 0.021 0.05 0.017 1.2869

51 ......... 1,558.286 15,603.62 402.462 9.0133 106 ......... 0.012 0.03 0.010 1.2030

52 ......... 1,422.603 14,045.34 382.208 8.8730 107 ......... 0.007 0.01 0.006 1.1214

53 ......... 1,297.406 12,622.73 362.388 8.7292 108 ......... 0.004 0.01 0.003 1.0420

54 ......... 1,181.853 11,325.33 342.940 8.5827 109 ......... 0.002 0.00 0.002 0.9650

x x x x x x x x

131
Table 11.I. -- Actuarial Functions at 9.0 Percent Interest for 1989-91 United States 

Black Males

x D N M a x D N M a

0 ......... 100,000.000 1,169,521.99 3,433.964 10.6952 55 ......... 647.637 5,724.20 174.996 7.8386

1 ......... 89,929.358 1,069,521.99 1,620.202 10.8929 56 ......... 582.960 5,076.56 163.794 7.7083

2 ......... 82,392.896 979,592.63 1,509.101 10.8893 57 ......... 523.974 4,493.60 152.943 7.5760

3 ......... 75,525.722 897,199.74 1,445.009 10.8794 58 ......... 470.228 3,969.63 142.461 7.4419

4 ......... 69,242.189 821,674.02 1,397.545 10.8667 59 ......... 421.309 3,499.40 132.368 7.3060

5 ......... 63,490.497 752,431.83 1,363.099 10.8511 60 ......... 376.831 3,078.09 122.676 7.1684

6 ......... 58,220.138 688,941.33 1,335.074 10.8334 61 ......... 336.481 2,701.26 113.441 7.0280

7 ......... 53,389.995 630,721.19 1,312.099 10.8135 62 ......... 299.924 2,364.78 104.667 6.8846

8 ......... 48,962.576 577,331.20 1,293.028 10.7913 63 ......... 266.817 2,064.86 96.324 6.7389

9 ......... 44,904.600 528,368.62 1,277.834 10.7665 64 ......... 236.830 1,798.04 88.368 6.5921

10 ......... 41,185.476 483,464.02 1,266.429 10.7387 65 ......... 209.695 1,561.21 80.788 6.4451

11 ......... 37,776.702 442,278.54 1,258.290 10.7077 66 ......... 185.186 1,351.51 73.593 6.2981

12 ......... 34,649.348 404,501.84 1,250.113 10.6742 67 ......... 163.118 1,166.33 66.815 6.1502

13 ......... 31,777.302 369,852.49 1,239.023 10.6389 68 ......... 143.297 1,003.21 60.463 6.0009

14 ......... 29,135.534 338,075.19 1,221.068 10.6035 69 ......... 125.536 859.91 54.534 5.8499

15 ......... 26,703.766 308,939.66 1,194.987 10.5691 70 ......... 109.639 734.38 49.003 5.6981

16 ......... 24,465.369 282,235.89 1,161.488 10.5361 71 ......... 95.426 624.74 43.842 5.5468

17 ......... 22,406.473 257,770.52 1,122.668 10.5043 72 ......... 82.732 529.31 39.027 5.3979

18 ......... 20,514.210 235,364.05 1,080.481 10.4732 73 ......... 71.433 446.58 34.560 5.2517

19 ......... 18,776.811 214,849.84 1,036.916 10.4423 74 ......... 61.437 375.15 30.461 5.1062

20 ......... 17,183.073 196,073.03 993.557 10.4108 75 ......... 52.644 313.71 26.742 4.9591

21 ......... 15,721.071 178,889.96 950.341 10.3790 76 ......... 44.951 261.07 23.395 4.8078

22 ......... 14,379.899 163,168.89 907.238 10.3470 77 ......... 38.234 216.11 20.390 4.6524

23 ......... 13,150.682 148,788.99 865.353 10.3142 78 ......... 32.386 177.88 17.699 4.4925

24 ......... 12,025.028 135,638.30 825.535 10.2797 79 ......... 27.291 145.49 15.278 4.3312

25 ......... 10,994.795 123,613.28 788.194 10.2429 80 ......... 22.856 118.20 13.096 4.1716

26 ......... 10,052.283 112,618.48 753.510 10.2033 81 ......... 18.998 95.35 11.125 4.0189

27 ......... 9,189.873 102,566.20 721.104 10.1608 82 ......... 15.656 76.35 9.352 3.8766

28 ......... 8,400.450 93,376.33 690.478 10.1156 83 ......... 12.793 60.69 7.781 3.7444

29 ......... 7,677.342 84,975.88 660.985 10.0684 84 ......... 10.378 47.90 6.423 3.6157

30 ......... 7,014.792 77,298.53 632.344 10.0194 85 ......... 8.373 37.52 5.274 3.4816

31 ......... 6,407.722 70,283.74 604.477 9.9686 86 ......... 6.720 29.15 4.313 3.3380

32 ......... 5,851.683 63,876.02 577.516 9.9158 87 ......... 5.358 22.43 3.506 3.1863

33 ......... 5,342.501 58,024.34 551.500 9.8609 88 ......... 4.238 17.07 2.828 3.0289

34 ......... 4,876.175 52,681.84 526.298 9.8039 89 ......... 3.315 12.83 2.255 2.8723

35 ......... 4,449.258 47,805.66 502.001 9.7446 90 ......... 2.557 9.52 1.771 2.7232

36 ......... 4,058.338 43,356.40 478.452 9.6833 91 ......... 1.941 6.96 1.366 2.5884

37 ......... 3,700.446 39,298.07 455.651 9.6198 92 ......... 1.447 5.02 1.032 2.4723

38 ......... 3,373.003 35,597.62 433.750 9.5537 93 ......... 1.059 3.58 0.764 2.3760

39 ......... 3,073.607 32,224.62 412.859 9.4843 94 ......... 0.766 2.52 0.558 2.2876

40 ......... 2,800.052 29,151.01 393.088 9.4109 95 ......... 0.548 1.75 0.404 2.1931

41 ......... 2,550.103 26,350.96 374.335 9.3333 96 ......... 0.389 1.20 0.290 2.0909

42 ......... 2,321.697 23,800.86 356.489 9.2515 97 ......... 0.272 0.81 0.205 1.9906

43 ......... 2,112.985 21,479.16 339.476 9.1653 95 ......... 0.187 0.54 0.143 1.8923

44 ......... 1,922.234 19,366.17 323.192 9.0748 99 ......... 0.127 0.35 0.097 1.7960

45 ......... 1,747.812 17,443.94 307.486 8.9804 100 ......... 0.084 0.23 0.065 1.7018

46 ......... 1,588.329 15,696.13 292.318 8.8822 101 ......... 0.055 0.14 0.043 1.6096

47 ......... 1,442.466 14,107.80 277.602 8.7803 102 ......... 0.035 0.09 0.028 1.5196

48 ......... 1,309.047 12,665.33 263.285 8.6752 103 ......... 0.022 0.05 0.018 1.4317

49 ......... 1,187.093 11,356.29 249.418 8.5665 104 ......... 0.013 0.03 0.011 1.3459

50 ......... 1,075.668 10,169.19 236.010 8.4538 105 ......... 0.008 0.02 0.006 1.2622

51 ......... 973.884 9,093.53 223.042 8.3374 106 ......... 0.005 0.01 0.004 1.1807

52 ......... 880.930 8,119.64 210.500 8.2171 107 ......... 0.003 0.01 0.002 1.1013

53 ......... 796.032 7,238.71 198.340 8.0935 108 ......... 0.001 0.00 0.001 1.0240

54 ......... 718.481 6,442.68 186.517 7.9671 109 ......... 0.001 0.00 0.001 0.9489

x x x x x x x x

132
Table 11.J. -- Actuarial Functions at 10.0 Percent Interest for 1989-91 United States 

Black Males

x D N M a x D N M a

0 ......... 100,000.000 1,066,234.16 3,069.622 9.6623 55 ......... 391.914 3,258.68 95.671 7.3148

1 ......... 89,111.818 966,234.16 1,272.349 9.8429 56 ......... 349.568 2,866.76 88.954 7.2009

2 ......... 80,901.653 877,122.34 1,163.258 9.8418 57 ......... 311.342 2,517.19 82.506 7.0850

3 ......... 73,484.598 796,220.69 1,100.899 9.8352 58 ......... 276.866 2,205.85 76.334 6.9672

4 ......... 66,758.418 722,736.09 1,055.137 9.8261 59 ......... 245.808 1,928.99 70.446 6.8475

5 ......... 60,656.562 655,977.67 1,022.228 9.8146 60 ......... 217.859 1,683.18 64.843 6.7260

6 ......... 55,115.799 595,321.11 995.698 9.8013 61 ......... 192.763 1,465.32 59.552 6.6017

7 ......... 50,083.719 540,205.31 974.145 9.7860 62 ......... 170.258 1,272.56 54.571 6.4743

8 ......... 45,512.927 490,121.59 956.418 9.7688 63 ......... 150.087 1,102.30 49.878 6.3444

9 ......... 41,361.393 444,608.67 942.423 9.7494 64 ......... 132.008 952.21 45.443 6.2133

10 ......... 37,590.856 403,247.28 932.013 9.7273 65 ......... 115.821 820.20 41.257 6.0817

11 ......... 34,166.145 365,656.42 924.653 9.7023 66 ......... 101.354 704.38 37.319 5.9497

12 ......... 31,052.804 331,490.27 917.324 9.6751 67 ......... 88.464 603.03 33.643 5.8166

13 ......... 28,219.973 300,437.47 907.476 9.6463 68 ......... 77.008 514.56 30.230 5.6819

14 ......... 25,638.721 272,217.50 891.676 9.6174 69 ......... 66.850 437.56 27.072 5.5454

15 ......... 23,285.186 246,578.78 868.933 9.5895 70 ......... 57.854 370.71 24.153 5.4076

16 ......... 21,139.406 223,293.59 839.989 9.5629 71 ......... 49.896 312.85 21.455 5.2700

17 ......... 19,184.404 202,154.18 806.751 9.5374 72 ......... 42.865 262.96 18.960 5.1344

18 ......... 17,404.575 182,969.78 770.959 9.5127 73 ......... 36.675 220.09 16.667 5.0011

19 ......... 15,785.715 165,565.20 734.333 9.4883 74 ......... 31.256 183.42 14.582 4.8682

20 ......... 14,314.530 149,779.49 698.213 9.4635 75 ......... 26.539 152.16 12.706 4.7334

21 ......... 12,977.535 135,464.96 662.538 9.4384 76 ......... 22.455 125.62 11.035 4.5944

22 ......... 11,762.502 122,487.42 627.282 9.4134 77 ......... 18.926 103.17 9.547 4.4510

23 ......... 10,659.233 110,724.92 593.331 9.3877 78 ......... 15.885 84.24 8.227 4.3030

24 ......... 9,658.232 100,065.69 561.351 9.3607 79 ......... 13.265 68.35 7.050 4.1532

25 ......... 8,750.491 90,407.46 531.632 9.3317 80 ......... 11.008 55.09 6.000 4.0045

26 ......... 7,927.639 81,656.97 504.278 9.3003 81 ......... 9.066 44.08 5.059 3.8621

27 ......... 7,181.620 73,729.33 478.954 9.2664 82 ......... 7.404 35.02 4.221 3.7293

28 ......... 6,505.030 66,547.71 455.239 9.2302 83 ......... 5.995 27.61 3.485 3.6060

29 ......... 5,891.033 60,042.68 432.608 9.1922 84 ......... 4.819 21.62 2.854 3.4859

30 ......... 5,333.707 54,151.64 410.830 9.1527 85 ......... 3.852 16.80 2.325 3.3604

31 ......... 4,827.829 48,817.94 389.835 9.1118 86 ......... 3.064 12.95 1.887 3.2254

32 ......... 4,368.806 43,990.11 369.706 9.0691 87 ......... 2.421 9.88 1.522 3.0822

33 ......... 3,952.396 39,621.30 350.459 9.0246 88 ......... 1.897 7.46 1.219 2.9329

34 ......... 3,574.612 35,668.91 331.984 8.9784 89 ......... 1.470 5.56 0.965 2.7840

35 ......... 3,231.997 32,094.29 314.334 8.9302 90 ......... 1.124 4.09 0.752 2.6419

36 ......... 2,921.228 28,862.30 297.383 8.8802 91 ......... 0.845 2.97 0.575 2.5132

37 ......... 2,639.399 25,941.07 281.120 8.8284 92 ......... 0.624 2.12 0.431 2.4023

38 ......... 2,383.974 23,301.67 265.641 8.7743 93 ......... 0.453 1.50 0.317 2.3106

39 ......... 2,152.618 20,917.70 251.010 8.7173 94 ......... 0.324 1.05 0.229 2.2264

40 ......... 1,943.205 18,765.08 237.289 8.6568 95 ......... 0.230 0.72 0.165 2.1361

41 ......... 1,753.654 16,821.87 224.393 8.5925 96 ......... 0.162 0.49 0.117 2.0381

42 ......... 1,582.070 15,068.22 212.232 8.5244 97 ......... 0.112 0.33 0.082 1.9419

43 ......... 1,426.758 13,486.15 200.745 8.4523 95 ......... 0.077 0.22 0.057 1.8474

44 ......... 1,286.157 12,059.39 189.849 8.3763 99 ......... 0.051 0.14 0.038 1.7547

45 ......... 1,158.821 10,773.23 179.436 8.2967 100 ......... 0.034 0.09 0.026 1.6639

46 ......... 1,043.508 9,614.41 169.471 8.2135 101 ......... 0.022 0.06 0.017 1.5749

47 ......... 939.063 8,570.90 159.890 8.1271 102 ......... 0.014 0.03 0.011 1.4879

48 ......... 844.458 7,631.84 150.654 8.0376 103 ......... 0.009 0.02 0.007 1.4028

49 ......... 758.825 6,787.38 141.790 7.9446 104 ......... 0.005 0.01 0.004 1.3196

50 ......... 681.348 6,028.56 133.297 7.8480 105 ......... 0.003 0.01 0.002 1.2384

51 ......... 611.268 5,347.21 125.158 7.7477 106 ......... 0.002 0.00 0.001 1.1591

52 ......... 547.898 4,735.94 117.358 7.6438 107 ......... 0.001 0.00 0.001 1.0819

53 ......... 490.594 4,188.04 109.863 7.5367 108 ......... 0.001 0.00 0.000 1.0066

54 ......... 438.774 3,697.45 102.643 7.4268 109 ......... 0.000 0.00 0.000 0.9333

x x x x x x x x

133
Table 11.K. -- Actuarial Functions at 11.0 Percent Interest for 1989-91 United States 

Black Males

x D N M a x D N M a

0 ......... 100,000.000 980,731.63 2,810.379 8.8073 55 ......... 238.246 1,870.55 52.876 6.8513

