#### § 20.2031-7 Valuation of annuities, interests for life or term of years, and remainder or reversionary interests.

(a) *In general.* Except as otherwise provided in paragraph (b) of this section and § 20.7520-3(b) (pertaining to certain limitations on the use of prescribed tables), the fair market value of annuities, life estates, terms of years, remainders, and reversionary interests for estates of decedents is the present value of such interests, determined under paragraph (d) of this section. The regulations in this and in related sections provide tables with standard actuarial factors and examples that illustrate how to use the tables to compute the present value of ordinary annuity, life, and remainder interests in property. These sections also refer to standard and special actuarial factors that may be necessary to compute the present value of similar interests in more unusual fact situations.

(b) *Commercial annuities and insurance contracts.* The value of annuities issued by companies regularly engaged in their sale, and of insurance policies on the lives of persons other than the decedent, is determined under § 20.2031-8. See § 20.2042-1 with respect to insurance policies on the decedent's life.

(c) *Actuarial valuations.* The present value of annuities, interests for life or a term of years, and remainder or reversionary interests for estates of decedents for which the valuation date of the gross estate is on or after June 1, 2023, is determined under paragraph (d) of this section. The present value of annuities, interests for life or a term of years, and remainder or reversionary interests for estates of decedents for which the valuation date of the gross estate is before June 1, 2023, is determined (subject to paragraph (d)(3) of this section) under the following sections:

| Valuation dates | Applicable
regulations |
| --- | --- |
| After | Before |
| | 01-01-52 | § 20.2031-7A(a) |
| 12-31-51 | 01-01-71 | 20.2031-7A(b) |
| 12-31-70 | 12-01-83 | 20.2031-7A(c) |
| 11-30-83 | 05-01-89 | 20.2031-7A(d) |
| 04-30-89 | 05-01-99 | 20.2031-7A(e) |
| 04-30-99 | 05-01-09 | § 20.2031-7A(f) |
| 04-30-09 | 06-01-23 | 20.2031-7A(g) |

Table 1 to Paragraph (c)

(d) *Actuarial valuations on or after June 1, 2023* —

(1) *In general.* Except as otherwise provided in paragraph (b) of this section and § 20.7520-3(b) (pertaining to certain limitations on the use of prescribed tables), if the valuation date for the gross estate of the decedent is on or after June 1, 2023, the fair market value of annuities, interests for life or a term of years, and remainder or reversionary interests is the present value determined by using standard or special section 7520 actuarial factors. Many of these standard factors are derived by using the actuarial formulas provided in paragraph (d)(2) of this section, the appropriate section 7520 interest rate, and, if applicable, the mortality component for the valuation date of the interest that is being valued. For purposes of the computations described in this section, the age of an individual is the age of that individual at the individual's nearest birthday. For the convenience of taxpayers, paragraph (d)(2) of this section provides for published tables of factors for specific types of interests. These published tables provide factors for rates from 0.2 to 20 percent, inclusive, at intervals of two-tenths of one percent. In general, appropriate factors instead may be computed directly from the actuarial formulas provided in paragraph (d)(2) of this section. In some cases, specific examples in this part and IRS publications illustrate approximation methods (for example, interpolation) for obtaining factors when the required valuation rate falls between two listed rates (such as in the case of a pooled income fund's rate of return or a unitrust's adjusted payout rate). Exact methods of obtaining the applicable actuarial factors are allowed, such as through software using the actual rate of return and the actuarial formulas provided in paragraph (d)(2) of this section, provided that the taxpayer uses at least the same number of decimal places as are provided in the published tables. The approximation method provided in this part, again using at least the same number of decimal places as provided in this part, must be used if more exact methods are not available. See §§ 20.7520-1 through 20.7520-4. The selected method must be applied consistently in valuing all interests in the same property.

(2) *Specific interests* —

(i) *Pooled income funds and charitable remainder trusts.* The fair market value of a remainder interest in a pooled income fund, as defined in § 1.642(c)-5 of this chapter, is its value determined under § 1.642(c)-6(e) of this chapter. The fair market value of a remainder interest in a charitable remainder annuity trust, as defined in § 1.664-2(a) of this chapter, is the present value determined under § 1.664-2(c) of this chapter. The fair market value of a remainder interest in a charitable remainder unitrust, as defined in § 1.664-3 of this chapter, is its present value determined under § 1.664-4(e) of this chapter. The fair market value of a life interest or an interest for a term of years in a charitable remainder unitrust is the fair market value of the property as of the date of valuation less the fair market value of the remainder interest on that date determined under § 1.664-4(e)(4) and (5) of this chapter.

(ii) *Ordinary remainder and reversionary interests* —

(A) *Remainder and reversionary interests for a term of years.* If the interest to be valued is a remainder or reversionary interest to take effect after a definite number of years, the present value of the interest is computed by multiplying the value of the property by the appropriate remainder factor (that corresponds to the applicable section 7520 interest rate and the stated term). The factor for an ordinary remainder interest following a term certain may be found using the formula in Figure 1 to this paragraph (d)(2)(ii)(A) and computing the result to at least six decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table B. Table B can be found on the IRS website at *https://www.irs.gov/retirement-plans/actuarial-tables* (or a corresponding URL as may be updated from time to time). Table B is referenced and explained in IRS Publication 1457, *Actuarial Valuations Version 4A,* which will be available within a reasonable time after June 1, 2023. The remainder factors from Table B also can be found in paragraph (d)(6) of this section, but only for interest rates from 4.2 to 14 percent, inclusive. For information about obtaining special factors for other situations, see paragraph (d)(4) of this section.

Figure 1 to Paragraph (d)(2)(ii)(A)—Formula for Determining Term Certain Remainder Factors

(B) *Remainder and reversionary interests dependent on the life of one individual.* If the interest to be valued is a remainder or reversionary interest to take effect after the death of one individual, the present value of the interest is computed by multiplying the value of the property by the appropriate remainder factor (that corresponds to the applicable section 7520 interest rate and the age of the measuring life of the life interest that precedes the remainder interest). The factor for an ordinary remainder interest following the death of one individual may be found using the formula in Figure 2 to this paragraph (d)(2)(ii)(B) and computing the result to at least five decimal places. The prescribed mortality table is Table 2010CM as set forth in paragraph (d)(7)(ii) of this section, or for periods before June 1, 2023, the appropriate table found in § 20.2031-7A. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table S. Table S currently is available, at no charge, electronically via the IRS website at *https://www.irs.gov/retirement-plans/actuarial-tables* (or a corresponding URL as may be updated from time to time). Table S is referenced and explained by IRS Publication 1457, *Actuarial Valuations Version 4A,* which will be available within a reasonable time after June 1, 2023. For information about obtaining special factors for other situations, see paragraph (d)(4) of this section.

Figure 2 to Paragraph (d)(2)(ii)(B)—Formula for Determining Single Life Remainder Factors

(iii) *Ordinary interests for a term of years and ordinary interests for life.* If the interest to be valued is the right of a person to receive the income of certain property, or to the use of certain property, for a term of years or for the life of one individual, the present value of the interest is computed by multiplying the value of the property by the appropriate actuarial factor for an interest for a term of years or for a life (that corresponds to the applicable section 7520 interest rate and the durational period). The actuarial factor for an ordinary income interest for a term certain may be found by subtracting from 1.000000 the factor for an ordinary remainder interest following the same term certain that is determined under the formula in paragraph (d)(2)(ii)(A) of this section. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in the “Income Interest” column of Table B which can be found on the IRS website at *https://www.irs.gov/retirement-plans/actuarial-tables* (or a corresponding URL as may be updated from time to time). The actuarial factor for an ordinary income interest for the life of one individual may be found by subtracting from 1.00000 the factor for an ordinary remainder interest following the life of the same individual that is determined in paragraph (d)(2)(ii)(B) of this section. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in the “Life Estate” column of Table S. Table S (applicable when the valuation date is on or after June 1, 2023) can be found on the IRS website at *https://www.irs.gov/retirement-plans/actuarial-tables*. Tables B and S are referenced and explained by IRS Publication 1457, *Actuarial Valuations Version 4A*. See § 20.2031-7A or earlier versions of Publication 1457 for valuation of interests before June 1, 2023. For information about obtaining special factors for other situations, see paragraph (d)(4) of this section.