1 ......... 88,309.009 880,731.63 1,029.298 8.9733 56 ......... 210.589 1,632.30 48.829 6.7511

2 ......... 79,450.532 792,422.62 922.164 8.9738 57 ......... 185.871 1,421.71 44.980 6.6489

3 ......... 71,516.367 712,972.08 861.475 8.9694 58 ......... 163.800 1,235.84 41.329 6.5448

4 ......... 64,385.024 641,455.72 817.340 8.9628 59 ......... 144.115 1,072.04 37.876 6.4388

5 ......... 57,973.073 577,070.69 785.887 8.9541 60 ......... 126.578 927.93 34.621 6.3309

6 ......... 52,202.866 519,097.62 760.759 8.9439 61 ......... 110.988 801.35 31.575 6.2202

7 ......... 47,009.379 466,894.75 740.530 8.9319 62 ......... 97.147 690.36 28.733 6.1063

8 ......... 42,334.303 419,885.38 724.040 8.9183 63 ......... 84.866 593.21 26.079 5.9900

9 ......... 38,126.111 377,551.07 711.140 8.9027 64 ......... 73.971 508.35 23.594 5.8723

10 ......... 34,338.339 339,424.96 701.631 8.8847 65 ......... 64.316 434.38 21.269 5.7538

11 ......... 30,928.777 305,086.62 694.968 8.8642 66 ......... 55.775 370.06 19.102 5.6349

12 ......... 27,857.189 274,157.85 688.394 8.8415 67 ......... 48.243 314.29 17.098 5.5146

13 ......... 25,087.811 246,300.66 679.638 8.8175 68 ......... 41.618 266.04 15.253 5.3925

14 ......... 22,587.712 221,212.84 665.718 8.7935 69 ......... 35.802 224.43 13.562 5.2685

15 ......... 20,329.435 198,625.13 645.863 8.7703 70 ......... 30.705 188.62 12.013 5.1430

16 ......... 18,289.763 178,295.70 620.820 8.7484 71 ......... 26.243 157.92 10.594 5.0175

17 ......... 16,448.766 160,005.93 592.322 8.7275 72 ......... 22.342 131.67 9.293 4.8935

18 ......... 14,788.296 143,557.17 561.910 8.7075 73 ......... 18.943 109.33 8.109 4.7715

19 ......... 13,291.950 128,768.87 531.071 8.6877 74 ......... 15.999 90.39 7.041 4.6497

20 ......... 11,944.589 115,476.92 500.930 8.6677 75 ......... 13.462 74.39 6.090 4.5258

21 ......... 10,731.391 103,532.33 471.430 8.6476 76 ......... 11.288 60.93 5.250 4.3977

22 ......... 9,639.028 92,800.94 442.538 8.6276 77 ......... 9.428 49.64 4.509 4.2651

23 ......... 8,656.239 83,161.91 414.968 8.6072 78 ......... 7.842 40.21 3.857 4.1277

24 ......... 7,772.676 74,505.68 389.231 8.5856 79 ......... 6.489 32.37 3.282 3.9882

25 ......... 6,978.709 66,733.00 365.529 8.5624 80 ......... 5.337 25.88 2.772 3.8493

26 ......... 6,265.507 59,754.29 343.911 8.5370 81 ......... 4.356 20.54 2.320 3.7162

27 ......... 5,624.767 53,488.78 324.076 8.5095 82 ......... 3.525 16.19 1.921 3.5920

28 ......... 5,048.950 47,864.02 305.669 8.4800 83 ......... 2.828 12.66 1.574 3.4768

29 ......... 4,531.197 42,815.07 288.262 8.4490 84 ......... 2.253 9.83 1.279 3.3645

30 ......... 4,065.560 38,283.87 271.663 8.4166 85 ......... 1.785 7.58 1.034 3.2467

31 ......... 3,646.807 34,218.31 255.803 8.3831 86 ......... 1.407 5.80 0.833 3.1196

32 ......... 3,270.344 30,571.50 240.735 8.3481 87 ......... 1.102 4.39 0.667 2.9842

33 ......... 2,931.978 27,301.16 226.458 8.3115 88 ......... 0.856 3.29 0.530 2.8425

34 ......... 2,627.840 24,369.18 212.876 8.2735 89 ......... 0.657 2.43 0.416 2.7007

35 ......... 2,354.565 21,741.34 200.018 8.2337 90 ......... 0.498 1.77 0.322 2.5650

36 ......... 2,108.992 19,386.78 187.780 8.1924 91 ......... 0.371 1.28 0.244 2.4420

37 ......... 1,888.358 17,277.78 176.145 8.1496 92 ......... 0.272 0.91 0.182 2.3359

38 ......... 1,690.248 15,389.43 165.170 8.1048 93 ......... 0.195 0.63 0.132 2.2484

39 ......... 1,512.466 13,699.18 154.890 8.0575 94 ......... 0.139 0.44 0.095 2.1681

40 ......... 1,353.028 12,186.71 145.336 8.0070 95 ......... 0.097 0.30 0.068 2.0818

41 ......... 1,210.046 10,833.68 136.438 7.9531 96 ......... 0.068 0.20 0.048 1.9878

42 ......... 1,081.816 9,623.64 128.122 7.8958 97 ......... 0.047 0.14 0.033 1.8954

43 ......... 966.825 8,541.82 120.338 7.8349 95 ......... 0.032 0.09 0.023 1.8045

44 ......... 863.696 7,575.00 113.021 7.7704 99 ......... 0.021 0.06 0.015 1.7152

45 ......... 771.175 6,711.30 106.091 7.7027 100 ......... 0.014 0.04 0.010 1.6276

46 ......... 688.181 5,940.13 99.519 7.6316 101 ......... 0.009 0.02 0.007 1.5416

47 ......... 613.721 5,251.95 93.258 7.5575 102 ......... 0.005 0.01 0.004 1.4574

48 ......... 546.920 4,638.22 87.276 7.4806 103 ......... 0.003 0.01 0.003 1.3750

49 ......... 487.032 4,091.30 81.587 7.4005 104 ......... 0.002 0.00 0.002 1.2943

50 ......... 433.365 3,604.27 76.185 7.3169 105 ......... 0.001 0.00 0.001 1.2154

51 ......... 385.289 3,170.91 71.055 7.2299 106 ......... 0.001 0.00 0.001 1.1383

52 ......... 342.235 2,785.62 66.183 7.1395 107 ......... 0.000 0.00 0.000 1.0631

53 ......... 303.681 2,443.38 61.543 7.0459 108 ......... 0.000 0.00 0.000 0.9897

54 ......... 269.157 2,139.70 57.114 6.9497 109 ......... 0.000 0.00 0.000 0.9182

x x x x x x x x

134
Table 11.L. -- Actuarial Functions at 12.0 Percent Interest for 1989-91 United States 

Black Males

x D N M a x D N M a

0 ......... 100,000.000 908,885.77 2,619.382 8.0889 55 ......... 145.478 1,082.22 29.526 6.4391

1 ......... 87,520.536 808,885.77 854.203 8.2422 56 ......... 127.442 936.75 27.077 6.3504

2 ......... 78,038.106 721,365.23 748.974 8.2438 57 ......... 111.479 809.30 24.768 6.2597

3 ......... 69,617.802 643,327.13 689.896 8.2408 58 ......... 97.364 697.82 22.598 6.1671

4 ......... 62,116.173 573,709.32 647.316 8.2361 59 ......... 84.899 600.46 20.564 6.0727

5 ......... 55,430.795 511,593.15 617.243 8.2294 60 ......... 73.902 515.56 18.663 5.9763

6 ......... 49,467.969 456,162.36 593.431 8.2214 61 ......... 64.221 441.66 16.900 5.8772

7 ......... 44,148.831 406,694.39 574.432 8.2119 62 ......... 55.711 377.44 15.271 5.7750

8 ......... 39,403.252 362,545.56 559.085 8.2009 63 ......... 48.233 321.73 13.762 5.6702

9 ......... 35,169.575 323,142.30 547.185 8.1881 64 ......... 41.666 273.49 12.363 5.5640

10 ......... 31,392.713 287,972.73 538.491 8.1732 65 ......... 35.904 231.83 11.065 5.4570

11 ......... 28,023.171 256,580.02 532.454 8.1560 66 ......... 30.858 195.93 9.866 5.3493

12 ......... 25,014.785 228,556.85 526.551 8.1369 67 ......... 26.453 165.07 8.767 5.2401

13 ......... 22,326.837 203,542.06 518.759 8.1165 68 ......... 22.616 138.61 7.764 5.1291

14 ......... 19,922.399 181,215.22 506.482 8.0961 69 ......... 19.282 116.00 6.854 5.0159

15 ......... 17,770.500 161,292.83 489.126 8.0764 70 ......... 16.389 96.72 6.027 4.9012

16 ......... 15,844.823 143,522.33 467.431 8.0580 71 ......... 13.883 80.33 5.276 4.7862

17 ......... 14,122.695 127,677.50 442.962 8.0406 72 ......... 11.713 66.44 4.594 4.6725

18 ......... 12,583.671 113,554.81 417.084 8.0240 73 ......... 9.843 54.73 3.979 4.5605

19 ......... 11,209.413 100,971.14 391.076 8.0077 74 ......... 8.239 44.89 3.429 4.4486

20 ......... 9,983.213 89,761.73 365.885 7.9913 75 ......... 6.870 36.65 2.944 4.3344

21 ......... 8,889.147 79,778.51 341.450 7.9748 76 ......... 5.709 29.78 2.519 4.2160

22 ......... 7,913.020 70,889.36 317.731 7.9586 77 ......... 4.726 24.07 2.147 4.0930

23 ......... 7,042.765 62,976.34 295.300 7.9420 78 ......... 3.896 19.34 1.823 3.9651

24 ......... 6,267.430 55,933.58 274.547 7.9245 79 ......... 3.195 15.45 1.540 3.8349

25 ......... 5,576.979 49,666.15 255.606 7.9056 80 ......... 2.604 12.25 1.291 3.7050

26 ......... 4,962.324 44,089.17 238.484 7.8848 81 ......... 2.107 9.65 1.073 3.5802

27 ......... 4,415.077 39,126.85 222.915 7.8621 82 ......... 1.690 7.54 0.882 3.4638

28 ......... 3,927.714 34,711.77 208.596 7.8377 83 ......... 1.344 5.85 0.717 3.3559

29 ......... 3,493.467 30,784.05 195.175 7.8119 84 ......... 1.061 4.51 0.578 3.2507

30 ......... 3,106.483 27,290.59 182.492 7.7850 85 ......... 0.833 3.45 0.463 3.1401

31 ......... 2,761.636 24,184.10 170.482 7.7572 86 ......... 0.651 2.62 0.370 3.0201

32 ......... 2,454.438 21,422.47 159.173 7.7281 87 ......... 0.505 1.96 0.294 2.8919

33 ......... 2,180.842 18,968.03 148.553 7.6976 88 ......... 0.389 1.46 0.232 2.7572

34 ......... 1,937.169 16,787.19 138.541 7.6658 89 ......... 0.296 1.07 0.181 2.6220

35 ......... 1,720.221 14,850.02 129.147 7.6326 90 ......... 0.222 0.78 0.139 2.4923

36 ......... 1,527.050 13,129.80 120.286 7.5981 91 ......... 0.164 0.55 0.105 2.3745

37 ......... 1,355.088 11,602.75 111.937 7.5624 92 ......... 0.119 0.39 0.077 2.2730

38 ......... 1,202.095 10,247.66 104.131 7.5248 93 ......... 0.085 0.27 0.056 2.1894

39 ......... 1,066.053 9,045.57 96.885 7.4851 94 ......... 0.060 0.19 0.040 2.1127

40 ......... 945.159 7,979.51 90.212 7.4425 95 ......... 0.042 0.13 0.028 2.0301

41 ......... 837.732 7,034.35 84.051 7.3969 96 ......... 0.029 0.08 0.020 1.9399

42 ......... 742.269 6,196.62 78.346 7.3482 97 ......... 0.020 0.06 0.014 1.8510

43 ......... 657.447 5,454.35 73.052 7.2963 95 ......... 0.013 0.04 0.009 1.7635

44 ......... 582.075 4,796.90 68.121 7.2410 99 ......... 0.009 0.02 0.006 1.6774

45 ......... 515.082 4,214.83 63.493 7.1828 100 ......... 0.006 0.01 0.004 1.5927

46 ......... 455.544 3,699.75 59.142 7.1216 101 ......... 0.004 0.01 0.003 1.5097

47 ......... 402.628 3,244.20 55.035 7.0576 102 ......... 0.002 0.01 0.002 1.4281

48 ......... 355.600 2,841.58 51.146 6.9909 103 ......... 0.001 0.00 0.001 1.3482

49 ......... 313.834 2,485.98 47.480 6.9213 104 ......... 0.001 0.00 0.001 1.2699

50 ......... 276.759 2,172.14 44.030 6.8485 105 ......... 0.000 0.00 0.000 1.1932

51 ......... 243.859 1,895.38 40.783 6.7724 106 ......... 0.000 0.00 0.000 1.1183

52 ......... 214.675 1,651.52 37.726 6.6931 107 ......... 0.000 0.00 0.000 1.0450

53 ......... 188.790 1,436.85 34.842 6.6108 108 ......... 0.000 0.00 0.000 0.9734

54 ......... 165.834 1,248.06 32.113 6.5260 109 ......... 0.000 0.00 0.000 0.9036

x x x x x x x x

135
Table 12.A. -- Actuarial Functions at 1.0 Percent Interest for 1989-91 United States 

Black Females

x D N M a x D N M a

0 ......... 100,000.000 5,176,403.20 48,748.483 50.7640 55 ......... 50,212.188 1,086,611.17 39,453.661 20.6404

1 ......... 97,382.178 5,076,403.20 47,120.760 51.1287 56 ......... 49,228.730 1,036,398.98 38,967.354 20.0527

2 ......... 96,308.205 4,979,021.02 47,010.967 50.6988 57 ......... 48,227.498 987,170.25 38,453.535 19.4690

3 ......... 95,288.658 4,882,712.81 46,944.967 50.2413 58 ......... 47,204.207 938,942.75 37,907.744 18.8911

4 ......... 94,297.157 4,787,424.16 46,896.918 49.7695 59 ......... 46,154.198 891,738.54 37,325.104 18.3209

5 ......... 93,326.415 4,693,127.00 46,859.811 49.2872 60 ......... 45,074.117 845,584.35 36,701.995 17.7599

6 ......... 92,367.535 4,599,800.58 46,824.955 48.7989 61 ......... 43,966.754 800,510.23 36,040.910 17.2072

7 ......... 91,424.091 4,507,433.05 46,796.041 48.3025 62 ......... 42,833.732 756,543.47 35,343.203 16.6623

8 ......... 90,493.968 4,416,008.96 46,771.107 47.7989 63 ......... 41,677.699 713,709.74 34,611.266 16.1245

9 ......... 89,576.044 4,325,514.99 46,749.163 47.2887 64 ......... 40,498.040 672,032.04 33,844.257 15.5942

10 ......... 88,669.236 4,235,938.95 46,729.247 46.7724 65 ......... 39,296.280 631,534.00 33,043.468 15.0711

11 ......... 87,772.500 4,147,269.71 46,710.424 46.2502 66 ......... 38,073.382 592,237.72 32,209.642 14.5552

12 ......... 86,883.054 4,059,497.21 46,690.012 45.7237 67 ......... 36,833.368 554,164.34 31,346.593 14.0452

13 ......... 86,001.738 3,972,614.16 46,668.924 45.1923 68 ......... 35,577.577 517,330.97 30,455.488 13.5409

14 ......... 85,125.877 3,886,612.42 46,644.566 44.6572 69 ......... 34,309.322 481,753.40 29,539.486 13.0415

15 ......... 84,255.483 3,801,486.54 46,617.002 44.1186 70 ......... 33,027.312 447,444.07 28,597.173 12.5477

16 ......... 83,388.863 3,717,231.06 46,584.595 43.5771 71 ......... 31,730.815 414,416.76 27,627.679 12.0604

17 ......... 82,526.078 3,633,842.20 46,547.443 43.0327 72 ......... 30,418.163 382,685.95 26,629.193 11.5808

18 ......... 81,667.187 3,551,316.12 46,505.642 42.4852 73 ......... 29,089.700 352,267.78 25,601.900 11.1097

19 ......... 80,811.420 3,469,648.93 46,458.460 41.9351 74 ......... 27,748.646 323,178.08 24,548.863 10.6466

20 ......... 79,959.676 3,388,837.51 46,406.829 41.3818 75 ......... 26,401.426 295,429.44 23,476.382 10.1899

21 ......... 79,111.196 3,308,877.83 46,350.029 40.8257 76 ......... 25,054.692 269,028.01 22,391.048 9.7376

22 ......... 78,266.055 3,229,766.64 46,288.168 40.2665 77 ......... 23,712.052 243,973.32 21,296.474 9.2890

23 ......... 77,422.736 3,151,500.58 46,219.760 39.7051 78 ......... 22,372.834 220,261.27 20,192.029 8.8450

24 ......... 76,582.930 3,074,077.85 46,146.516 39.1405 79 ......... 21,030.473 197,888.43 19,071.182 8.4096

25 ......... 75,746.707 2,997,494.92 46,068.539 38.5726 80 ......... 19,678.667 176,857.96 17,927.598 7.9873

26 ......... 74,913.358 2,921,748.21 45,985.158 38.0017 81 ......... 18,313.155 157,179.29 16,756.924 7.5829

27 ......... 74,084.500 2,846,834.85 45,898.016 37.4269 82 ......... 16,938.702 138,866.14 15,563.790 7.1982

28 ......... 73,257.899 2,772,750.35 45,804.925 36.8492 83 ......... 15,566.903 121,927.44 14,359.701 6.8325

29 ......... 72,432.161 2,699,492.45 45,704.513 36.2693 84 ......... 14,219.307 106,360.53 13,166.233 6.4800

30 ......... 71,605.948 2,627,060.29 45,595.451 35.6877 85 ......... 12,914.898 92,141.22 12,002.609 6.1345

31 ......... 70,780.181 2,555,454.34 45,478.653 35.1041 86 ......... 11,662.123 79,226.33 10,877.704 5.7935

32 ......... 69,955.018 2,484,674.16 45,354.284 34.5182 87 ......... 10,458.135 67,564.20 9,789.183 5.4604

33 ......... 69,129.895 2,414,719.15 45,221.785 33.9302 88 ......... 9,305.591 57,106.07 8,740.184 5.1367

34 ......... 68,306.411 2,345,589.25 45,082.755 33.3392 89 ......... 8,206.192 47,800.48 7,732.920 4.8249

35 ......... 67,484.692 2,277,282.84 44,937.337 32.7452 90 ......... 7,161.548 39,594.29 6,769.525 4.5287

36 ......... 66,663.462 2,209,798.15 44,784.272 32.1486 91 ......... 6,172.772 32,432.74 5,851.656 4.2542

37 ......... 65,842.882 2,143,134.69 44,623.727 31.5492 92 ......... 5,247.713 26,259.97 4,987.713 4.0041

38 ......... 65,022.425 2,077,291.80 44,455.179 30.9473 93 ......... 4,399.823 21,012.25 4,191.781 3.7757

39 ......... 64,201.584 2,012,269.38 44,278.125 30.3430 94 ......... 3,644.738 16,612.43 3,480.258 3.5579

40 ......... 63,379.877 1,948,067.79 44,092.077 29.7364 95 ......... 2,986.939 12,967.69 2,858.546 3.3415

41 ......... 62,556.177 1,884,687.92 43,895.901 29.1279 96 ......... 2,417.824 9,980.75 2,319.004 3.1280

42 ......... 61,728.749 1,822,131.74 43,687.841 28.5184 97 ......... 1,925.737 7,562.93 1,850.856 2.9273

43 ......... 60,898.535 1,760,402.99 43,468.802 27.9071 95 ......... 1,507.299 5,637.19 1,451.485 2.7399

44 ......... 60,064.510 1,699,504.46 43,237.733 27.2947 99 ......... 1,157.874 4,129.89 1,116.984 2.5668

45 ......... 59,225.053 1,639,439.95 42,992.975 26.6815 100 ......... 874.046 2,972.02 844.620 2.4003

46 ......... 58,379.248 1,580,214.89 42,733.556 26.0681 101 ......... 647.452 2,097.97 626.680 2.2404

47 ......... 57,524.966 1,521,835.65 42,457.286 25.4552 102 ......... 469.915 1,450.52 455.554 2.0868

48 ......... 56,659.547 1,464,310.68 42,161.422 24.8440 103 ......... 333.607 980.61 323.898 1.9394

49 ......... 55,782.290 1,407,651.13 41,845.151 24.2347 104 ......... 231.233 647.00 224.827 1.7980

50 ......... 54,891.921 1,351,868.84 41,507.081 23.6278 105 ......... 156.153 415.77 152.037 1.6626

51 ......... 53,987.225 1,296,976.92 41,145.870 23.0238 106 ......... 102.501 259.61 99.931 1.5328

52 ......... 53,067.049 1,242,989.70 40,760.220 22.4230 107 ......... 65.231 157.11 63.676 1.4085

53 ......... 52,131.474 1,189,922.65 40,350.061 21.8254 108 ......... 40.129 91.88 39.219 1.2896

54 ......... 51,180.007 1,137,791.17 39,914.748 21.2312 109 ......... 23.784 51.75 23.271 1.1759

x x x x x x x x

136
Table 12.B. -- Actuarial Functions at 2.0 Percent Interest for 1989-91 United States 

Black Females

x D N M a x D N M a

0 ......... 100,000.000 3,818,850.73 25,120.574 37.1885 55 ......... 29,206.213 555,392.07 18,316.173 18.0162

1 ......... 96,427.451 3,718,850.73 23,508.809 37.5663 56 ......... 28,353.452 526,185.85 18,036.083 17.5581

2 ......... 94,429.066 3,622,423.28 23,401.158 37.3613 57 ......... 27,504.468 497,832.40 17,743.048 17.1001

3 ......... 92,513.438 3,527,994.22 23,337.080 37.1349 58 ......... 26,656.948 470,327.93 17,434.831 16.6437

4 ......... 90,653.256 3,435,480.78 23,290.888 36.8969 59 ......... 25,808.462 443,670.99 17,109.031 16.1909

5 ......... 88,840.418 3,344,827.52 23,255.565 36.6498 60 ......... 24,957.401 417,862.52 16,764.018 15.7430

6 ......... 87,065.594 3,255,987.11 23,222.710 36.3969 61 ......... 24,105.588 392,905.12 16,401.566 15.2993

7 ......... 85,331.438 3,168,921.51 23,195.722 36.1366 62 ......... 23,254.149 368,799.53 16,022.785 14.8595

8 ......... 83,635.228 3,083,590.07 23,172.678 35.8695 63 ......... 22,404.717 345,545.39 15,629.317 14.4229

9 ......... 81,975.240 2,999,954.85 23,152.596 35.5959 64 ......... 21,557.130 323,140.67 15,221.038 13.9900

10 ......... 80,349.835 2,917,979.61 23,134.548 35.3159 65 ......... 20,712.359 301,583.54 14,798.957 13.5606

11 ......... 78,757.458 2,837,629.77 23,117.659 35.0300 66 ......... 19,871.049 280,871.18 14,363.771 13.1347

12 ......... 77,195.059 2,758,872.31 23,099.523 34.7390 67 ......... 19,035.398 261,000.13 13,917.749 12.7113

13 ......... 75,662.877 2,681,677.25 23,080.971 34.4424 68 ......... 18,206.150 241,964.73 13,461.743 12.2903

14 ......... 74,158.071 2,606,014.38 23,059.750 34.1413 69 ......... 17,385.015 223,758.58 12,997.592 11.8708

15 ......... 72,680.215 2,531,856.31 23,035.974 33.8356 70 ......... 16,571.330 206,373.57 12,524.790 11.4537

16 ......... 71,227.432 2,459,176.09 23,008.293 33.5257 71 ......... 15,764.731 189,802.24 12,043.119 11.0397

17 ......... 69,799.392 2,387,948.66 22,976.869 33.2116 72 ......... 14,964.407 174,037.51 11,551.907 10.6301

18 ......... 68,395.769 2,318,149.27 22,941.862 32.8932 73 ......... 14,170.559 159,073.10 11,051.479 10.2256

19 ......... 67,015.549 2,249,753.50 22,902.735 32.5706 74 ......... 13,384.765 144,902.54 10,543.539 9.8259

20 ......... 65,659.121 2,182,737.95 22,860.338 32.2435 75 ......... 12,610.071 131,517.77 10,031.291 9.4296

21 ......... 64,325.503 2,117,078.83 22,814.153 31.9120 76 ......... 11,849.511 118,907.70 9,517.987 9.0348

22 ......... 63,014.412 2,052,753.33 22,764.347 31.5759 77 ......... 11,104.569 107,058.19 9,005.388 8.6409

23 ......... 61,724.298 1,989,738.91 22,709.809 31.2359 78 ......... 10,374.681 95,953.62 8,493.238 8.2488

24 ......... 60,456.197 1,928,014.62 22,651.989 30.8911 79 ......... 9,656.595 85,578.94 7,978.576 7.8622

25 ......... 59,209.829 1,867,558.42 22,591.036 30.5414 80 ......... 8,947.297 75,922.35 7,458.623 7.4855

26 ......... 57,984.313 1,808,348.59 22,526.498 30.1869 81 ......... 8,244.808 66,975.05 6,931.572 7.1233

27 ......... 56,780.578 1,750,364.28 22,459.709 29.8268 82 ......... 7,551.248 58,730.24 6,399.674 6.7776

28 ......... 55,596.585 1,693,583.70 22,389.061 29.4620 83 ......... 6,871.665 51,179.00 5,868.156 6.4478

29 ......... 54,430.999 1,637,987.11 22,313.604 29.0929 84 ......... 6,215.262 44,307.33 5,346.490 6.1288

30 ......... 53,282.570 1,583,556.11 22,232.450 28.7200 85 ......... 5,589.760 38,092.07 4,842.857 5.8146

31 ......... 52,151.755 1,530,273.54 22,146.392 28.3427 86 ......... 4,998.055 32,502.31 4,360.754 5.5030

32 ......... 51,038.434 1,478,121.79 22,055.653 27.9610 87 ......... 4,438.118 27,504.25 3,898.819 5.1973

33 ......... 49,941.958 1,427,083.36 21,959.931 27.5748 88 ......... 3,910.297 23,066.14 3,458.020 4.8988

34 ......... 48,863.248 1,377,141.40 21,860.476 27.1836 89 ......... 3,414.512 19,155.84 3,038.907 4.6101

35 ......... 47,802.140 1,328,278.15 21,757.470 26.7870 90 ......... 2,950.632 15,741.33 2,641.979 4.3349

36 ......... 46,757.484 1,280,476.01 21,650.111 26.3855 91 ......... 2,518.313 12,790.70 2,267.515 4.0791

37 ......... 45,729.169 1,233,718.53 21,538.610 25.9788 92 ......... 2,119.926 10,272.38 1,918.506 3.8456

38 ......... 44,716.607 1,187,989.36 21,422.698 25.5671 93 ......... 1,759.977 8,152.46 1,600.125 3.6321

39 ......... 43,719.242 1,143,272.75 21,302.129 25.1503 94 ......... 1,443.641 6,392.48 1,318.299 3.4280

40 ......... 42,736.551 1,099,553.51 21,176.678 24.7286 95 ......... 1,171.495 4,948.84 1,074.459 3.2244

41 ......... 41,767.597 1,056,816.96 21,045.695 24.3023 96 ......... 938.988 3,777.34 864.922 3.0228

42 ......... 40,811.068 1,015,049.36 20,908.139 23.8719 97 ......... 740.549 2,838.36 684.894 2.8328

43 ......... 39,867.457 974,238.29 20,764.745 23.4369 95 ......... 573.954 2,097.81 532.821 2.6550

44 ......... 38,935.954 934,370.84 20,614.958 22.9976 99 ......... 436.577 1,523.85 406.697 2.4905

45 ......... 38,015.399 895,434.88 20,457.852 22.5545 100 ......... 326.328 1,087.28 305.009 2.3319

46 ......... 37,105.116 857,419.48 20,292.969 22.1079 101 ......... 239.358 760.95 224.438 2.1791

47 ......... 36,203.692 820,314.37 20,119.097 21.6583 102 ......... 172.021 521.59 161.794 2.0321

48 ......... 35,309.437 784,110.67 19,934.718 21.2068 103 ......... 120.926 349.57 114.072 1.8908

49 ......... 34,421.932 748,801.24 19,739.555 20.7536 104 ......... 82.995 228.64 78.512 1.7549

50 ......... 33,540.423 714,379.31 19,532.985 20.2991 105 ......... 55.498 145.65 52.642 1.6244