(iv) *Annuities.*

(A) If the interest to be valued is the right of a person to receive an annuity that is payable at the end of each year for a term of years or for the life of one individual, the present value of the interest is computed by multiplying the aggregate amount payable annually by the appropriate annuity factor (that corresponds to the applicable section 7520 interest rate and annuity period). The appropriate annuity factor for an annuity payable for a term of years is computed by subtracting from 1.000000 the factor for an ordinary remainder interest following the same term certain that is determined under the formula in paragraph (d)(2)(ii)(A) of this section and then dividing the result by the applicable section 7520 interest rate expressed to at least four decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in the “Annuity” column of Table B which can be found on the IRS website at *https://www.irs.gov/retirement-plans/actuarial-tables* (or a corresponding URL as may be updated from time to time). The appropriate annuity factor for an annuity payable for the life of one individual is computed by subtracting from 1.00000 the factor for an ordinary remainder interest following the life of the same individual that is determined under the formula in paragraph (d)(2)(ii)(B) of this section and then dividing the result by the applicable section 7520 interest rate expressed to at least four decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in the “Annuity” column of Table S. Table S (applicable when the valuation date is on or after June 1, 2023) can be found on the IRS website at *https://www.irs.gov/retirement-plans/actuarial-tables*. Tables B and S are referenced and explained in IRS Publication 1457, *Actuarial Valuations Version 4A*. See § 20.2031-7A or earlier versions of Publication 1457 for valuation of interests before June 1, 2023. For information about obtaining special factors for other situations, see paragraph (d)(4) of this section.

(B) If the annuity is payable at the end of semiannual, quarterly, monthly, or weekly periods, the product obtained by multiplying the annuity factor by the aggregate amount payable annually is then multiplied by the applicable adjustment factor at the appropriate interest rate component for payments made at the end of the specified periods. The applicable adjustment factor may be found using the formula in Figure 3 to this paragraph (d)(2)(iv)(B) and calculating the result to at least four decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table K. Table K, which is referenced and explained by Publication 1457, can be found on the IRS website at *https://www.irs.gov/retirement-plans/actuarial-tables*. The provisions of this paragraph (d)(2)(iv)(B) are illustrated by the example in paragraph (d)(2)(iv)(B)(*2*) of this section.

Figure 3 to Paragraph (d)(2)(iv)(B)—Formula for Determining Annuity Adjustment Factor at the End of the Specified Period

(*1*) *Sample factors from actuarial Tables S and K.* For purposes of the example in paragraph (d)(2)(iv)(B)(*2*) of this section, the following factors from Tables S and K will be used:

| Age | Annuity | Life estate | Remainder |
| --- | --- | --- | --- |
| **Interest at 3.2 Percent** |
| 75 | 9.4053 | 0.30097 | 0.69903 |
| **Factors from Table K** |
| **Adjustment Factors for Annuities Payable at the End of Each Interval** |
| Interest rate | Semi-annually | Quarterly | Monthly |
| 3.2% | 1.0079 | 1.0119 | 1.0146 |

Table 2 to Paragraph (d)(2)(iv)(B)(*1*)

Factors From Table S—Based on Table 2010CM

(*2*) *Example.* At the time of the decedent's death, the survivor/annuitant, age 75, is entitled to receive an annuity of $15,000 per year for life payable in equal monthly installments at the end of each month. The section 7520 rate for the month in which the decedent died is 3.2 percent. Under Table S, the annuity factor at 3.2 percent for an individual aged 75 is 9.4053. Under Table K, the adjustment factor under the column for payments made at the end of each monthly period at the rate of 3.2 percent is 1.0146. The aggregate annual amount, $15,000, is multiplied by the factor 9.4053 and the product then is multiplied by 1.0146. The present value of the annuity at the date of the decedent's death is, therefore, $143,139.26 ($15,000 × 9.4053 × 1.0146).

(C) If an annuity is payable at the beginning of annual, semiannual, quarterly, monthly, or weekly periods for a term of years, the value of the annuity is computed by multiplying the aggregate amount payable annually by the annuity factor described in paragraph (d)(2)(iv)(A) of this section; and the product so obtained then is multiplied by the applicable adjustment factor at the appropriate interest rate component for payments made at the beginning of specified periods. The applicable adjustment factor may be found using the formula in Figure 4 to this paragraph (d)(2)(iv)(C) and calculating the result to at least four decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table J. Table J, which is referenced and explained by Publication 1457, can be found on the IRS website at *https://www.irs.gov/retirement-plans/actuarial-tables*. If an annuity is payable at the beginning of annual, semiannual, quarterly, monthly, or weekly periods for one or more lives, the value of the annuity is the sum of the first payment plus the present value of a similar annuity, the first payment of which is not to be made until the end of the payment period, determined as provided in paragraph (d)(2)(iv)(B) of this section.

Figure 4 to Paragraph (d)(2)(iv)(C)—Formula for Determining Annuity Adjustment Factor at the Beginning of the Specified Period

(v) *Annuity and unitrust interests for a term of years or until the prior death of an individual.* See § 25.2512-5(d)(2)(v) of this chapter for examples explaining how to compute the present value of an annuity or unitrust interest that is payable until the earlier of the lapse of a term of years or the death of an individual.

(3) *Transitional rule.* If a decedent dies after April 30, 2019, and on or before June 1, 2023, the fair market value of annuities, interests for life or a term of years, and remainder or reversionary interests based on one or more measuring lives included in the gross estate of the decedent is their present value determined under this section by using the section 7520 interest rate for the month in which the valuation date occurs (see §§ 20.7520-1(b) and 20.7520-2(a)(2)) and factors derived from the selected mortality table, either Table 2010CM in paragraph (d)(7)(ii) of this section or Table 2000CM in § 20.2031-7A(g)(4), at the option of the donor or the decedent's executor, as the case may be. If any previously filed estate tax return is supplemented to use the actuarial factors based on Table 2010CM, the supplemental return must state at the top “AMENDED PURSUANT TO TD 9974.” For the convenience of taxpayers, actuarial factors based on Table 2010CM appear in the current version of Table S, and actuarial factors based on Table 2000CM appear in the previous version of Table S. Both versions of Table S will be available as provided in paragraph (d)(4) of this section. The decedent's executor must consistently use the same mortality basis with respect to each interest (income, remainder, partial, etc.) in the same property, and with respect to all transfers occurring on the same valuation date. For example, gift and income tax charitable deductions with respect to the same transfer must be determined based on factors with the same mortality basis, and all assets includible in the gross estate and/or estate tax deductions claimed must be valued based on factors with the same mortality basis.

(4) *Publications and actuarial computations by the Internal Revenue Service.* The factor for determining the present value of a remainder interest that is dependent on the termination of the life of one individual may be computed by using the formula in paragraph (d)(2)(ii)(B) of this section to derive a remainder factor from the appropriate mortality table expressed to at least five decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table S. The remainder factor for determining the present value of a remainder interest following a term certain may be computed by using the formula in paragraph (d)(2)(ii)(A) of this section expressed to at least six decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table B. Adjustment factors for term certain annuities payable at the beginning of each interval may be computed by using the formula in paragraph (d)(2)(iv)(C) of this section expressed to at least four decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table J. Adjustment factors for annuities payable at the end of each interval may be computed by using the formula in paragraph (d)(2)(iv)(B) of this section expressed to at least four decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table K. These tables currently are available, at no charge, electronically via the IRS website at *https://www.irs.gov/retirement-plans/actuarial-tables* (or a corresponding URL as may be updated from time to time). IRS Publication 1457, *Actuarial Valuations Version 4A* (2023), references and explains the factors contained in the actuarial tables and also includes examples that illustrate how to compute many special factors for more unusual situations. This publication will be available within a reasonable time after June 1, 2023. Tables B, J, and K also can be found in paragraph (d)(6) of this section, but only for interest rates from 4.2 to 14 percent, inclusive. If a special factor is required in the case of an actual decedent, the special factor may be calculated by the executor using the actuarial formulas in paragraph (d)(2) of this section or the executor may request a ruling to obtain the factor from the Internal Revenue Service. The request for a ruling must be accompanied by a recitation of the facts including a statement of the date of birth for each measuring life, the date of the decedent's death, any other applicable dates, and a copy of the will, trust, or other relevant documents. A request for a ruling must comply with the instructions for requesting a ruling published periodically in the Internal Revenue Bulletin (see §§ 601.201 and 601.601(d)(2)(ii)(*b*) of this chapter) and must include payment of the required user fee.