51 ......... 32,664.221 680,838.88 19,314.439 19.8436 106 ......... 36.073 90.15 34.305 1.4991

52 ......... 31,792.702 648,174.66 19,083.395 19.3875 107 ......... 22.731 54.08 21.671 1.3790

53 ......... 30,925.997 616,381.96 18,840.076 18.9309 108 ......... 13.847 31.35 13.232 1.2638

54 ......... 30,063.895 585,455.96 18,584.367 18.4737 109 ......... 8.126 17.50 7.783 1.1534

x x x x x x x x

137
Table 12.C. -- Actuarial Functions at 3.0 Percent Interest for 1989-91 United States 

Black Females

x D N M a x D N M a

0 ......... 100,000.000 2,956,981.19 13,874.334 28.5698 55 ......... 17,078.013 288,374.00 8,678.770 15.8857

1 ......... 95,491.262 2,856,981.19 12,278.218 28.9188 56 ......... 16,418.406 271,295.99 8,516.581 15.5239

2 ......... 92,604.392 2,761,489.93 12,172.647 28.8203 57 ......... 15,772.162 254,877.58 8,348.543 15.1600

3 ......... 89,844.948 2,668,885.54 12,110.417 28.7055 58 ......... 15,137.751 239,105.42 8,173.515 14.7953

4 ......... 87,183.680 2,579,040.59 12,065.993 28.5817 59 ......... 14,513.629 223,967.67 7,990.299 14.4315

5 ......... 84,610.708 2,491,856.91 12,032.351 28.4508 60 ......... 13,898.764 209,454.04 7,798.161 14.0700

6 ......... 82,115.331 2,407,246.20 12,001.364 28.3154 61 ......... 13,294.056 195,555.28 7,598.271 13.7100

7 ......... 79,698.417 2,325,130.87 11,976.159 28.1741 62 ......... 12,699.984 182,261.22 7,391.404 13.3513

8 ......... 77,355.790 2,245,432.45 11,954.844 28.0273 63 ......... 12,117.279 169,561.24 7,178.603 12.9933

9 ......... 75,084.314 2,168,076.66 11,936.450 27.8752 64 ......... 11,545.681 157,443.96 6,959.934 12.6366

10 ......... 72,881.023 2,092,992.35 11,920.080 27.7179 65 ......... 10,985.533 145,898.28 6,736.069 12.2809

11 ......... 70,743.104 2,020,111.33 11,904.910 27.5556 66 ......... 10,436.991 134,912.74 6,507.493 11.9264

12 ......... 68,666.493 1,949,368.22 11,888.778 27.3889 67 ......... 9,901.008 124,475.75 6,275.501 11.5720

13 ......... 66,650.155 1,880,701.73 11,872.435 27.2175 68 ......... 9,377.747 114,574.74 6,040.618 11.2177

14 ......... 64,690.377 1,814,051.57 11,853.924 27.0421 69 ......... 8,867.852 105,197.00 5,803.861 10.8627

15 ......... 62,785.652 1,749,361.20 11,833.384 26.8624 70 ......... 8,370.736 96,329.15 5,565.033 10.5078

16 ......... 60,933.263 1,686,575.54 11,809.704 26.6791 71 ......... 7,885.983 87,958.41 5,324.087 10.1538

17 ......... 59,131.887 1,625,642.28 11,783.083 26.4918 72 ......... 7,412.961 80,072.43 5,080.754 9.8017

18 ......... 57,380.230 1,566,510.39 11,753.713 26.3005 73 ......... 6,951.558 72,659.47 4,835.262 9.4523

19 ......... 55,676.455 1,509,130.16 11,721.207 26.1054 74 ......... 6,502.327 65,707.91 4,588.505 9.1053

20 ......... 54,019.929 1,453,453.71 11,686.325 25.9059 75 ......... 6,066.505 59,205.58 4,342.071 8.7594

21 ......... 52,408.904 1,399,433.78 11,648.697 25.7022 76 ......... 5,645.266 53,139.08 4,097.526 8.4130

22 ......... 50,842.246 1,347,024.88 11,608.511 25.4942 77 ......... 5,239.003 47,493.81 3,855.688 8.0654

23 ......... 49,317.828 1,296,182.63 11,564.936 25.2822 78 ......... 4,847.130 42,254.81 3,616.407 7.7175

24 ......... 47,835.637 1,246,864.80 11,519.186 25.0656 79 ......... 4,467.832 37,407.68 3,378.288 7.3727

25 ......... 46,394.605 1,199,029.17 11,471.425 24.8442 80 ......... 4,099.469 32,939.85 3,140.056 7.0351

26 ......... 44,993.227 1,152,634.56 11,421.346 24.6180 81 ......... 3,740.927 28,840.38 2,900.916 6.7094

27 ......... 43,631.423 1,107,641.33 11,370.025 24.3863 82 ......... 3,392.973 25,099.45 2,661.921 6.3975

28 ......... 42,306.844 1,064,009.91 11,316.264 24.1498 83 ......... 3,057.642 21,706.48 2,425.414 6.0991

29 ......... 41,017.744 1,021,703.07 11,259.402 23.9088 84 ......... 2,738.716 18,648.84 2,195.546 5.8093

30 ......... 39,762.490 980,685.32 11,198.840 23.6636 85 ......... 2,439.179 15,910.12 1,975.777 5.5227

31 ......... 38,540.761 940,922.83 11,135.242 23.4137 86 ......... 2,159.804 13,470.94 1,767.447 5.2371

32 ......... 37,351.809 902,382.07 11,068.836 23.1590 87 ......... 1,899.220 11,311.14 1,569.769 4.9557

33 ......... 36,194.520 865,030.26 10,999.463 22.8995 88 ......... 1,657.101 9,411.92 1,382.968 4.6797

34 ......... 35,068.932 828,835.74 10,928.085 22.6345 89 ......... 1,432.950 7,754.82 1,207.081 4.4118

35 ......... 33,974.297 793,766.81 10,854.876 22.3637 90 ......... 1,226.254 6,321.87 1,042.122 4.1554

36 ......... 32,909.193 759,792.51 10,779.314 22.0875 91 ......... 1,036.425 5,095.61 888.009 3.9165

37 ......... 31,872.956 726,883.32 10,701.598 21.8056 92 ......... 863.996 4,059.19 745.767 3.6982

38 ......... 30,864.612 695,010.36 10,621.592 21.5180 93 ......... 710.332 3,195.19 617.268 3.4982

39 ......... 29,883.231 664,145.75 10,539.180 21.2247 94 ......... 577.001 2,484.86 504.626 3.3065

40 ......... 28,927.930 634,262.52 10,454.264 20.9256 95 ......... 463.682 1,907.86 408.114 3.1146

41 ......... 27,997.568 605,334.59 10,366.464 20.6210 96 ......... 368.047 1,444.18 325.983 2.9239

42 ......... 27,090.794 577,337.02 10,275.153 20.3112 97 ......... 287.448 1,076.13 256.104 2.7437

43 ......... 26,207.479 550,246.23 10,180.890 19.9958 95 ......... 220.621 788.68 197.649 2.5748

44 ......... 25,346.646 524,038.75 10,083.381 19.6749 99 ......... 166.185 568.06 149.640 2.4182

45 ......... 24,507.114 498,692.10 9,982.101 19.3489 100 ......... 123.012 401.88 111.307 2.2670

46 ......... 23,688.052 474,184.99 9,876.839 19.0179 101 ......... 89.352 278.86 81.230 2.1209

47 ......... 22,888.186 450,496.94 9,766.916 18.6825 102 ......... 63.592 189.51 58.072 1.9801

48 ......... 22,106.106 427,608.75 9,651.483 18.3435 103 ......... 44.269 125.92 40.602 1.8444

49 ......... 21,341.240 405,502.64 9,530.483 18.0009 104 ......... 30.089 81.65 27.710 1.7136

50 ......... 20,592.823 384,161.41 9,403.656 17.6551 105 ......... 19.924 51.56 18.423 1.5878

51 ......... 19,860.154 363,568.58 9,270.778 17.3064 106 ......... 12.825 31.64 11.903 1.4668

52 ......... 19,142.590 343,708.43 9,131.665 16.9552 107 ......... 8.003 18.81 7.455 1.3506

53 ......... 18,439.957 324,565.84 8,986.583 16.6012 108 ......... 4.828 10.81 4.513 1.2389

54 ......... 17,751.882 306,125.88 8,835.594 16.2447 109 ......... 2.806 5.98 2.632 1.1317

x x x x x x x x

138
Table 12.D. -- Actuarial Functions at 4.0 Percent Interest for 1989-91 United States 

Black Females

x D N M a x D N M a

0 ......... 100,000.000 2,383,324.21 8,333.684 22.8332 55 ......... 10,038.089 151,943.01 4,194.127 14.1366

1 ......... 94,573.077 2,283,324.21 6,752.915 23.1435 56 ......... 9,557.594 141,904.93 4,099.712 13.8473

2 ......... 90,832.101 2,188,751.13 6,649.365 23.0967 57 ......... 9,093.115 132,347.33 4,002.833 13.5547

3 ......... 87,278.107 2,097,919.03 6,588.913 23.0372 58 ......... 8,643.442 123,254.22 3,902.895 13.2599

4 ......... 83,878.516 2,010,640.93 6,546.173 22.9709 59 ......... 8,207.393 114,610.78 3,799.287 12.9643

5 ......... 80,620.364 1,926,762.41 6,514.118 22.8992 60 ......... 7,784.116 106,403.38 3,691.678 12.6693

6 ......... 77,490.339 1,846,142.05 6,484.876 22.8242 61 ......... 7,373.854 98,619.27 3,580.805 12.3742

7 ......... 74,486.384 1,768,651.71 6,461.318 22.7446 62 ......... 6,976.604 91,245.41 3,467.165 12.0788

8 ......... 71,601.795 1,694,165.32 6,441.590 22.6609 63 ......... 6,592.496 84,268.81 3,351.388 11.7825

9 ......... 68,831.017 1,622,563.53 6,424.728 22.5731 64 ......... 6,221.115 77,676.31 3,233.564 11.4859

10 ......... 66,168.808 1,553,732.51 6,409.865 22.4813 65 ......... 5,862.376 71,455.20 3,114.099 11.1888

11 ......... 63,610.213 1,487,563.70 6,396.224 22.3856 66 ......... 5,516.095 65,592.82 2,993.294 10.8912

12 ......... 61,149.300 1,423,953.49 6,381.858 22.2865 67 ......... 5,182.505 60,076.73 2,871.862 10.5922

13 ......... 58,782.990 1,362,804.19 6,367.445 22.1836 68 ......... 4,861.415 54,894.22 2,750.099 10.2918

14 ......... 56,505.937 1,304,021.20 6,351.275 22.0776 69 ......... 4,552.883 50,032.81 2,628.545 9.9893

15 ......... 54,314.863 1,247,515.26 6,333.507 21.9682 70 ......... 4,256.333 45,479.92 2,507.106 9.6852

16 ......... 52,205.541 1,193,200.40 6,313.218 21.8558 71 ......... 3,971.291 41,223.59 2,385.768 9.3804

17 ......... 50,175.048 1,140,994.86 6,290.630 21.7403 72 ......... 3,697.187 37,252.30 2,264.407 9.0758

18 ......... 48,220.557 1,090,819.81 6,265.949 21.6215 73 ......... 3,433.727 33,555.11 2,143.146 8.7722

19 ......... 46,338.865 1,042,599.25 6,238.894 21.4995 74 ......... 3,180.946 30,121.38 2,022.432 8.4693

20 ......... 44,527.849 996,260.39 6,210.142 21.3739 75 ......... 2,939.206 26,940.44 1,903.035 8.1659

21 ......... 42,784.521 951,732.54 6,179.423 21.2448 76 ......... 2,708.817 24,001.23 1,785.693 7.8604

22 ......... 41,106.472 908,948.02 6,146.933 21.1120 77 ......... 2,489.704 21,292.42 1,670.765 7.5522

23 ......... 39,490.561 867,841.55 6,112.040 20.9759 78 ......... 2,281.328 18,802.71 1,558.147 7.2420

24 ......... 37,935.412 828,350.99 6,075.759 20.8358 79 ......... 2,082.590 16,521.38 1,447.152 6.9331

25 ......... 36,438.846 790,415.57 6,038.247 20.6916 80 ......... 1,892.511 14,438.79 1,337.173 6.6294

26 ......... 34,998.398 753,976.73 5,999.293 20.5432 81 ......... 1,710.385 12,546.28 1,227.836 6.3354

27 ......... 33,612.768 718,978.33 5,959.756 20.3900 82 ......... 1,536.381 10,835.90 1,119.616 6.0529

28 ......... 32,278.952 685,365.56 5,918.738 20.2326 83 ......... 1,371.226 9,299.52 1,013.552 5.7819

29 ......... 30,994.486 653,086.61 5,875.771 20.0711 84 ......... 1,216.391 7,928.29 911.457 5.5179

30 ......... 29,757.068 622,092.12 5,830.448 19.9057 85 ......... 1,072.936 6,711.90 814.786 5.2556

31 ......... 28,565.428 592,335.06 5,783.311 19.7361 86 ......... 940.911 5,638.96 724.028 4.9931

32 ......... 27,418.013 563,769.63 5,734.566 19.5620 87 ......... 819.433 4,698.05 638.738 4.7333

33 ......... 26,313.041 536,351.61 5,684.132 19.3835 88 ......... 708.094 3,878.62 558.917 4.4775

34 ......... 25,249.608 510,038.57 5,632.740 19.1999 89 ......... 606.425 3,170.52 484.481 4.2282

35 ......... 24,226.266 484,788.97 5,580.536 19.0109 90 ......... 513.961 2,564.10 415.342 3.9889

36 ......... 23,241.123 460,562.70 5,527.173 18.8167 91 ......... 430.221 2,050.14 351.369 3.7653

37 ......... 22,292.876 437,321.58 5,472.816 18.6171 92 ......... 355.197 1,619.92 292.892 3.5606

38 ......... 21,380.038 415,028.70 5,417.396 18.4120 93 ......... 289.216 1,264.72 240.573 3.3729

39 ......... 20,501.191 393,648.66 5,360.858 18.2013 94 ......... 232.671 975.50 195.151 3.1926

40 ......... 19,654.987 373,147.47 5,303.162 17.9849 95 ......... 185.178 742.83 156.608 3.0115

41 ......... 18,839.944 353,492.48 5,244.080 17.7629 96 ......... 145.571 557.66 124.123 2.8308

42 ......... 18,054.477 334,652.54 5,183.226 17.5357 97 ......... 112.599 412.08 96.750 2.6597

43 ......... 17,297.858 316,598.06 5,121.009 17.3027 95 ......... 85.591 299.49 74.072 2.4990

44 ......... 16,568.815 299,300.20 5,057.269 17.0641 99 ......... 63.852 213.89 55.626 2.3498

45 ......... 15,865.984 282,731.39 4,991.700 16.8200 100 ......... 46.810 150.04 41.039 2.2053

46 ......... 15,188.262 266,865.41 4,924.208 16.5705 101 ......... 33.674 103.23 29.704 2.0656

47 ......... 14,534.296 251,677.14 4,854.406 16.3161 102 ......... 23.736 69.56 21.060 1.9305

48 ......... 13,902.687 237,142.85 4,781.809 16.0573 103 ......... 16.365 45.82 14.602 1.8001

49 ......... 13,292.603 223,240.16 4,706.443 15.7943 104 ......... 11.016 29.46 9.883 1.6742

50 ......... 12,703.113 209,947.56 4,628.207 15.5273 105 ......... 7.224 18.44 6.515 1.5528

51 ......... 12,133.351 197,244.44 4,547.026 15.2564 106 ......... 4.605 11.22 4.174 1.4359

52 ......... 11,582.511 185,111.09 4,462.854 14.9819 107 ......... 2.846 6.61 2.592 1.3233

53 ......... 11,050.090 173,528.58 4,375.914 14.7038 108 ......... 1.700 3.77 1.556 1.2149

54 ......... 10,535.477 162,478.49 4,286.304 14.4220 109 ......... 0.979 2.07 0.899 1.1108

x x x x x x x x

139
Table 12.E. -- Actuarial Functions at 5.0 Percent Interest for 1989-91 United States 

Black Females

x D N M a x D N M a

0 ......... 100,000.000 1,984,503.70 5,499.824 18.8450 55 ......... 5,930.253 81,159.44 2,065.518 12.6857

1 ......... 93,672.381 1,884,503.70 3,934.110 19.1180 56 ......... 5,592.614 75,229.19 2,010.271 12.4515

2 ......... 89,110.204 1,790,831.32 3,832.522 19.0968 57 ......... 5,270.150 69,636.57 1,954.123 12.2134

3 ......... 84,808.120 1,701,721.11 3,773.781 19.0655 58 ......... 4,961.820 64,366.42 1,896.753 11.9723

4 ......... 80,728.503 1,616,912.99 3,732.646 19.0290 59 ......... 4,666.633 59,404.60 1,837.842 11.7297

5 ......... 76,853.731 1,536,184.49 3,702.089 18.9884 60 ......... 4,383.810 54,737.97 1,777.240 11.4864

6 ......... 73,166.420 1,459,330.76 3,674.479 18.9454 61 ......... 4,113.211 50,354.16 1,715.394 11.2421

7 ......... 69,660.273 1,386,164.34 3,652.448 18.8989 62 ......... 3,854.558 46,240.95 1,652.608 10.9964

8 ......... 66,324.843 1,316,504.07 3,634.173 18.8493 63 ......... 3,607.650 42,386.39 1,589.251 10.7490

9 ......... 63,151.046 1,250,179.22 3,618.702 18.7967 64 ......... 3,371.994 38,778.74 1,525.387 10.5002

10 ......... 60,130.348 1,187,028.18 3,605.196 18.7409 65 ......... 3,147.287 35,406.75 1,461.251 10.2499

11 ......... 57,254.719 1,126,897.83 3,592.918 18.6822 66 ......... 2,933.178 32,259.46 1,397.013 9.9981

12 ......... 54,515.497 1,069,643.11 3,580.111 18.6209 67 ......... 2,729.546 29,326.28 1,333.056 9.7440

13 ......... 51,906.793 1,015,127.61 3,567.383 18.5567 68 ......... 2,536.048 26,596.74 1,269.537 9.4875

14 ......... 49,420.899 963,220.82 3,553.241 18.4902 69 ......... 2,352.476 24,060.69 1,206.729 9.2278

15 ......... 47,052.131 913,799.92 3,537.848 18.4210 70 ......... 2,178.304 21,708.21 1,144.579 8.9656

16 ......... 44,794.145 866,747.79 3,520.440 18.3496 71 ......... 2,013.068 19,529.91 1,083.073 8.7016

17 ......... 42,641.893 821,953.65 3,501.243 18.2757 72 ......... 1,856.275 17,516.84 1,022.140 8.4366

18 ......... 40,590.551 779,311.75 3,480.467 18.1993 73 ......... 1,707.579 15,660.57 961.837 8.1712

19 ......... 38,635.110 738,721.20 3,457.910 18.1205 74 ......... 1,566.806 13,952.99 902.378 7.9054

20 ......... 36,771.599 700,086.09 3,434.166 18.0388 75 ......... 1,433.947 12,386.18 844.129 7.6378

21 ......... 34,995.445 663,314.49 3,409.040 17.9543 76 ......... 1,308.961 10,952.23 787.426 7.3671

22 ......... 33,302.673 628,319.05 3,382.718 17.8669 77 ......... 1,191.623 9,643.27 732.420 7.0926

23 ......... 31,688.832 595,016.38 3,354.719 17.7768 78 ......... 1,081.491 8,451.65 679.031 6.8148

24 ......... 30,151.004 563,327.54 3,325.882 17.6835 79 ......... 977.874 7,370.16 626.914 6.5369

25 ......... 28,685.711 533,176.54 3,296.352 17.5868 80 ......... 880.160 6,392.28 575.766 6.2626

26 ......... 27,289.351 504,490.83 3,265.978 17.4867 81 ......... 787.882 5,512.12 525.400 5.9961

27 ......... 25,959.323 477,201.48 3,235.443 17.3827 82 ......... 700.987 4,724.24 476.024 5.7394

28 ......... 24,691.789 451,242.15 3,204.067 17.2750 83 ......... 619.676 4,023.25 428.092 5.4925

29 ......... 23,483.434 426,550.37 3,171.512 17.1639 84 ......... 544.468 3,403.58 382.393 5.2512

30 ......... 22,331.163 403,066.93 3,137.500 17.0495 85 ......... 475.683 2,859.11 339.535 5.0105

31 ......... 21,232.737 380,735.77 3,102.462 16.9315 86 ......... 413.177 2,383.43 299.680 4.7685

32 ......... 20,185.767 359,503.03 3,066.575 16.8097 87 ......... 356.406 1,970.25 262.584 4.5281

33 ......... 19,187.764 339,317.26 3,029.799 16.6840 88 ......... 305.047 1,613.85 228.197 4.2905

34 ......... 18,236.942 320,129.50 2,992.680 16.5539 89 ......... 258.760 1,308.80 196.436 4.0580

35 ......... 17,331.170 301,892.56 2,955.334 16.4191 90 ......... 217.217 1,050.04 167.215 3.8341

36 ......... 16,468.064 284,561.39 2,917.522 16.2796 91 ......... 180.094 832.82 140.436 3.6244

37 ......... 15,645.722 268,093.32 2,879.373 16.1352 92 ......... 147.272 652.73 116.190 3.4321

38 ......... 14,862.162 252,447.60 2,840.848 15.9859 93 ......... 118.773 505.46 94.704 3.2556

39 ......... 14,115.513 237,585.44 2,801.920 15.8315 94 ......... 94.641 386.68 76.228 3.0858

40 ......... 13,403.999 223,469.93 2,762.574 15.6719 95 ......... 74.606 292.04 60.699 2.9145

41 ......... 12,725.805 210,065.93 2,722.666 15.5071 96 ......... 58.090 217.44 47.736 2.7431

42 ......... 12,079.101 197,340.12 2,681.952 15.3373 97 ......... 44.505 159.35 36.917 2.5804

43 ......... 11,462.677 185,261.02 2,640.724 15.1621 95 ......... 33.508 114.84 28.039 2.4273

44 ......... 10,874.999 173,798.35 2,598.887 14.9815 99 ......... 24.759 81.33 20.886 2.2849

45 ......... 10,314.515 162,923.35 2,556.261 14.7955 100 ......... 17.978 56.57 15.284 2.1468

46 ......... 9,779.889 152,608.83 2,512.802 14.6044 101 ......... 12.810 38.60 10.972 2.0129

47 ......... 9,269.662 142,828.94 2,468.283 14.4082 102 ......... 8.943 25.79 7.715 1.8833

48 ......... 8,782.389 133,559.28 2,422.424 14.2076 103 ......... 6.107 16.84 5.305 1.7578

49 ......... 8,317.025 124,776.89 2,375.268 14.0026 104 ......... 4.072 10.74 3.561 1.6365

50 ......... 7,872.491 116,459.87 2,326.783 13.7933 105 ......... 2.645 6.66 2.328 1.5192

51 ......... 7,447.780 108,587.38 2,276.952 13.5798 106 ......... 1.670 4.02 1.479 1.4061

52 ......... 7,041.948 101,139.60 2,225.777 13.3624 107 ......... 1.022 2.35 0.911 1.2970

53 ......... 6,654.263 94,097.65 2,173.423 13.1410 108 ......... 0.605 1.33 0.542 1.1918

54 ......... 6,283.945 87,443.39 2,119.974 12.9154 109 ......... 0.345 0.72 0.311 1.0906

x x x x x x x x

140
Table 12.F. -- Actuarial Functions at 6.0 Percent Interest for 1989-91 United States 

Black Females

x D N M a x D N M a

0 ......... 100,000.000 1,696,176.15 3,990.029 15.9618 55 ......... 3,520.968 43,906.37 1,035.702 11.4700

1 ......... 92,788.679 1,596,176.15 2,439.086 16.2023 56 ......... 3,289.176 40,385.41 1,003.210 11.2783

2 ......... 87,436.810 1,503,387.47 2,339.406 16.1940 57 ......... 3,070.285 37,096.23 970.499 11.0823

3 ......... 82,430.463 1,415,950.66 2,282.312 16.1775 58 ......... 2,863.388 34,025.94 937.391 10.8831

4 ......... 77,724.983 1,333,520.20 2,242.708 16.1569 59 ......... 2,667.634 31,162.56 903.716 10.6817

5 ......... 73,296.312 1,255,795.21 2,213.565 16.1331 60 ......... 2,482.320 28,494.92 869.400 10.4792

6 ......... 69,121.381 1,182,498.90 2,187.481 16.1076 61 ......... 2,307.121 26,012.60 834.710 10.2749

7 ......... 65,188.233 1,113,377.52 2,166.864 16.0794 62 ......... 2,141.645 23,705.48 799.825 10.0688

8 ......... 61,481.393 1,048,189.29 2,149.924 16.0489 63 ......... 1,985.550 21,563.84 764.955 9.8604

9 ......... 57,987.109 986,707.89 2,135.718 16.0160 64 ......... 1,838.343 19,578.29 730.138 9.6500

10 ......... 54,692.535 928,720.78 2,123.434 15.9808 65 ......... 1,699.650 17,739.94 695.502 9.4374

11 ......... 51,585.668 874,028.25 2,112.371 15.9432 66 ......... 1,569.080 16,040.29 661.139 9.2227

12 ......... 48,654.295 822,442.58 2,100.941 15.9038 67 ......... 1,446.374 14,471.21 627.248 9.0052

13 ......... 45,889.026 773,788.29 2,089.689 15.8622 68 ......... 1,331.162 13,024.84 593.907 8.7846

14 ......... 43,279.149 727,899.26 2,077.304 15.8187 69 ......... 1,223.157 11,693.68 561.251 8.5602

15 ......... 40,816.034 684,620.11 2,063.952 15.7733 70 ......... 1,121.912 10,470.52 529.241 8.3327

16 ......... 38,490.734 643,804.08 2,048.993 15.7262 71 ......... 1,027.028 9,348.61 497.862 8.1026

17 ......... 36,295.673 605,313.34 2,032.653 15.6773 72 ......... 938.101 8,321.58 467.068 7.8707

18 ......... 34,223.684 569,017.67 2,015.136 15.6264 73 ......... 854.813 7,383.48 436.881 7.6375

19 ......... 32,267.655 534,793.99 1,996.297 15.5737 74 ......... 776.943 6,528.67 407.396 7.4030

20 ......... 30,421.540 502,526.33 1,976.653 15.5188 75 ......... 704.353 5,751.72 378.784 7.1660

21 ......... 28,678.975 472,104.79 1,956.062 15.4617 76 ......... 636.895 5,047.37 351.195 6.9250

22 ......... 27,034.269 443,425.82 1,934.694 15.4024 77 ......... 574.332 4,410.47 324.683 6.6793

23 ......... 25,481.513 416,391.55 1,912.180 15.3409 78 ......... 516.334 3,836.14 299.194 6.4296

24 ......... 24,016.194 390,910.04 1,889.211 15.2769 79 ......... 462.460 3,319.81 274.546 6.1786

25 ......... 22,633.487 366,893.84 1,865.911 15.2102 80 ......... 412.322 2,857.35 250.585 5.9299

26 ......... 21,328.607 344,260.36 1,842.172 15.1408 81 ......... 365.611 2,445.03 227.213 5.6875

27 ......... 20,097.687 322,931.75 1,818.532 15.0681 82 ......... 322.220 2,079.42 204.517 5.4534

28 ......... 18,936.020 302,834.06 1,794.469 14.9925 83 ......... 282.156 1,757.20 182.692 5.2277

29 ......... 17,839.439 283,898.04 1,769.738 14.9141 84 ......... 245.573 1,475.04 162.080 5.0065

30 ......... 16,804.065 266,058.60 1,744.144 14.8330 85 ......... 212.525 1,229.47 142.932 4.7851

31 ......... 15,826.775 249,254.54 1,718.028 14.7489 86 ......... 182.857 1,016.94 125.294 4.5614

32 ......... 14,904.422 233,427.76 1,691.530 14.6616 87 ......... 156.244 834.09 109.032 4.3383

33 ......... 14,033.877 218,523.34 1,664.632 14.5711 88 ......... 132.467 677.84 94.099 4.1170

34 ......... 13,212.614 204,489.46 1,637.739 14.4768 89 ......... 111.307 545.37 80.437 3.8997

35 ......... 12,437.929 191,276.85 1,610.937 14.3785 90 ......... 92.556 434.07 67.986 3.6898

36 ......... 11,707.015 178,838.92 1,584.057 14.2762 91 ......... 76.014 341.51 56.683 3.4928

37 ......... 11,017.490 167,131.90 1,557.193 14.1697 92 ......... 61.574 265.50 46.546 3.3119

38 ......... 10,366.985 156,114.42 1,530.320 14.0588 93 ......... 49.190 203.92 37.647 3.1456

39 ......... 9,753.277 145,747.43 1,503.423 13.9434 94 ......... 38.826 154.73 30.068 2.9853