(5) *Examples.* The provisions of this section are illustrated by the examples in this paragraph (d)(5). For purposes of these examples, the following factors from Tables S, B, and K will be used:

| Age | Annuity | Life estate | Remainder |
| --- | --- | --- | --- |
| **Factors From Table S—Based on Table 2010CM** |
| **Interest at 3.2 Percent** |
| 31 | 23.8334 | 0.76267 | 0.23733 |
| 46 | 20.0146 | 0.64047 | 0.35953 |
| **Interest at 4.6 Percent** |
| 65 | 11.7691 | 0.54138 | 0.45862 |
| **Factors from Table B** |
| **Annuity, Income, and Remainder Interests for a Term Certain** |
| **Interest at 2.6 Percent** |
| Years | Annuity | Income interest | Remainder |
| 5 | 4.6325 | 0.120445 | 0.879555 |
| Factors From Table K |
| Adjustment Factors for Annuities Payable at the End of Each Interval |
| Interest Rate | Semi-annually | Quarterly | Monthly |
| 2.6% | 1.0065 | 1.0097 | 1.0119 |
| 3.2% | 1.0079 | 1.0119 | 1.0146 |

Table 3 to Paragraph (d)(5)

(i) *Example 1: Remainder payable at an individual's death.* The decedent, or the decedent's estate, was entitled to receive certain property worth $50,000 upon the death of A, to whom the income was bequeathed for life. At the time of the decedent's death, A was 65 years and 5 months old. In the month in which the decedent died, the section 7520 rate was 4.6 percent. Under Table S, the remainder factor at 4.6 percent for determining the present value of the remainder interest due at the death of a person aged 65, A's age at A's nearest birthday to the date of the decedent's death, is 0.45862. The present value of the remainder interest at the date of the decedent's death is, therefore, $22,931 ($50,000 times 0.45862).

(ii) *Example 2: Income payable for an individual's life.* A's parent bequeathed an income interest in property to A for life, with the remainder interest passing to B at A's death. At the time of the parent's death, the value of the property was $50,000 and A was 30 years and 10 months old. The section 7520 rate at the time of the parent's death was 3.2 percent. Under Table S, the factor at 3.2 percent for determining the present value of the life estate given to a person aged 31, A's age at A's nearest birthday to the date of the decedent's death, is 0.76267. The present value of A's income interest at the time of the parent's death is, therefore, $38,133.50 ($50,000.00 × 0.76267).

(iii) *Example 3: Annuity payable for an individual's life.* A purchased an annuity for the benefit of both A and B. Under the terms of the annuity contract, at A's death, a survivor annuity of $10,000 per year, payable in equal semiannual installments made at the end of each interval is payable to B for life. At A's death, B was 45 years and 7 months old. Also, at A's death, the section 7520 rate was 3.2 percent. Under Table S, the factor at 3.2 percent for determining the present value of an annuity interest payable until the death of a person age 46 (B's age at B's nearest birthday to the date of A's death) is 20.0146. The adjustment factor from Table K at an interest rate of 3.2 percent for semiannual annuity payments made at the end of the period is 1.0079. The present value of the annuity at the date of A's death is, therefore, $201,727.15 ($10,000 × 20.0146 × 1.0079).

(iv) *Example 4: Annuity payable for a term of years.* The decedent, or the decedent's estate, was entitled to receive an annuity of $10,000 per year payable in equal quarterly installments at the end of each quarter throughout a term certain. At the time of the decedent's death, the section 7520 rate was 2.6 percent. A quarterly payment had been made immediately prior to the decedent's death and payments were to continue for 5 more years. Under Table B for the interest rate of 2.6 percent, the factor for the present value of an annuity with a term of 5 years is 4.6325. The adjustment factor from Table K at an interest rate of 2.6 percent for quarterly annuity payments made at the end of the quarter is 1.0097. The present value of the annuity is, therefore, $46,774.35 ($10,000 × 4.6325 × 1.0097).

(6) *Actuarial Table B, Table J, and Table K where the valuation date is after April 30, 1989.* Except as provided in § 20.7520-3(b) (pertaining to certain limitations on prescribed tables), for determination of the present value of an interest that is dependent on a term of years, the tables in this paragraph (d)(6) must be used in the application of the provisions of this section when the section 7520 interest rate component is between 4.2 and 14 percent.

| Years | Interest rate |
| --- | --- |
| 4.2% | 4.4% | 4.6% | 4.8% | 5.0% | 5.2% | 5.4% | 5.6% | 5.8% | 6.0% |
| 1 | .959693 | .957854 | .956023 | .954198 | .952381 | .950570 | .948767 | .946970 | .945180 | .943396 |
| 2 | .921010 | .917485 | .913980 | .910495 | .907029 | .903584 | .900158 | .896752 | .893364 | .889996 |
| 3 | .883887 | .878817 | .873786 | .868793 | .863838 | .858920 | .854040 | .849197 | .844390 | .839619 |
| 4 | .848260 | .841779 | .835359 | .829001 | .822702 | .816464 | .810285 | .804163 | .798100 | .792094 |
| 5 | .814069 | .806302 | .798623 | .791031 | .783526 | .776106 | .768771 | .761518 | .754348 | .747258 |
| 6 | .781257 | .772320 | .763501 | .754801 | .746215 | .737744 | .729384 | .721135 | .712994 | .704961 |
| 7 | .749766 | .739770 | .729925 | .720230 | .710681 | .701277 | .692015 | .682893 | .673908 | .665057 |
| 8 | .719545 | .708592 | .697825 | .687242 | .676839 | .666613 | .656561 | .646679 | .636964 | .627412 |
| 9 | .690543 | .678728 | .667137 | .655765 | .644609 | .633663 | .622923 | .612385 | .602045 | .591898 |
| 10 | .662709 | .650122 | .637798 | .625730 | .613913 | .602341 | .591009 | .579910 | .569041 | .558395 |
| 11 | .635997 | .622722 | .609750 | .597071 | .584679 | .572568 | .560729 | .549157 | .537846 | .526788 |
| 12 | .610362 | .596477 | .582935 | .569724 | .556837 | .544266 | .532001 | .520035 | .508361 | .496969 |
| 13 | .585760 | .571339 | .557299 | .543630 | .530321 | .517363 | .504745 | .492458 | .480492 | .468839 |
| 14 | .562150 | .547259 | .532790 | .518731 | .505068 | .491790 | .478885 | .466343 | .454151 | .442301 |
| 15 | .539491 | .524195 | .509360 | .494972 | .481017 | .467481 | .454350 | .441612 | .429255 | .417265 |
| 16 | .517746 | .502102 | .486960 | .472302 | .458112 | .444374 | .431072 | .418194 | .405723 | .393646 |
| 17 | .496877 | .480941 | .465545 | .450670 | .436297 | .422408 | .408987 | .396017 | .383481 | .371364 |
| 18 | .476849 | .460671 | .445071 | .430028 | .415521 | .401529 | .388033 | .375016 | .362458 | .350344 |
| 19 | .457629 | .441256 | .425498 | .410332 | .395734 | .381681 | .368153 | .355129 | .342588 | .330513 |
| 20 | .439183 | .422659 | .406786 | .391538 | .376889 | .362815 | .349291 | .336296 | .323807 | .311805 |
| 21 | .421481 | .404846 | .388897 | .373605 | .358942 | .344881 | .331396 | .318462 | .306056 | .294155 |
| 22 | .404492 | .387783 | .371794 | .356494 | .341850 | .327834 | .314417 | .301574 | .289278 | .277505 |
| 23 | .388188 | .371440 | .355444 | .340166 | .325571 | .311629 | .298309 | .285581 | .273420 | .261797 |
| 24 | .372542 | .355785 | .339813 | .324586 | .310068 | .296225 | .283025 | .270437 | .258431 | .246979 |
| 25 | .357526 | .340791 | .324869 | .309719 | .295303 | .281583 | .268525 | .256096 | .244263 | .232999 |
| 26 | .343115 | .326428 | .310582 | .295533 | .281241 | .267664 | .254768 | .242515 | .230873 | .219810 |
| 27 | .329285 | .312670 | .296923 | .281998 | .267848 | .254434 | .241715 | .229654 | .218216 | .207368 |
| 28 | .316012 | .299493 | .283866 | .269082 | .255094 | .241857 | .229331 | .217475 | .206253 | .195630 |
| 29 | .303275 | .286870 | .271382 | .256757 | .242946 | .229902 | .217582 | .205943 | .194947 | .184557 |
| 30 | .291051 | .274780 | .259447 | .244997 | .231377 | .218538 | .206434 | .195021 | .184260 | .174110 |
| 31 | .279319 | .263199 | .248038 | .233776 | .220359 | .207736 | .195858 | .184679 | .174158 | .164255 |
| 32 | .268061 | .252106 | .237130 | .223069 | .209866 | .197468 | .185823 | .174886 | .164611 | .154957 |
| 33 | .257256 | .241481 | .226702 | .212852 | .199873 | .187707 | .176303 | .165612 | .155587 | .146186 |
| 34 | .246887 | .231304 | .216732 | .203103 | .190355 | .178429 | .167270 | .156829 | .147058 | .137912 |
| 35 | .236935 | .221556 | .207201 | .193801 | .181290 | .169609 | .158701 | .148512 | .138996 | .130105 |
| 36 | .227385 | .212218 | .198089 | .184924 | .172657 | .161225 | .150570 | .140637 | .131376 | .122741 |
| 37 | .218220 | .203274 | .189377 | .176454 | .164436 | .153256 | .142856 | .133179 | .124174 | .115793 |
| 38 | .209424 | .194707 | .181049 | .168373 | .156605 | .145681 | .135537 | .126116 | .117367 | .109239 |
| 39 | .200983 | .186501 | .173087 | .160661 | .149148 | .138480 | .128593 | .119428 | .110933 | .103056 |
| 40 | .192882 | .178641 | .165475 | .153302 | .142046 | .131635 | .122004 | .113095 | .104851 | .097222 |
| 41 | .185107 | .171112 | .158198 | .146281 | .135282 | .125128 | .115754 | .107098 | .099103 | .091719 |
| 42 | .177646 | .163900 | .151241 | .139581 | .128840 | .118943 | .109823 | .101418 | .093670 | .086527 |
| 43 | .170486 | .156992 | .144590 | .133188 | .122704 | .113064 | .104197 | .096040 | .088535 | .081630 |
| 44 | .163614 | .150376 | .138231 | .127088 | .116861 | .107475 | .098858 | .090947 | .083682 | .077009 |
| 45 | .157019 | .144038 | .132152 | .121267 | .111297 | .102163 | .093793 | .086124 | .079094 | .072650 |
| 46 | .150690 | .137968 | .126340 | .115713 | .105997 | .097113 | .088988 | .081557 | .074758 | .068538 |
| 47 | .144616 | .132153 | .120784 | .110413 | .100949 | .092312 | .084429 | .077232 | .070660 | .064658 |
| 48 | .138787 | .126583 | .115473 | .105356 | .096142 | .087749 | .080103 | .073136 | .066786 | .060998 |
| 49 | .133193 | .121248 | .110395 | .100530 | .091564 | .083412 | .075999 | .069258 | .063125 | .057546 |
| 50 | .127824 | .116138 | .105540 | .095926 | .087204 | .079289 | .072106 | .065585 | .059665 | .054288 |
| 51 | .122672 | .111243 | .100898 | .091532 | .083051 | .075370 | .068411 | .062107 | .056394 | .051215 |
| 52 | .117728 | .106555 | .096461 | .087340 | .079096 | .071644 | .064907 | .058813 | .053302 | .048316 |
| 53 | .112982 | .102064 | .092219 | .083340 | .075330 | .068103 | .061581 | .055695 | .050380 | .045582 |
| 54 | .108428 | .097763 | .088164 | .079523 | .071743 | .064737 | .058426 | .052741 | .047618 | .043001 |
| 55 | .104058 | .093642 | .084286 | .075880 | .068326 | .061537 | .055433 | .049944 | .045008 | .040567 |
| 56 | .099864 | .089696 | .080580 | .072405 | .065073 | .058495 | .052593 | .047296 | .042541 | .038271 |
| 57 | .095839 | .085916 | .077036 | .069089 | .061974 | .055604 | .049898 | .044787 | .040208 | .036105 |
| 58 | .091976 | .082295 | .073648 | .065924 | .059023 | .052855 | .047342 | .042412 | .038004 | .034061 |
| 59 | .088268 | .078826 | .070409 | .062905 | .056212 | .050243 | .044916 | .040163 | .035921 | .032133 |
| 60 | .084710 | .075504 | .067313 | .060024 | .053536 | .047759 | .042615 | .038033 | .033952 | .030314 |