40 ......... 9,174.275 135,994.15 1,476.492 13.8234 95 ......... 30.318 115.91 23.757 2.8231

41 ......... 8,627.919 126,819.88 1,449.435 13.6988 96 ......... 23.384 85.59 18.539 2.6602

42 ......... 8,112.203 118,191.96 1,422.093 13.5696 97 ......... 17.746 62.21 14.225 2.5053

43 ......... 7,625.595 110,079.76 1,394.665 13.4356 95 ......... 13.235 44.46 10.718 2.3593

44 ......... 7,166.388 102,454.16 1,367.096 13.2965 99 ......... 9.687 31.22 7.920 2.2233

45 ......... 6,732.918 95,287.77 1,339.271 13.1525 100 ......... 6.968 21.54 5.749 2.0911

46 ......... 6,323.709 88,554.85 1,311.170 13.0036 101 ......... 4.918 14.57 4.093 1.9627

47 ......... 5,937.249 82,231.15 1,282.656 12.8500 102 ......... 3.401 9.65 2.855 1.8381

48 ......... 5,572.082 76,293.90 1,253.560 12.6922 103 ......... 2.301 6.25 1.947 1.7173

49 ......... 5,227.045 70,721.81 1,223.924 12.5300 104 ......... 1.519 3.95 1.296 1.6003

50 ......... 4,900.990 65,494.77 1,193.739 12.3636 105 ......... 0.978 2.43 0.840 1.4870

51 ......... 4,592.847 60,593.78 1,163.010 12.1931 106 ......... 0.611 1.45 0.529 1.3775

52 ......... 4,301.613 56,000.93 1,131.749 12.0186 107 ......... 0.371 0.84 0.323 1.2717

53 ......... 4,026.447 51,699.32 1,100.070 11.8399 108 ......... 0.217 0.47 0.191 1.1696

54 ......... 3,766.499 47,672.87 1,068.034 11.6571 109 ......... 0.123 0.25 0.108 1.0711

x x x x x x x x

141
Table 12.G. -- Actuarial Functions at 7.0 Percent Interest for 1989-91 United States 

Black Females

x D N M a x D N M a

0 ......... 100,000.000 1,480,434.40 3,149.151 13.8043 55 ......... 2,100.762 24,036.72 528.267 10.4419

1 ......... 91,921.495 1,380,434.40 1,612.703 14.0175 56 ......... 1,944.124 21,935.95 509.062 10.2832

2 ......... 85,810.114 1,288,512.91 1,514.878 14.0159 57 ......... 1,797.785 19,991.83 489.908 10.1203

3 ......... 80,140.860 1,202,702.79 1,459.369 14.0074 58 ......... 1,660.968 18,194.04 470.704 9.9539

4 ......... 74,859.856 1,122,561.93 1,421.225 13.9955 59 ......... 1,532.955 16,533.08 451.352 9.7851

5 ......... 69,934.675 1,047,702.08 1,393.418 13.9812 60 ......... 1,413.133 15,000.12 431.817 9.6148

6 ......... 65,334.855 977,767.40 1,368.763 13.9655 61 ......... 1,301.121 13,586.99 412.253 9.4425

7 ......... 61,041.307 912,432.55 1,349.458 13.9478 62 ......... 1,196.512 12,285.87 392.763 9.2681

8 ......... 57,032.236 851,391.24 1,333.744 13.9282 63 ......... 1,098.936 11,089.36 373.464 9.0910

9 ......... 53,288.101 794,359.00 1,320.690 13.9069 64 ......... 1,007.953 9,990.42 354.374 8.9116

10 ......... 49,790.780 741,070.90 1,309.506 13.8837 65 ......... 923.199 8,982.47 335.561 8.7297

11 ......... 46,523.462 691,280.12 1,299.529 13.8587 66 ......... 844.312 8,059.27 317.070 8.5454

12 ......... 43,469.659 644,756.66 1,289.317 13.8323 67 ......... 771.011 7,214.96 299.004 8.3578

13 ......... 40,615.890 601,287.00 1,279.357 13.8042 68 ......... 702.964 6,443.95 281.397 8.1668

14 ......... 37,947.917 560,671.11 1,268.499 13.7748 69 ......... 639.891 5,740.98 264.313 7.9718

15 ......... 35,453.745 522,723.19 1,256.900 13.7438 70 ......... 581.440 5,101.09 247.724 7.7732

16 ......... 33,121.469 487,269.45 1,244.028 13.7116 71 ......... 527.291 4,519.65 231.613 7.5715

17 ......... 30,940.715 454,147.98 1,230.099 13.6780 72 ......... 477.133 3,992.36 215.951 7.3674

18 ......... 28,901.763 423,207.26 1,215.306 13.6430 73 ......... 430.709 3,515.23 200.741 7.1615

19 ......... 26,995.232 394,305.50 1,199.545 13.6065 74 ......... 387.814 3,084.52 186.024 6.9536

20 ......... 25,212.908 367,310.27 1,183.265 13.5683 75 ......... 348.295 2,696.70 171.875 6.7426

21 ......... 23,546.560 342,097.36 1,166.359 13.5285 76 ......... 311.994 2,348.41 158.360 6.5271

22 ......... 21,988.751 318,550.80 1,148.979 13.4870 77 ......... 278.717 2,036.41 145.494 6.3064

23 ......... 20,532.093 296,562.05 1,130.837 13.4438 78 ......... 248.230 1,757.70 133.240 6.0809

24 ......... 19,170.537 276,029.96 1,112.503 13.3987 79 ......... 220.252 1,509.47 121.501 5.8534

25 ......... 17,897.965 256,859.42 1,094.078 13.3513 80 ......... 194.538 1,289.22 110.196 5.6271

26 ......... 16,708.473 238,961.46 1,075.481 13.3018 81 ......... 170.887 1,094.68 99.272 5.4059

27 ......... 15,597.049 222,252.98 1,057.135 13.2497 82 ......... 149.198 923.79 88.763 5.1917

28 ......... 14,558.182 206,655.93 1,038.635 13.1952 83 ......... 129.426 774.59 78.752 4.9848

29 ......... 13,586.942 192,097.75 1,019.800 13.1384 84 ......... 111.593 645.17 69.386 4.7814

30 ......... 12,678.766 178,510.81 1,000.489 13.0795 85 ......... 95.672 533.57 60.766 4.5771

31 ......... 11,829.793 165,832.04 980.968 13.0182 86 ......... 81.548 437.90 52.900 4.3699

32 ......... 11,036.261 154,002.25 961.347 12.9542 87 ......... 69.028 356.35 45.715 4.1625

33 ......... 10,294.531 142,965.99 941.616 12.8876 88 ......... 57.977 287.33 39.180 3.9559

34 ......... 9,601.514 132,671.46 922.073 12.8178 89 ......... 48.260 229.35 33.256 3.7524

35 ......... 8,954.083 123,069.94 902.779 12.7446 90 ......... 39.755 181.09 27.908 3.5551

36 ......... 8,349.132 114,115.86 883.608 12.6680 91 ......... 32.345 141.33 23.098 3.3696

37 ......... 7,783.947 105,766.73 864.629 12.5878 92 ......... 25.955 108.99 18.825 3.1991

38 ......... 7,255.909 97,982.78 845.820 12.5039 93 ......... 20.541 83.03 15.109 3.0423

39 ......... 6,762.573 90,726.87 827.171 12.4160 94 ......... 16.062 62.49 11.974 2.8907

40 ......... 6,301.664 83,964.30 808.672 12.3241 95 ......... 12.425 46.43 9.388 2.7369

41 ......... 5,870.994 77,662.64 790.261 12.2282 96 ......... 9.494 34.01 7.269 2.5819

42 ......... 5,468.479 71,791.64 771.829 12.1283 97 ......... 7.137 24.51 5.534 2.4343

43 ......... 5,092.411 66,323.16 753.513 12.0239 95 ......... 5.273 17.37 4.137 2.2948

44 ......... 4,741.024 61,230.75 735.274 11.9151 99 ......... 3.824 12.10 3.032 2.1648

45 ......... 4,412.628 56,489.73 717.038 11.8018 100 ......... 2.725 8.28 2.183 2.0381

46 ......... 4,105.707 52,077.10 698.794 11.6841 101 ......... 1.905 5.55 1.542 1.9148

47 ......... 3,818.769 47,971.39 680.454 11.5620 102 ......... 1.305 3.65 1.066 1.7950

48 ......... 3,550.404 44,152.62 661.914 11.4359 103 ......... 0.875 2.34 0.721 1.6786

49 ......... 3,299.427 40,602.22 643.207 11.3058 104 ......... 0.572 1.47 0.476 1.5656

50 ......... 3,064.702 37,302.79 624.332 11.1718 105 ......... 0.365 0.90 0.306 1.4561

51 ......... 2,845.171 34,238.09 605.296 11.0338 106 ......... 0.226 0.53 0.191 1.3500

52 ......... 2,639.854 31,392.92 586.112 10.8919 107 ......... 0.136 0.31 0.116 1.2474

53 ......... 2,447.894 28,753.07 566.852 10.7460 108 ......... 0.079 0.17 0.068 1.1481

54 ......... 2,268.457 26,305.17 547.558 10.5961 109 ......... 0.044 0.09 0.038 1.0522

x x x x x x x x

142
Table 12.H. -- Actuarial Functions at 8.0 Percent Interest for 1989-91 United States 

Black Females

x D N M a x D N M a

0 ......... 100,000.000 1,314,118.93 2,657.857 12.1412 55 ......... 1,259.442 13,305.85 273.824 9.5649

1 ......... 91,070.370 1,214,118.93 1,135.634 12.3317 56 ......... 1,154.743 12,046.41 262.416 9.4321

2 ......... 84,228.395 1,123,048.56 1,039.613 12.3334 57 ......... 1,057.935 10,891.66 251.145 9.2952

3 ......... 77,935.274 1,038,820.17 985.632 12.3293 58 ......... 968.373 9,833.73 239.948 9.1549

4 ......... 72,125.539 960,884.89 948.880 12.3224 59 ......... 885.464 8,865.35 228.771 9.0121

5 ......... 66,756.364 888,759.36 922.338 12.3135 60 ......... 808.694 7,979.89 217.591 8.8676

6 ......... 61,788.132 822,002.99 899.021 12.3036 61 ......... 737.699 7,171.20 206.499 8.7210

7 ......... 57,193.145 760,214.86 880.933 12.2921 62 ......... 672.107 6,433.50 195.551 8.5721

8 ......... 52,942.029 703,021.71 866.346 12.2791 63 ......... 611.581 5,761.39 184.811 8.4205

9 ......... 49,008.391 650,079.69 854.340 12.2647 64 ......... 555.753 5,149.81 174.285 8.2664

10 ......... 45,367.949 601,071.30 844.150 12.2488 65 ......... 504.309 4,594.06 164.008 8.1096

11 ......... 41,998.354 555,703.35 835.143 12.2316 66 ......... 456.945 4,089.75 154.001 7.9502

12 ......... 38,878.231 513,704.99 826.010 12.2132 67 ......... 413.411 3,632.80 144.314 7.7874

13 ......... 35,989.537 474,826.76 817.185 12.1935 68 ......... 373.434 3,219.39 134.961 7.6210

14 ......... 33,314.113 438,837.22 807.652 12.1727 69 ......... 336.781 2,845.96 125.969 7.4505

15 ......... 30,836.313 405,523.11 797.564 12.1508 70 ......... 303.184 2,509.18 117.319 7.2761

16 ......... 28,541.050 374,686.80 786.472 12.1280 71 ......... 272.403 2,205.99 108.996 7.0983

17 ......... 26,415.006 346,145.75 774.581 12.1041 72 ......... 244.209 1,933.59 100.980 6.9178

18 ......... 24,445.827 319,730.74 762.068 12.0792 73 ......... 218.406 1,689.38 93.267 6.7350

19 ......... 22,621.817 295,284.91 748.860 12.0531 74 ......... 194.834 1,470.97 85.873 6.5499

20 ......... 20,932.610 272,663.10 735.344 12.0258 75 ......... 173.360 1,276.14 78.831 6.3612

21 ......... 19,368.141 251,730.49 721.438 11.9971 76 ......... 153.854 1,102.78 72.166 6.1677

22 ......... 17,919.300 232,362.35 707.275 11.9672 77 ......... 136.171 948.93 65.880 5.9686

23 ......... 16,577.298 214,443.05 692.628 11.9359 78 ......... 120.153 812.76 59.949 5.7643

24 ......... 15,334.684 197,865.75 677.961 11.9032 79 ......... 105.624 692.60 54.320 5.5573

25 ......... 14,184.179 182,531.06 663.360 11.8686 80 ......... 92.428 586.98 48.948 5.3506

26 ......... 13,118.898 168,346.89 648.758 11.8324 81 ......... 80.440 494.55 43.806 5.1481

27 ......... 12,132.856 155,227.99 634.487 11.7940 82 ......... 69.580 414.11 38.905 4.9516

28 ......... 11,219.869 143,095.13 620.229 11.7537 83 ......... 59.800 344.53 34.280 4.7613

29 ......... 10,374.385 131,875.26 605.847 11.7116 84 ......... 51.083 284.73 29.992 4.5739

30 ......... 9,591.304 121,500.88 591.239 11.6678 85 ......... 43.390 233.65 26.083 4.3848

31 ......... 8,866.206 111,909.57 576.608 11.6220 86 ......... 36.641 190.26 22.548 4.1924

32 ......... 8,194.881 103,043.37 562.039 11.5741 87 ......... 30.729 153.62 19.350 3.9991

33 ......... 7,573.337 94,848.49 547.524 11.5240 88 ......... 25.570 122.89 16.467 3.8059

34 ......... 6,998.106 87,275.15 533.280 11.4713 89 ......... 21.088 97.32 13.879 3.6148

35 ......... 6,465.795 80,277.04 519.347 11.4157 90 ......... 17.210 76.23 11.564 3.4292

36 ......... 5,973.132 73,811.25 505.632 11.3572 91 ......... 13.873 59.02 9.501 3.2543

37 ......... 5,517.225 67,838.12 492.180 11.2957 92 ......... 11.029 45.15 7.685 3.0932

38 ......... 5,095.334 62,320.89 478.972 11.2310 93 ......... 8.648 34.12 6.121 2.9450

39 ......... 4,704.927 57,225.56 465.996 11.1629 94 ......... 6.700 25.47 4.813 2.8015

40 ......... 4,343.663 52,520.63 453.246 11.0913 95 ......... 5.135 18.77 3.744 2.6554

41 ......... 4,009.337 48,176.97 440.673 11.0162 96 ......... 3.887 13.63 2.877 2.5078