Table B—Term Certain Remainder Factors Applicable After April 30, 1989

| Years | Interest rate |
| --- | --- |
| 6.2% | 6.4% | 6.6% | 6.8% | 7.0% | 7.2% | 7.4% | 7.6% | 7.8% | 8.0% |
| 1 | .941620 | .939850 | .938086 | .936330 | .934579 | .932836 | .931099 | .929368 | .927644 | .925926 |
| 2 | .886647 | .883317 | .880006 | .876713 | .873439 | .870183 | .866945 | .863725 | .860523 | .857339 |
| 3 | .834885 | .830185 | .825521 | .820892 | .816298 | .811738 | .807211 | .802718 | .798259 | .793832 |
| 4 | .786144 | .780249 | .774410 | .768626 | .762895 | .757218 | .751593 | .746021 | .740500 | .735030 |
| 5 | .740248 | .733317 | .726464 | .719687 | .712986 | .706360 | .699808 | .693328 | .686920 | .680583 |
| 6 | .697032 | .689208 | .681486 | .673864 | .666342 | .658918 | .651590 | .644357 | .637217 | .630170 |
| 7 | .656339 | .647752 | .639292 | .630959 | .622750 | .614662 | .606694 | .598845 | .591111 | .583490 |
| 8 | .618022 | .608789 | .599711 | .590786 | .582009 | .573379 | .564892 | .556547 | .548340 | .540269 |
| 9 | .581942 | .572170 | .562581 | .553170 | .543934 | .534868 | .525971 | .517237 | .508664 | .500249 |
| 10 | .547968 | .537754 | .527750 | .517950 | .508349 | .498944 | .489731 | .480704 | .471859 | .463193 |
| 11 | .515977 | .505408 | .495075 | .484972 | .475093 | .465433 | .455987 | .446750 | .437717 | .428883 |
| 12 | .485854 | .475007 | .464423 | .454093 | .444012 | .434173 | .424569 | .415196 | .406046 | .397114 |
| 13 | .457490 | .446436 | .435669 | .425181 | .414964 | .405012 | .395316 | .385870 | .376666 | .367698 |
| 14 | .430781 | .419582 | .408695 | .398109 | .387817 | .377810 | .368078 | .358615 | .349412 | .340461 |
| 15 | .405632 | .394344 | .383391 | .372762 | .362446 | .352434 | .342717 | .333285 | .324130 | .315242 |
| 16 | .381951 | .370624 | .359654 | .349028 | .338735 | .328763 | .319103 | .309745 | .300677 | .291890 |
| 17 | .359653 | .348331 | .337386 | .326805 | .316574 | .306682 | .297117 | .287867 | .278921 | .270269 |
| 18 | .338656 | .327379 | .316498 | .305997 | .295864 | .286084 | .276645 | .267534 | .258739 | .250249 |
| 19 | .318885 | .307687 | .296902 | .286514 | .276508 | .266870 | .257584 | .248638 | .240018 | .231712 |
| 20 | .300268 | .289179 | .278520 | .268272 | .258419 | .248946 | .239836 | .231076 | .222651 | .214548 |
| 21 | .282739 | .271785 | .261276 | .251191 | .241513 | .232225 | .223311 | .214755 | .206541 | .198656 |
| 22 | .266232 | .255437 | .245099 | .235197 | .225713 | .216628 | .207925 | .199586 | .191596 | .183941 |
| 23 | .250689 | .240073 | .229924 | .220222 | .210947 | .202078 | .193598 | .185489 | .177733 | .170315 |
| 24 | .236054 | .225632 | .215689 | .206201 | .197147 | .188506 | .180259 | .172387 | .164873 | .157699 |
| 25 | .222273 | .212060 | .202334 | .193072 | .184249 | .175845 | .167839 | .160211 | .152943 | .146018 |
| 26 | .209297 | .199305 | .189807 | .180779 | .172195 | .164035 | .156275 | .148895 | .141877 | .135202 |
| 27 | .197078 | .187317 | .178056 | .169269 | .160930 | .153017 | .145507 | .138379 | .131611 | .125187 |
| 28 | .185572 | .176049 | .167031 | .158491 | .150402 | .142740 | .135482 | .128605 | .122088 | .115914 |
| 29 | .174739 | .165460 | .156690 | .148400 | .140563 | .133153 | .126147 | .119521 | .113255 | .107328 |
| 30 | .164537 | .155507 | .146989 | .138951 | .131367 | .124210 | .117455 | .111079 | .105060 | .099377 |
| 31 | .154932 | .146154 | .137888 | .130104 | .122773 | .115868 | .109362 | .103233 | .097458 | .092016 |
| 32 | .145887 | .137362 | .129351 | .121820 | .114741 | .108085 | .101827 | .095942 | .090406 | .085200 |
| 33 | .137370 | .129100 | .121342 | .114064 | .107235 | .100826 | .094811 | .089165 | .083865 | .078889 |
| 34 | .129350 | .121335 | .113830 | .106802 | .100219 | .094054 | .088278 | .082867 | .077797 | .073045 |
| 35 | .121798 | .114036 | .106782 | .100001 | .093663 | .087737 | .082196 | .077014 | .072168 | .067635 |
| 36 | .114688 | .107177 | .100171 | .093634 | .087535 | .081844 | .076532 | .071574 | .066946 | .062625 |
| 37 | .107992 | .100730 | .093969 | .087673 | .081809 | .076347 | .071259 | .066519 | .062102 | .057986 |
| 38 | .101688 | .094671 | .088151 | .082090 | .076457 | .071219 | .066349 | .061821 | .057609 | .053690 |
| 39 | .095751 | .088977 | .082693 | .076864 | .071455 | .066436 | .061778 | .057454 | .053440 | .049713 |
| 40 | .090161 | .083625 | .077573 | .071970 | .066780 | .061974 | .057521 | .053396 | .049573 | .046031 |
| 41 | .084897 | .078595 | .072770 | .067387 | .062412 | .057811 | .053558 | .049625 | .045987 | .042621 |
| 42 | .079941 | .073867 | .068265 | .063097 | .058329 | .053929 | .049868 | .046120 | .042659 | .039464 |
| 43 | .075274 | .069424 | .064038 | .059079 | .054513 | .050307 | .046432 | .042862 | .039572 | .036541 |
| 44 | .070880 | .065248 | .060074 | .055318 | .050946 | .046928 | .043233 | .039835 | .036709 | .033834 |
| 45 | .066742 | .061323 | .056354 | .051796 | .047613 | .043776 | .040254 | .037021 | .034053 | .031328 |
| 46 | .062845 | .057635 | .052865 | .048498 | .044499 | .040836 | .037480 | .034406 | .031589 | .029007 |
| 47 | .059176 | .054168 | .049592 | .045410 | .041587 | .038093 | .034898 | .031976 | .029303 | .026859 |
| 48 | .055722 | .050910 | .046522 | .042519 | .038867 | .035535 | .032493 | .029717 | .027183 | .024869 |
| 49 | .052469 | .047848 | .043641 | .039812 | .036324 | .033148 | .030255 | .027618 | .025216 | .023027 |
| 50 | .049405 | .044970 | .040939 | .037277 | .033948 | .030922 | .028170 | .025668 | .023392 | .021321 |
| 51 | .046521 | .042265 | .038405 | .034903 | .031727 | .028845 | .026229 | .023855 | .021699 | .019742 |
| 52 | .043805 | .039722 | .036027 | .032681 | .029651 | .026907 | .024422 | .022170 | .020129 | .018280 |
| 53 | .041248 | .037333 | .033796 | .030600 | .027711 | .025100 | .022739 | .020604 | .018673 | .016925 |
| 54 | .038840 | .035087 | .031704 | .028652 | .025899 | .023414 | .021172 | .019149 | .017322 | .015672 |
| 55 | .036572 | .032977 | .029741 | .026828 | .024204 | .021842 | .019714 | .017796 | .016068 | .014511 |
| 56 | .034437 | .030993 | .027900 | .025119 | .022621 | .020375 | .018355 | .016539 | .014906 | .013436 |
| 57 | .032427 | .029129 | .026172 | .023520 | .021141 | .019006 | .017091 | .015371 | .013827 | .012441 |
| 58 | .030534 | .027377 | .024552 | .022023 | .019758 | .017730 | .015913 | .014285 | .012827 | .011519 |
| 59 | .028751 | .025730 | .023032 | .020620 | .018465 | .016539 | .014817 | .013276 | .011899 | .010666 |
| 60 | .027073 | .024183 | .021606 | .019307 | .017257 | .015428 | .013796 | .012339 | .011038 | .009876 |