42 ......... 3,699.878 44,167.63 428.202 10.9376 97 ......... 2.895 9.75 2.173 2.3669

43 ......... 3,413.536 40,467.75 415.924 10.8551 95 ......... 2.119 6.85 1.612 2.2335

44 ......... 3,148.568 37,054.22 403.812 10.7686 99 ......... 1.522 4.73 1.172 2.1090

45 ......... 2,903.343 33,905.65 391.813 10.6781 100 ......... 1.075 3.21 0.837 1.9875

46 ......... 2,676.387 31,002.31 379.920 10.5836 101 ......... 0.745 2.14 0.586 1.8691

47 ......... 2,466.292 28,325.92 368.075 10.4852 102 ......... 0.505 1.39 0.402 1.7537

48 ......... 2,271.741 25,859.63 356.213 10.3832 103 ......... 0.335 0.89 0.270 1.6415

49 ......... 2,091.605 23,587.89 344.354 10.2774 104 ......... 0.217 0.55 0.177 1.5323

50 ......... 1,924.817 21,496.28 332.499 10.1680 105 ......... 0.137 0.33 0.113 1.4264

51 ......... 1,770.392 19,571.47 320.654 10.0549 106 ......... 0.084 0.20 0.070 1.3235

52 ......... 1,627.425 17,801.07 308.827 9.9382 107 ......... 0.050 0.11 0.042 1.2239

53 ......... 1,495.112 16,173.65 297.064 9.8177 108 ......... 0.029 0.06 0.024 1.1274

54 ......... 1,372.688 14,678.54 285.389 9.6933 109 ......... 0.016 0.03 0.014 1.0340

x x x x x x x x

143
Table 12.I. -- Actuarial Functions at 9.0 Percent Interest for 1989-91 United States 

Black Females

x D N M a x D N M a

0 ......... 100,000.000 1,182,579.21 2,355.845 10.8258 55 ......... 758.625 7,442.55 144.103 8.8106

1 ......... 90,234.862 1,082,579.21 847.588 10.9973 56 ......... 689.178 6,683.92 137.295 8.6984

2 ......... 82,690.009 992,344.35 753.320 11.0008 57 ......... 625.609 5,994.74 130.630 8.5823

3 ......... 75,809.885 909,654.34 700.812 10.9992 58 ......... 567.392 5,369.13 124.069 8.4628

4 ......... 69,514.932 833,844.45 665.390 10.9952 59 ......... 514.054 4,801.74 117.580 8.3409

5 ......... 63,749.820 764,329.52 640.043 10.9895 60 ......... 465.179 4,287.69 111.149 8.2173

6 ......... 58,464.011 700,579.70 617.981 10.9831 61 ......... 420.448 3,822.51 104.828 8.0915

7 ......... 53,619.750 642,115.69 601.023 10.9754 62 ......... 379.549 3,402.06 98.645 7.9634

8 ......... 49,178.880 588,495.94 587.473 10.9664 63 ......... 342.201 3,022.51 92.635 7.8326

9 ......... 45,107.189 539,317.06 576.422 10.9563 64 ......... 308.110 2,680.31 86.800 7.6992

10 ......... 41,373.449 494,209.87 567.129 10.9451 65 ......... 277.025 2,372.20 81.155 7.5631

11 ......... 37,949.154 452,836.42 558.991 10.9327 66 ......... 248.704 2,095.18 75.708 7.4244

12 ......... 34,807.561 414,887.27 550.814 10.9195 67 ......... 222.945 1,846.47 70.484 7.2822

13 ......... 31,925.714 380,079.70 542.986 10.9051 68 ......... 199.539 1,623.53 65.486 7.1364

14 ......... 29,281.267 348,153.99 534.607 10.8900 69 ......... 178.303 1,423.99 60.726 6.9863

15 ......... 26,854.762 318,872.72 525.822 10.8740 70 ......... 159.043 1,245.69 56.188 6.8324

16 ......... 24,627.825 292,017.96 516.251 10.8572 71 ......... 141.585 1,086.64 51.862 6.6748

17 ......... 22,584.168 267,390.14 506.083 10.8397 72 ......... 125.766 945.06 47.734 6.5144

18 ......... 20,708.821 244,805.97 495.484 10.8213 73 ......... 111.446 819.29 43.798 6.3514

19 ......... 18,987.832 224,097.15 484.398 10.8021 74 ......... 98.506 707.84 40.060 6.1858

20 ......... 17,408.788 205,109.32 473.157 10.7819 75 ......... 86.845 609.34 36.532 6.0164

21 ......... 15,959.906 187,700.53 461.698 10.7608 76 ......... 76.366 522.49 33.224 5.8420

22 ......... 14,630.552 171,740.62 450.134 10.7385 77 ......... 66.969 446.13 30.133 5.6617

23 ......... 13,410.676 157,110.07 438.284 10.7153 78 ......... 58.549 379.16 27.243 5.4759

24 ......... 12,291.616 143,699.39 426.529 10.6908 79 ......... 50.997 320.61 24.525 5.2868

25 ......... 11,265.116 131,407.78 414.932 10.6650 80 ......... 44.217 269.61 21.955 5.0975

26 ......... 10,323.478 120,142.66 403.442 10.6378 81 ......... 38.128 225.40 19.518 4.9115

27 ......... 9,459.953 109,819.18 392.314 10.6089 82 ......... 32.678 187.27 17.216 4.7306

28 ......... 8,667.842 100,359.23 381.300 10.5783 83 ......... 27.828 154.59 15.063 4.5552

29 ......... 7,941.140 91,691.39 370.291 10.5464 84 ......... 23.553 126.76 13.087 4.3820

30 ......... 7,274.370 83,750.25 359.212 10.5131 85 ......... 19.822 103.21 11.301 4.2067

31 ......... 6,662.739 76,475.88 348.217 10.4781 86 ......... 16.586 83.39 9.701 4.0276

32 ......... 6,101.757 69,813.14 337.369 10.4415 87 ......... 13.782 66.80 8.266 3.8470

33 ......... 5,587.233 63,711.38 326.660 10.4030 88 ......... 11.363 53.02 6.985 3.6659

34 ......... 5,115.490 58,124.15 316.248 10.3624 89 ......... 9.285 41.66 5.846 3.4863

35 ......... 4,683.019 53,008.66 306.157 10.3193 90 ......... 7.508 32.37 4.836 3.3113

36 ......... 4,286.506 48,325.64 296.315 10.2739 91 ......... 5.997 24.86 3.944 3.1460

37 ......... 3,923.008 44,039.14 286.750 10.2259 92 ......... 4.724 18.87 3.166 2.9936

38 ......... 3,589.785 40,116.13 277.444 10.1751 93 ......... 3.670 14.14 2.502 2.8534

39 ......... 3,284.323 36,526.34 268.387 10.1214 94 ......... 2.817 10.47 1.952 2.7173

40 ......... 3,004.322 33,242.02 259.568 10.0647 95 ......... 2.139 7.65 1.507 2.5784

41 ......... 2,747.642 30,237.70 250.951 10.0050 96 ......... 1.604 5.52 1.149 2.4376

42 ......... 2,512.304 27,490.06 242.483 9.9422 97 ......... 1.184 3.91 0.861 2.3029

43 ......... 2,296.606 24,977.75 234.223 9.8759 95 ......... 0.859 2.73 0.634 2.1752

44 ......... 2,098.904 22,681.14 226.148 9.8062 99 ......... 0.611 1.87 0.457 2.0559

45 ......... 1,917.674 20,582.24 218.223 9.7329 100 ......... 0.428 1.26 0.324 1.9393

46 ......... 1,751.551 18,664.57 210.440 9.6560 101 ......... 0.293 0.83 0.225 1.8254

47 ......... 1,599.247 16,913.02 202.759 9.5756 102 ......... 0.197 0.54 0.153 1.7142

48 ......... 1,459.577 15,313.77 195.138 9.4919 103 ......... 0.130 0.34 0.102 1.6059

49 ......... 1,331.513 13,854.19 187.588 9.4049 104 ......... 0.083 0.21 0.066 1.5004

50 ......... 1,214.094 12,522.68 180.111 9.3144 105 ......... 0.052 0.13 0.042 1.3978

51 ......... 1,106.445 11,308.59 172.708 9.2207 106 ......... 0.032 0.07 0.026 1.2981

52 ......... 1,007.763 10,202.14 165.385 9.1235 107 ......... 0.019 0.04 0.015 1.2013

53 ......... 917.336 9,194.38 158.167 9.0229 108 ......... 0.011 0.02 0.009 1.1074

54 ......... 834.495 8,277.04 151.069 8.9186 109 ......... 0.006 0.01 0.005 1.0164

x x x x x x x x

144
Table 12.J. -- Actuarial Functions at 10.0 Percent Interest for 1989-91 United States 

Black Females

x D N M a x D N M a

0 ......... 100,000.000 1,076,238.31 2,160.154 9.7624 55 ......... 459.079 4,203.71 76.923 8.1568

1 ......... 89,414.545 976,238.31 665.609 9.9181 56 ......... 413.262 3,744.63 72.841 8.0612

2 ......... 81,193.388 886,823.76 573.047 9.9224 57 ......... 371.732 3,331.37 68.880 7.9618

3 ......... 73,761.082 805,630.37 521.957 9.9222 58 ......... 334.076 2,959.64 65.017 7.8592

4 ......... 67,021.378 731,869.29 487.806 9.9199 59 ......... 299.919 2,625.56 61.231 7.7542

5 ......... 60,904.310 664,847.91 463.591 9.9163 60 ......... 268.936 2,325.65 57.513 7.6476

6 ......... 55,346.669 603,943.60 442.705 9.9120 61 ......... 240.865 2,056.71 53.892 7.5388

7 ......... 50,299.246 548,596.93 426.797 9.9067 62 ......... 215.459 1,815.84 50.382 7.4278

8 ......... 45,713.991 498,297.69 414.201 9.9003 63 ......... 192.491 1,600.39 47.002 7.3141

9 ......... 41,547.995 452,583.70 404.023 9.8930 64 ......... 171.739 1,407.89 43.749 7.1978

10 ......... 37,762.423 411,035.70 395.541 9.8848 65 ......... 153.009 1,236.15 40.631 7.0790

11 ......... 34,322.115 373,273.28 388.181 9.8756 66 ......... 136.118 1,083.15 37.650 6.9574

12 ......... 31,194.594 338,951.16 380.852 9.8657 67 ......... 120.910 947.03 34.817 6.8325

13 ......... 28,351.770 307,756.57 373.900 9.8549 68 ......... 107.233 826.12 32.131 6.7040

14 ......... 25,766.963 279,404.80 366.527 9.8435 69 ......... 94.949 718.88 29.596 6.5712

15 ......... 23,416.851 253,637.84 358.866 9.8314 70 ......... 83.923 623.94 27.202 6.4346

16 ......... 21,279.777 230,220.98 350.597 9.8188 71 ......... 74.032 540.01 24.940 6.2943

17 ......... 19,336.547 208,941.21 341.891 9.8055 72 ......... 65.163 465.98 22.801 6.1510

18 ......... 17,569.686 189,604.66 332.898 9.7916 73 ......... 57.218 400.82 20.780 6.0051

19 ......... 15,963.122 172,034.97 323.578 9.7770 74 ......... 50.115 343.60 18.878 5.8563

20 ......... 14,502.564 156,071.85 314.214 9.7617 75 ......... 43.780 293.49 17.100 5.7036

21 ......... 13,174.690 141,569.29 304.755 9.7455 76 ......... 38.148 249.70 15.447 5.5457

22 ......... 11,967.532 128,394.60 295.296 9.7286 77 ......... 33.150 211.56 13.917 5.3819

23 ......... 10,869.970 116,427.07 285.691 9.7109 78 ......... 28.718 178.41 12.499 5.2123

24 ......... 9,872.349 105,557.10 276.249 9.6922 79 ......... 24.787 149.69 11.178 5.0391

25 ......... 8,965.633 95,684.75 267.020 9.6724 80 ......... 21.296 124.90 9.941 4.8652

26 ......... 8,141.514 86,719.11 257.958 9.6515 81 ......... 18.196 103.61 8.778 4.6938

27 ......... 7,392.681 78,577.60 249.262 9.6291 82 ......... 15.454 85.41 7.689 4.5269

28 ......... 6,712.090 71,184.92 240.733 9.6055 83 ......... 13.040 69.96 6.680 4.3647

29 ......... 6,093.452 64,472.83 232.286 9.5807 84 ......... 10.937 56.92 5.763 4.2042

30 ......... 5,531.078 58,379.38 223.862 9.5548 85 ......... 9.121 45.98 4.941 4.0413

31 ......... 5,019.969 52,848.30 215.578 9.5276 86 ......... 7.562 36.86 4.211 3.8742

32 ......... 4,555.509 47,828.33 207.479 9.4990 87 ......... 6.227 29.30 3.563 3.7051

33 ......... 4,133.449 43,272.82 199.556 9.4689 88 ......... 5.087 23.07 2.990 3.5351

34 ......... 3,750.048 39,139.37 191.924 9.4370 89 ......... 4.119 17.98 2.484 3.3659

35 ......... 3,401.805 35,389.32 184.593 9.4031 90 ......... 3.301 13.86 2.040 3.2006

36 ......... 3,085.465 31,987.52 177.509 9.3672 91 ......... 2.612 10.56 1.652 3.0441

37 ......... 2,798.146 28,902.05 170.686 9.3290 92 ......... 2.039 7.95 1.316 2.8998

38 ......... 2,537.192 26,103.91 164.109 9.2885 93 ......... 1.570 5.91 1.032 2.7669

39 ......... 2,300.195 23,566.72 157.766 9.2455 94 ......... 1.194 4.34 0.799 2.6377

40 ......... 2,084.966 21,266.52 151.646 9.1999 95 ......... 0.898 3.15 0.612 2.5054

41 ......... 1,889.498 19,181.56 145.720 9.1517 96 ......... 0.668 2.25 0.463 2.3710

42 ......... 1,711.955 17,292.06 139.950 9.1008 97 ......... 0.488 1.58 0.344 2.2421

43 ......... 1,550.745 15,580.10 134.372 9.0468 95 ......... 0.351 1.09 0.251 2.1197

44 ......... 1,404.366 14,029.36 128.970 8.9898 99 ......... 0.248 0.74 0.180 2.0053

45 ......... 1,271.442 12,624.99 123.715 8.9297 100 ......... 0.172 0.50 0.126 1.8932

46 ......... 1,150.743 11,353.55 118.602 8.8663 101 ......... 0.117 0.32 0.087 1.7836

47 ......... 1,041.129 10,202.81 113.601 8.7997 102 ......... 0.078 0.21 0.059 1.6764