Table B—Term Certain Remainder Factors Applicable After April 30, 1989

| Years | Interest rate |
| --- | --- |
| 8.2% | 8.4% | 8.6% | 8.8% | 9.0% | 9.2% | 9.4% | 9.6% | 9.8% | 10.0% |
| 1 | .924214 | .922509 | .920810 | .919118 | .917431 | .915751 | .914077 | .912409 | .910747 | .909091 |
| 2 | .854172 | .851023 | .847892 | .844777 | .841680 | .838600 | .835536 | .832490 | .829460 | .826446 |
| 3 | .789438 | .785077 | .780747 | .776450 | .772183 | .767948 | .763744 | .759571 | .755428 | .751315 |
| 4 | .729610 | .724241 | .718920 | .713649 | .708425 | .703250 | .698121 | .693039 | .688003 | .683013 |
| 5 | .674316 | .668119 | .661989 | .655927 | .649931 | .644001 | .638136 | .632335 | .626597 | .620921 |
| 6 | .623213 | .616346 | .609566 | .602874 | .596267 | .589745 | .583305 | .576948 | .570671 | .564474 |
| 7 | .575982 | .568585 | .561295 | .554112 | .547034 | .540059 | .533186 | .526412 | .519737 | .513158 |
| 8 | .532331 | .524524 | .516846 | .509294 | .501866 | .494560 | .487373 | .480303 | .473349 | .466507 |
| 9 | .491988 | .483879 | .475917 | .468101 | .460428 | .452894 | .445496 | .438233 | .431101 | .424098 |
| 10 | .454703 | .446383 | .438230 | .430240 | .422411 | .414738 | .407218 | .399848 | .392624 | .385543 |
| 11 | .420243 | .411792 | .403526 | .395441 | .387533 | .379797 | .372228 | .364824 | .357581 | .350494 |
| 12 | .388394 | .379882 | .371571 | .363457 | .355535 | .347799 | .340245 | .332869 | .325666 | .318631 |
| 13 | .358960 | .350445 | .342147 | .334060 | .326179 | .318497 | .311010 | .303713 | .296599 | .289664 |
| 14 | .331756 | .323288 | .315052 | .307040 | .299246 | .291664 | .284287 | .277110 | .270127 | .263331 |
| 15 | .306613 | .298236 | .290103 | .282206 | .274538 | .267092 | .259860 | .252838 | .246017 | .239392 |
| 16 | .283376 | .275126 | .267130 | .259381 | .251870 | .244589 | .237532 | .230691 | .224059 | .217629 |
| 17 | .261901 | .253806 | .245976 | .238401 | .231073 | .223983 | .217123 | .210485 | .204061 | .197845 |
| 18 | .242052 | .234139 | .226497 | .219119 | .211994 | .205113 | .198467 | .192048 | .185848 | .179859 |
| 19 | .223708 | .215995 | .208561 | .201396 | .194490 | .187832 | .181414 | .175226 | .169260 | .163508 |
| 20 | .206754 | .199257 | .192045 | .185107 | .178431 | .172007 | .165826 | .159878 | .154153 | .148644 |
| 21 | .191085 | .183817 | .176837 | .170135 | .163698 | .157516 | .151578 | .145874 | .140395 | .135131 |
| 22 | .176604 | .169573 | .162834 | .156374 | .150182 | .144245 | .138554 | .133097 | .127864 | .122846 |
| 23 | .163220 | .156432 | .149939 | .143726 | .137781 | .132093 | .126649 | .121439 | .116452 | .111678 |
| 24 | .150850 | .144310 | .138065 | .132101 | .126405 | .120964 | .115767 | .110802 | .106058 | .101526 |
| 25 | .139418 | .133128 | .127132 | .121416 | .115968 | .110773 | .105820 | .101097 | .096592 | .092296 |
| 26 | .128852 | .122811 | .117064 | .111596 | .106393 | .101441 | .096727 | .092241 | .087971 | .083905 |
| 27 | .119087 | .113295 | .107794 | .102570 | .097608 | .092894 | .088416 | .084162 | .080119 | .076278 |
| 28 | .110062 | .104515 | .099258 | .094274 | .089548 | .085068 | .080819 | .076790 | .072968 | .069343 |
| 29 | .101721 | .096416 | .091398 | .086649 | .082155 | .077901 | .073875 | .070064 | .066456 | .063039 |
| 30 | .094012 | .088945 | .084160 | .079640 | .075371 | .071338 | .067527 | .063927 | .060524 | .057309 |
| 31 | .086887 | .082053 | .077495 | .073199 | .069148 | .065328 | .061725 | .058327 | .055122 | .052099 |
| 32 | .080302 | .075694 | .071358 | .067278 | .063438 | .059824 | .056422 | .053218 | .050202 | .047362 |
| 33 | .074216 | .069829 | .065708 | .061837 | .058200 | .054784 | .051574 | .048557 | .045722 | .043057 |
| 34 | .068592 | .064418 | .060504 | .056835 | .053395 | .050168 | .047142 | .044304 | .041641 | .039143 |
| 35 | .063394 | .059426 | .055713 | .052238 | .048986 | .045942 | .043092 | .040423 | .037924 | .035584 |
| 36 | .058589 | .054821 | .051301 | .048013 | .044941 | .042071 | .039389 | .036882 | .034539 | .032349 |
| 37 | .054149 | .050573 | .047239 | .044130 | .041231 | .038527 | .036005 | .033652 | .031457 | .029408 |
| 38 | .050045 | .046654 | .043498 | .040560 | .037826 | .035281 | .032911 | .030704 | .028649 | .026735 |
| 39 | .046253 | .043039 | .040053 | .037280 | .034703 | .032309 | .030083 | .028015 | .026092 | .024304 |
| 40 | .042747 | .039703 | .036881 | .034264 | .031838 | .029587 | .027498 | .025561 | .023763 | .022095 |
| 41 | .039508 | .036627 | .033961 | .031493 | .029209 | .027094 | .025136 | .023322 | .021642 | .020086 |
| 42 | .036514 | .033789 | .031271 | .028946 | .026797 | .024811 | .022976 | .021279 | .019711 | .018260 |
| 43 | .033746 | .031170 | .028795 | .026605 | .024584 | .022721 | .021002 | .019415 | .017951 | .016600 |
| 44 | .031189 | .028755 | .026515 | .024453 | .022555 | .020807 | .019197 | .017715 | .016349 | .015091 |
| 45 | .028825 | .026527 | .024415 | .022475 | .020692 | .019054 | .017548 | .016163 | .014890 | .013719 |
| 46 | .026641 | .024471 | .022482 | .020657 | .018984 | .017449 | .016040 | .014747 | .013561 | .012472 |
| 47 | .024622 | .022575 | .020701 | .018986 | .017416 | .015978 | .014662 | .013456 | .012351 | .011338 |
| 48 | .022756 | .020825 | .019062 | .017451 | .015978 | .014632 | .013402 | .012277 | .011248 | .010307 |
| 49 | .021031 | .019212 | .017552 | .016039 | .014659 | .013400 | .012250 | .011202 | .010244 | .009370 |
| 50 | .019437 | .017723 | .016163 | .014742 | .013449 | .012271 | .011198 | .010221 | .009330 | .008519 |
| 51 | .017964 | .016350 | .014883 | .013550 | .012338 | .011237 | .010236 | .009325 | .008497 | .007744 |
| 52 | .016603 | .015083 | .013704 | .012454 | .011319 | .010290 | .009356 | .008508 | .007739 | .007040 |
| 53 | .015345 | .013914 | .012619 | .011446 | .010385 | .009423 | .008552 | .007763 | .007048 | .006400 |
| 54 | .014182 | .012836 | .011620 | .010521 | .009527 | .008629 | .007817 | .007083 | .006419 | .005818 |
| 55 | .013107 | .011841 | .010699 | .009670 | .008741 | .007902 | .007146 | .006463 | .005846 | .005289 |
| 56 | .012114 | .010923 | .009852 | .008888 | .008019 | .007237 | .006532 | .005897 | .005324 | .004809 |
| 57 | .011196 | .010077 | .009072 | .008169 | .007357 | .006627 | .005971 | .005380 | .004849 | .004371 |
| 58 | .010347 | .009296 | .008354 | .007508 | .006749 | .006069 | .005458 | .004909 | .004416 | .003974 |
| 59 | .009563 | .008576 | .007692 | .006901 | .006192 | .005557 | .004989 | .004479 | .004022 | .003613 |
| 60 | .008838 | .007911 | .007083 | .006343 | .005681 | .005089 | .004560 | .004087 | .003663 | .003284 |

Table B—Term Certain Remainder Factors Applicable After April 30, 1989

| Years | Interest rate |
| --- | --- |
| 10.2% | 10.4% | 10.6% | 10.8% | 11.0% | 11.2% | 11.4% | 11.6% | 11.8% | 12.0% |
| 1 | .907441 | .905797 | .904159 | .902527 | .900901 | .899281 | .897666 | .896057 | .894454 | .892857 |
| 2 | .823449 | .820468 | .817504 | .814555 | .811622 | .808706 | .805804 | .802919 | .800049 | .797194 |
| 3 | .747232 | .743178 | .739153 | .735158 | .731191 | .727253 | .723343 | .719461 | .715607 | .711780 |
| 4 | .678069 | .673168 | .668312 | .663500 | .658731 | .654005 | .649321 | .644679 | .640078 | .635518 |
| 5 | .615307 | .609754 | .604261 | .598827 | .593451 | .588134 | .582873 | .577669 | .572520 | .567427 |
| 6 | .558355 | .552313 | .546348 | .540457 | .534641 | .528897 | .523225 | .517625 | .512093 | .506631 |
| 7 | .506674 | .500284 | .493985 | .487777 | .481658 | .475627 | .469682 | .463821 | .458044 | .452349 |
| 8 | .459777 | .453156 | .446641 | .440232 | .433926 | .427722 | .421617 | .415610 | .409700 | .403883 |
| 9 | .417221 | .410467 | .403835 | .397322 | .390925 | .384642 | .378472 | .372411 | .366458 | .360610 |
| 10 | .378603 | .371800 | .365131 | .358593 | .352184 | .345901 | .339741 | .333701 | .327780 | .321973 |
| 11 | .343560 | .336775 | .330137 | .323640 | .317283 | .311062 | .304974 | .299016 | .293184 | .287476 |
| 12 | .311760 | .305050 | .298496 | .292094 | .285841 | .279732 | .273765 | .267935 | .262240 | .256675 |
| 13 | .282904 | .276313 | .269888 | .263623 | .257514 | .251558 | .245749 | .240085 | .234561 | .229174 |
| 14 | .256719 | .250284 | .244022 | .237927 | .231995 | .226221 | .220601 | .215130 | .209804 | .204620 |
| 15 | .232957 | .226706 | .220634 | .214735 | .209004 | .203436 | .198026 | .192769 | .187661 | .182696 |
| 16 | .211395 | .205350 | .199489 | .193804 | .188292 | .182946 | .177761 | .172732 | .167854 | .163122 |
| 17 | .191828 | .186005 | .180369 | .174914 | .169633 | .164520 | .159570 | .154778 | .150138 | .145644 |
| 18 | .174073 | .168483 | .163083 | .157864 | .152822 | .147950 | .143241 | .138690 | .134291 | .130040 |
| 19 | .157961 | .152612 | .147453 | .142477 | .137678 | .133048 | .128582 | .124274 | .120117 | .116107 |
| 20 | .143340 | .138235 | .133321 | .128589 | .124034 | .119648 | .115424 | .111357 | .107439 | .103667 |
| 21 | .130073 | .125213 | .120543 | .116055 | .111742 | .107597 | .103612 | .099782 | .096100 | .092560 |
| 22 | .118033 | .113418 | .108990 | .104743 | .100669 | .096760 | .093009 | .089410 | .085957 | .082643 |
| 23 | .107108 | .102733 | .098544 | .094533 | .090693 | .087014 | .083491 | .080117 | .076884 | .073788 |
| 24 | .097195 | .093056 | .089100 | .085319 | .081705 | .078250 | .074947 | .071789 | .068770 | .065882 |
| 25 | .088198 | .084289 | .080560 | .077003 | .073608 | .070369 | .067278 | .064327 | .061511 | .058823 |
| 26 | .080035 | .076349 | .072839 | .069497 | .066314 | .063281 | .060393 | .057641 | .055019 | .052521 |
| 27 | .072627 | .069157 | .065858 | .062723 | .059742 | .056908 | .054213 | .051650 | .049212 | .046894 |
| 28 | .065905 | .062642 | .059547 | .056609 | .053822 | .051176 | .048665 | .046281 | .044018 | .041869 |
| 29 | .059804 | .056741 | .053840 | .051091 | .048488 | .046022 | .043685 | .041470 | .039372 | .037383 |
| 30 | .054269 | .051396 | .048680 | .046111 | .043683 | .041386 | .039214 | .037160 | .035216 | .033378 |
| 31 | .049246 | .046554 | .044014 | .041617 | .039354 | .037218 | .035201 | .033297 | .031500 | .029802 |
| 32 | .044688 | .042169 | .039796 | .037560 | .035454 | .033469 | .031599 | .029836 | .028175 | .026609 |
| 33 | .040552 | .038196 | .035982 | .033899 | .031940 | .030098 | .028365 | .026735 | .025201 | .023758 |
| 34 | .036798 | .034598 | .032533 | .030595 | .028775 | .027067 | .025463 | .023956 | .022541 | .021212 |
| 35 | .033392 | .031339 | .029415 | .027613 | .025924 | .024341 | .022857 | .021466 | .020162 | .018940 |
| 36 | .030301 | .028387 | .026596 | .024921 | .023355 | .021889 | .020518 | .019235 | .018034 | .016910 |
| 37 | .027497 | .025712 | .024047 | .022492 | .021040 | .019684 | .018418 | .017236 | .016131 | .015098 |
| 38 | .024952 | .023290 | .021742 | .020300 | .018955 | .017702 | .016533 | .015444 | .014428 | .013481 |
| 39 | .022642 | .021096 | .019658 | .018321 | .017077 | .015919 | .014841 | .013839 | .012905 | .012036 |
| 40 | .020546 | .019109 | .017774 | .016535 | .015384 | .014316 | .013323 | .012400 | .011543 | .010747 |
| 41 | .018645 | .017309 | .016071 | .014923 | .013860 | .012874 | .011959 | .011111 | .010325 | .009595 |
| 42 | .016919 | .015678 | .014531 | .013469 | .012486 | .011577 | .010735 | .009956 | .009235 | .008567 |
| 43 | .015353 | .014201 | .013138 | .012156 | .011249 | .010411 | .009637 | .008922 | .008260 | .007649 |
| 44 | .013932 | .012864 | .011879 | .010971 | .010134 | .009362 | .008651 | .007994 | .007389 | .006830 |
| 45 | .012642 | .011652 | .010740 | .009902 | .009130 | .008419 | .007765 | .007163 | .006609 | .006098 |
| 46 | .011472 | .010554 | .009711 | .008937 | .008225 | .007571 | .006971 | .006419 | .005911 | .005445 |
| 47 | .010410 | .009560 | .008780 | .008065 | .007410 | .006809 | .006257 | .005752 | .005287 | .004861 |
| 48 | .009447 | .008659 | .007939 | .007279 | .006676 | .006123 | .005617 | .005154 | .004729 | .004340 |
| 49 | .008572 | .007844 | .007178 | .006570 | .006014 | .005506 | .005042 | .004618 | .004230 | .003875 |
| 50 | .007779 | .007105 | .006490 | .005929 | .005418 | .004952 | .004526 | .004138 | .003784 | .003460 |
| 51 | .007059 | .006435 | .005868 | .005351 | .004881 | .004453 | .004063 | .003708 | .003384 | .003089 |
| 52 | .006406 | .005829 | .005306 | .004830 | .004397 | .004005 | .003647 | .003322 | .003027 | .002758 |
| 53 | .005813 | .005280 | .004797 | .004359 | .003962 | .003601 | .003274 | .002977 | .002708 | .002463 |
| 54 | .005275 | .004783 | .004337 | .003934 | .003569 | .003238 | .002939 | .002668 | .002422 | .002199 |
| 55 | .004786 | .004332 | .003922 | .003551 | .003215 | .002912 | .002638 | .002390 | .002166 | .001963 |
| 56 | .004343 | .003924 | .003546 | .003205 | .002897 | .002619 | .002368 | .002142 | .001938 | .001753 |
| 57 | .003941 | .003554 | .003206 | .002892 | .002610 | .002355 | .002126 | .001919 | .001733 | .001565 |
| 58 | .003577 | .003220 | .002899 | .002610 | .002351 | .002118 | .001908 | .001720 | .001550 | .001398 |
| 59 | .003246 | .002916 | .002621 | .002356 | .002118 | .001905 | .001713 | .001541 | .001387 | .001248 |
| 60 | .002945 | .002642 | .002370 | .002126 | .001908 | .001713 | .001538 | .001381 | .001240 | .001114 |