48 ......... 941.565 9,161.68 108.685 8.7303 103 ......... 0.051 0.13 0.039 1.5718

49 ......... 851.142 8,220.11 103.859 8.6577 104 ......... 0.032 0.08 0.025 1.4697

50 ......... 769.029 7,368.97 99.123 8.5822 105 ......... 0.020 0.05 0.016 1.3703

51 ......... 694.471 6,599.94 94.476 8.5036 106 ......... 0.012 0.03 0.010 1.2735

52 ......... 626.782 5,905.47 89.921 8.4219 107 ......... 0.007 0.02 0.006 1.1794

53 ......... 565.354 5,278.69 85.473 8.3370 108 ......... 0.004 0.01 0.003 1.0880

54 ......... 509.624 4,713.34 81.139 8.2487 109 ......... 0.002 0.00 0.002 0.9994

x x x x x x x x

145
Table 12.K. -- Actuarial Functions at 11.0 Percent Interest for 1989-91 United States 

Black Females

x D N M a x D N M a

0 ......... 100,000.000 988,641.96 2,026.472 8.8864 55 ......... 279.075 2,396.21 41.613 7.5862

1 ......... 88,609.009 888,641.96 545.391 9.0288 56 ......... 248.960 2,117.13 39.154 7.5039

2 ......... 79,737.034 800,032.95 454.489 9.0334 57 ......... 221.923 1,868.17 36.789 7.4181

3 ......... 71,785.445 720,295.92 404.768 9.0340 58 ......... 197.646 1,646.25 34.504 7.3293

4 ......... 64,638.636 648,510.47 371.832 9.0329 59 ......... 175.840 1,448.60 32.284 7.2382

5 ......... 58,209.860 583,871.84 348.687 9.0305 60 ......... 156.254 1,272.76 30.124 7.1455

6 ......... 52,421.534 525,661.98 328.906 9.0276 61 ......... 138.684 1,116.51 28.039 7.0507

7 ......... 47,211.676 473,240.44 313.974 9.0238 62 ......... 122.938 977.83 26.036 6.9538

8 ......... 42,521.325 426,028.77 302.258 9.0192 63 ......... 108.844 854.89 24.125 6.8543

9 ......... 38,298.118 383,507.44 292.876 9.0137 64 ......... 96.235 746.04 22.302 6.7523

10 ......... 34,495.061 345,209.33 285.128 9.0075 65 ......... 84.966 649.81 20.571 6.6478

11 ......... 31,069.969 310,714.26 278.465 9.0005 66 ......... 74.906 564.84 18.930 6.5407

12 ......... 27,984.388 279,644.30 271.891 8.9929 67 ......... 65.938 489.94 17.385 6.4303

13 ......... 25,204.980 251,659.91 265.710 8.9845 68 ......... 57.952 424.00 15.934 6.3164

14 ......... 22,700.694 226,454.93 259.214 8.9757 69 ......... 50.851 366.05 14.576 6.1984

15 ......... 20,444.387 203,754.23 252.526 8.9663 70 ......... 44.541 315.20 13.305 6.0765

16 ......... 18,411.212 183,309.85 245.371 8.9564 71 ......... 38.937 270.66 12.116 5.9510

17 ......... 16,579.213 164,898.63 237.907 8.9461 72 ......... 33.964 231.72 11.001 5.8225

18 ......... 14,928.587 148,319.42 230.266 8.9353 73 ......... 29.554 197.75 9.957 5.6912

19 ......... 13,441.330 133,390.83 222.419 8.9239 74 ......... 25.652 168.20 8.984 5.5570

20 ......... 12,101.492 119,949.50 214.604 8.9120 75 ......... 22.208 142.55 8.082 5.4188

21 ......... 10,894.423 107,848.01 206.782 8.8994 76 ......... 19.176 120.34 7.251 5.2754

22 ......... 9,807.044 96,953.59 199.031 8.8861 77 ......... 16.514 101.16 6.489 5.1260

23 ......... 8,827.375 87,146.54 191.231 8.8723 78 ......... 14.177 84.65 5.789 4.9708

24 ......... 7,944.992 78,319.17 183.633 8.8577 79 ......... 12.126 70.47 5.142 4.8116

25 ......... 7,150.290 70,374.18 176.272 8.8421 80 ......... 10.324 58.35 4.542 4.6513

26 ......... 6,434.540 63,223.89 169.110 8.8257 81 ......... 8.742 48.02 3.984 4.4929

27 ......... 5,790.073 56,789.35 162.300 8.8081 82 ......... 7.358 39.28 3.465 4.3385

28 ......... 5,209.662 50,999.27 155.680 8.7894 83 ......... 6.153 31.92 2.989 4.1882

29 ......... 4,686.891 45,789.61 149.182 8.7697 84 ......... 5.114 25.77 2.560 4.0391

30 ......... 4,216.003 41,102.72 142.761 8.7492 85 ......... 4.226 20.65 2.179 3.8873

31 ......... 3,791.944 36,886.72 136.503 8.7277 86 ......... 3.472 16.43 1.844 3.7311

32 ......... 3,410.103 33,094.77 130.441 8.7049 87 ......... 2.833 12.96 1.549 3.5726

33 ......... 3,066.288 29,684.67 124.564 8.6810 88 ......... 2.294 10.12 1.291 3.4126

34 ......... 2,756.810 26,618.38 118.953 8.6555 89 ......... 1.841 7.83 1.065 3.2530

35 ......... 2,478.273 23,861.57 113.612 8.6283 90 ......... 1.462 5.99 0.868 3.0966

36 ......... 2,227.563 21,383.30 108.498 8.5994 91 ......... 1.146 4.53 0.698 2.9483

37 ......... 2,001.933 19,155.74 103.616 8.5686 92 ......... 0.887 3.38 0.552 2.8114

38 ......... 1,798.880 17,153.80 98.953 8.5358 93 ......... 0.677 2.49 0.429 2.6851

39 ......... 1,616.156 15,354.92 94.496 8.5009 94 ......... 0.510 1.82 0.330 2.5624

40 ......... 1,451.734 13,738.77 90.235 8.4637 95 ......... 0.380 1.31 0.251 2.4362

41 ......... 1,303.780 12,287.03 86.146 8.4242 96 ......... 0.280 0.93 0.188 2.3077

42 ......... 1,170.631 10,983.25 82.201 8.3823 97 ......... 0.203 0.65 0.139 2.1842

43 ......... 1,050.843 9,812.62 78.421 8.3379 95 ......... 0.145 0.44 0.101 2.0669

44 ......... 943.077 8,761.78 74.793 8.2906 99 ......... 0.101 0.30 0.071 1.9570

45 ......... 846.122 7,818.70 71.296 8.2406 100 ......... 0.069 0.20 0.050 1.8492

46 ......... 758.900 6,972.58 67.924 8.1877 101 ......... 0.047 0.13 0.034 1.7435

47 ......... 680.426 6,213.68 64.656 8.1320 102 ......... 0.031 0.08 0.023 1.6401

48 ......... 609.812 5,533.25 61.472 8.0737 103 ......... 0.020 0.05 0.015 1.5390

49 ......... 546.283 4,923.44 58.374 8.0126 104 ......... 0.013 0.03 0.010 1.4402

50 ......... 489.134 4,377.16 55.362 7.9488 105 ......... 0.008 0.02 0.006 1.3438

51 ......... 437.733 3,888.02 52.433 7.8822 106 ......... 0.005 0.01 0.004 1.2498

52 ......... 391.509 3,450.29 49.588 7.8128 107 ......... 0.003 0.01 0.002 1.1583

53 ......... 349.957 3,058.78 46.835 7.7404 108 ......... 0.001 0.00 0.001 1.0693

54 ......... 312.618 2,708.82 44.176 7.6650 109 ......... 0.001 0.00 0.001 0.9829

x x x x x x x x

146
Table 12.L. -- Actuarial Functions at 12.0 Percent Interest for 1989-91 United States 

Black Females

x D N M a x D N M a

0 ......... 100,000.000 915,316.66 1,930.358 8.1532 55 ......... 170.409 1,377.74 22.794 7.0849

1 ......... 87,817.857 815,316.66 462.500 8.2842 56 ......... 150.663 1,207.33 21.306 7.0135

2 ......... 78,319.515 727,498.81 373.215 8.2889 57 ......... 133.102 1,056.67 19.888 6.9388

3 ......... 69,879.738 649,179.29 324.814 8.2900 58 ......... 117.483 923.57 18.529 6.8613

4 ......... 62,360.847 579,299.55 293.038 8.2895 59 ......... 103.588 806.08 17.222 6.7817

5 ......... 55,657.198 516,938.71 270.908 8.2879 60 ......... 91.228 702.50 15.961 6.7004

6 ......... 49,675.181 461,281.51 252.163 8.2860 61 ......... 80.247 611.27 14.754 6.6173

7 ......... 44,338.818 411,606.33 238.140 8.2832 62 ......... 70.501 531.02 13.606 6.5321

8 ......... 39,577.325 367,267.51 227.235 8.2797 63 ......... 61.861 460.52 12.519 6.4445

9 ......... 35,328.243 327,690.18 218.580 8.2756 64 ......... 54.206 398.66 11.493 6.3545

10 ......... 31,535.991 292,361.94 211.497 8.2707 65 ......... 47.432 344.45 10.526 6.2621

11 ......... 28,151.097 260,825.95 205.460 8.2652 66 ......... 41.442 297.02 9.618 6.1672

12 ......... 25,129.005 232,674.85 199.557 8.2592 67 ......... 36.155 255.58 8.771 6.0691

13 ......... 22,431.111 207,545.85 194.056 8.2526 68 ......... 31.492 219.43 7.982 5.9676

14 ......... 20,022.049 185,114.74 188.327 8.2455 69 ......... 27.387 187.93 7.251 5.8621

15 ......... 17,870.983 165,092.69 182.481 8.2380 70 ......... 23.774 160.55 6.573 5.7529

16 ......... 15,950.036 147,221.70 176.282 8.2302 71 ......... 20.598 136.77 5.944 5.6402

17 ......... 14,234.695 131,271.67 169.874 8.2220 72 ......... 17.806 116.17 5.359 5.5243

18 ......... 12,703.047 117,036.97 163.372 8.2133 73 ......... 15.356 98.37 4.817 5.4057

19 ......... 11,335.389 104,333.93 156.754 8.2043 74 ......... 13.210 83.01 4.315 5.2842

20 ......... 10,114.352 92,998.54 150.223 8.1947 75 ......... 11.334 69.80 3.855 5.1587

21 ......... 9,024.192 82,884.18 143.744 8.1847 76 ......... 9.699 58.47 3.435 5.0280

22 ......... 8,050.951 73,859.99 137.380 8.1741 77 ......... 8.278 48.77 3.053 4.8914

23 ......... 7,182.003 65,809.04 131.034 8.1630 78 ......... 7.043 40.49 2.705 4.7488

24 ......... 6,406.376 58,627.04 124.907 8.1514 79 ......... 5.971 33.45 2.387 4.6021

25 ......... 5,714.096 52,220.66 119.025 8.1389 80 ......... 5.038 27.48 2.094 4.4539

26 ......... 5,096.199 46,506.57 113.353 8.1257 81 ......... 4.228 22.44 1.824 4.3072

27 ......... 4,544.832 41,410.37 108.007 8.1115 82 ......... 3.527 18.21 1.575 4.1639

28 ......... 4,052.736 36,865.54 102.857 8.0965 83 ......... 2.923 14.68 1.349 4.0242

29 ......... 3,613.505 32,812.80 97.848 8.0806 84 ......... 2.407 11.76 1.147 3.8855

30 ......... 3,221.437 29,199.30 92.941 8.0641 85 ......... 1.972 9.35 0.970 3.7438

31 ......... 2,871.545 25,977.86 88.202 8.0467 86 ......... 1.606 7.38 0.815 3.5975

32 ......... 2,559.329 23,106.31 83.652 8.0283 87 ......... 1.299 5.78 0.680 3.4486

33 ......... 2,280.744 20,546.99 79.281 8.0089 88 ......... 1.042 4.48 0.562 3.2978

34 ......... 2,032.242 18,266.24 75.145 7.9882 89 ......... 0.829 3.44 0.460 3.1469

35 ......... 1,810.600 16,234.00 71.243 7.9661 90 ......... 0.652 2.61 0.373 2.9987

36 ......... 1,612.904 14,423.40 67.540 7.9425 91 ......... 0.507 1.96 0.297 2.8579

37 ......... 1,436.590 12,810.50 64.037 7.9173 92 ......... 0.389 1.45 0.233 2.7278

38 ......... 1,279.353 11,373.91 60.721 7.8904 93 ......... 0.294 1.06 0.180 2.6078

39 ......... 1,139.138 10,094.55 57.579 7.8616 94 ......... 0.219 0.77 0.137 2.4909

40 ......... 1,014.111 8,955.41 54.602 7.8308 95 ......... 0.162 0.55 0.104 2.3706

41 ......... 902.625 7,941.30 51.772 7.7980 96 ......... 0.118 0.38 0.077 2.2475

42 ......... 803.208 7,038.68 49.064 7.7632 97 ......... 0.085 0.27 0.057 2.1291

43 ......... 714.580 6,235.47 46.494 7.7261 95 ......... 0.060 0.18 0.041 2.0164

44 ......... 635.573 5,520.89 44.049 7.6865 99 ......... 0.042 0.12 0.029 1.9109

45 ......... 565.140 4,885.32 41.714 7.6444 100 ......... 0.028 0.08 0.020 1.8071

46 ......... 502.357 4,320.18 39.481 7.5998 101 ......... 0.019 0.05 0.013 1.7052

47 ......... 446.389 3,817.82 37.337 7.5527 102 ......... 0.012 0.03 0.009 1.6053

48 ......... 396.492 3,371.43 35.267 7.5032 103 ......... 0.008 0.02 0.006 1.5075

49 ......... 352.014 2,974.94 33.271 7.4512 104 ......... 0.005 0.01 0.004 1.4118

50 ......... 312.375 2,622.92 31.347 7.3967 105 ......... 0.003 0.01 0.002 1.3182

51 ......... 277.052 2,310.55 29.494 7.3398 106 ......... 0.002 0.00 0.001 1.2270

52 ......... 245.584 2,033.50 27.709 7.2803 107 ......... 0.001 0.00 0.001 1.1380

53 ......... 217.559 1,787.91 25.997 7.2180 108 ......... 0.001 0.00 0.000 1.0513

54 ......... 192.611 1,570.35 24.359 7.1530 109 ......... 0.000 0.00 0.000 0.9669

x x x x x x x x

147