Table B—Term Certain Remainder Factors Applicable After April 30, 1989

| Years | Interest rate |
| --- | --- |
| 12.2% | 12.4% | 12.6% | 12.8% | 13.0% | 13.2% | 13.4% | 13.6% | 13.8% | 14.0% |
| 1 | .891266 | .889680 | .888099 | .886525 | .884956 | .883392 | .881834 | .880282 | .878735 | .877193 |
| 2 | .794354 | .791530 | .788721 | .785926 | .783147 | .780382 | .777632 | .774896 | .772175 | .769468 |
| 3 | .707981 | .704208 | .700462 | .696743 | .693050 | .689383 | .685742 | .682127 | .678536 | .674972 |
| 4 | .630999 | .626520 | .622080 | .617680 | .613319 | .608996 | .604711 | .600464 | .596254 | .592080 |
| 5 | .562388 | .557402 | .552469 | .547589 | .542760 | .537982 | .533255 | .528577 | .523949 | .519369 |
| 6 | .501237 | .495909 | .490648 | .485451 | .480319 | .475249 | .470242 | .465297 | .460412 | .455587 |
| 7 | .446735 | .441200 | .435744 | .430364 | .425061 | .419831 | .414676 | .409592 | .404580 | .399637 |
| 8 | .398160 | .392527 | .386984 | .381529 | .376160 | .370876 | .365675 | .360557 | .355518 | .350559 |
| 9 | .354866 | .349223 | .343680 | .338235 | .332885 | .327629 | .322465 | .317391 | .312406 | .307508 |
| 10 | .316280 | .310697 | .305222 | .299853 | .294588 | .289425 | .284361 | .279394 | .274522 | .269744 |
| 11 | .281889 | .276421 | .271068 | .265827 | .260698 | .255676 | .250759 | .245945 | .241232 | .236617 |
| 12 | .251238 | .245926 | .240735 | .235663 | .230706 | .225862 | .221128 | .216501 | .211979 | .207559 |
| 13 | .223920 | .218795 | .213797 | .208921 | .204165 | .199525 | .194998 | .190582 | .186273 | .182069 |
| 14 | .199572 | .194658 | .189873 | .185213 | .180677 | .176258 | .171956 | .167766 | .163685 | .159710 |
| 15 | .177872 | .173183 | .168626 | .164196 | .159891 | .155705 | .151637 | .147681 | .143835 | .140096 |
| 16 | .158531 | .154077 | .149757 | .145564 | .141496 | .137549 | .133718 | .130001 | .126393 | .122892 |
| 17 | .141293 | .137080 | .132999 | .129046 | .125218 | .121510 | .117917 | .114438 | .111066 | .107800 |
| 18 | .125930 | .121957 | .118116 | .114403 | .110812 | .107341 | .103984 | .100737 | .097598 | .094561 |
| 19 | .112237 | .108503 | .104899 | .101421 | .098064 | .094824 | .091696 | .088677 | .085762 | .082948 |
| 20 | .100033 | .096533 | .093161 | .089912 | .086782 | .083767 | .080861 | .078061 | .075362 | .072762 |
| 21 | .089156 | .085883 | .082736 | .079709 | .076798 | .073999 | .071306 | .068716 | .066224 | .063826 |
| 22 | .079462 | .076408 | .073478 | .070664 | .067963 | .065370 | .062880 | .060489 | .058193 | .055988 |
| 23 | .070821 | .067979 | .065255 | .062646 | .060144 | .057747 | .055450 | .053247 | .051136 | .049112 |
| 24 | .063121 | .060480 | .057953 | .055537 | .053225 | .051014 | .048898 | .046873 | .044935 | .043081 |
| 25 | .056257 | .053807 | .051468 | .049235 | .047102 | .045065 | .043119 | .041261 | .039486 | .037790 |
| 26 | .050140 | .047871 | .045709 | .043648 | .041683 | .039810 | .038024 | .036321 | .034698 | .033149 |
| 27 | .044688 | .042590 | .040594 | .038695 | .036888 | .035168 | .033531 | .031973 | .030490 | .029078 |
| 28 | .039829 | .037892 | .036052 | .034304 | .032644 | .031067 | .029569 | .028145 | .026793 | .025507 |
| 29 | .035498 | .033711 | .032017 | .030411 | .028889 | .027444 | .026075 | .024776 | .023544 | .022375 |
| 30 | .031638 | .029992 | .028435 | .026960 | .025565 | .024244 | .022994 | .021810 | .020689 | .019627 |
| 31 | .028198 | .026684 | .025253 | .023901 | .022624 | .021417 | .020277 | .019199 | .018180 | .017217 |
| 32 | .025132 | .023740 | .022427 | .021189 | .020021 | .018920 | .017881 | .016900 | .015975 | .015102 |
| 33 | .022399 | .021121 | .019917 | .018785 | .017718 | .016714 | .015768 | .014877 | .014038 | .013248 |
| 34 | .019964 | .018791 | .017689 | .016653 | .015680 | .014765 | .013905 | .013096 | .012336 | .011621 |
| 35 | .017793 | .016718 | .015709 | .014763 | .013876 | .013043 | .012261 | .011528 | .010840 | .010194 |
| 36 | .015858 | .014873 | .013951 | .013088 | .012279 | .011522 | .010813 | .010148 | .009525 | .008942 |
| 37 | .014134 | .013233 | .012390 | .011603 | .010867 | .010178 | .009535 | .008933 | .008370 | .007844 |
| 38 | .012597 | .011773 | .011004 | .010286 | .009617 | .008992 | .008408 | .007864 | .007355 | .006880 |
| 39 | .011227 | .010474 | .009772 | .009119 | .008510 | .007943 | .007415 | .006922 | .006463 | .006035 |
| 40 | .010007 | .009319 | .008679 | .008084 | .007531 | .007017 | .006538 | .006093 | .005679 | .005294 |
| 41 | .008919 | .008291 | .007708 | .007167 | .006665 | .006199 | .005766 | .005364 | .004991 | .004644 |
| 42 | .007949 | .007376 | .006845 | .006354 | .005898 | .005476 | .005085 | .004722 | .004386 | .004074 |
| 43 | .007084 | .006562 | .006079 | .005633 | .005219 | .004837 | .004484 | .004157 | .003854 | .003573 |
| 44 | .006314 | .005838 | .005399 | .004993 | .004619 | .004273 | .003954 | .003659 | .003386 | .003135 |
| 45 | .005628 | .005194 | .004795 | .004427 | .004088 | .003775 | .003487 | .003221 | .002976 | .002750 |
| 46 | .005016 | .004621 | .004258 | .003924 | .003617 | .003335 | .003075 | .002835 | .002615 | .002412 |
| 47 | .004470 | .004111 | .003782 | .003479 | .003201 | .002946 | .002711 | .002496 | .002298 | .002116 |
| 48 | .003984 | .003658 | .003359 | .003084 | .002833 | .002602 | .002391 | .002197 | .002019 | .001856 |
| 49 | .003551 | .003254 | .002983 | .002734 | .002507 | .002299 | .002108 | .001934 | .001774 | .001628 |
| 50 | .003165 | .002895 | .002649 | .002424 | .002219 | .002031 | .001859 | .001702 | .001559 | .001428 |
| 51 | .002821 | .002576 | .002353 | .002149 | .001963 | .001794 | .001640 | .001499 | .001370 | .001253 |
| 52 | .002514 | .002292 | .002089 | .001905 | .001737 | .001585 | .001446 | .001319 | .001204 | .001099 |
| 53 | .002241 | .002039 | .001856 | .001689 | .001538 | .001400 | .001275 | .001161 | .001058 | .000964 |
| 54 | .001997 | .001814 | .001648 | .001497 | .001361 | .001237 | .001124 | .001022 | .000930 | .000846 |
| 55 | .001780 | .001614 | .001463 | .001327 | .001204 | .001093 | .000991 | .000900 | .000817 | .000742 |
| 56 | .001586 | .001436 | .001300 | .001177 | .001066 | .000965 | .000874 | .000792 | .000718 | .000651 |
| 57 | .001414 | .001277 | .001154 | .001043 | .000943 | .000853 | .000771 | .000697 | .000631 | .000571 |
| 58 | .001260 | .001136 | .001025 | .000925 | .000835 | .000753 | .000680 | .000614 | .000554 | .000501 |
| 59 | .001123 | .001011 | .000910 | .000820 | .000739 | .000665 | .000600 | .000540 | .000487 | .000439 |
| 60 | .001001 | .000900 | .000809 | .000727 | .000654 | .000588 | .000529 | .000476 | .000428 | .000385 |

Table B—Term Certain Remainder Factors Applicable After April 30, 1989

| Interest rate | Annually | Semiannually | Quarterly | Monthly | Weekly |
| --- | --- | --- | --- | --- | --- |
| 4.2 | 1.0420 | 1.0314 | 1.0261 | 1.0226 | 1.0213 |
| 4.4 | 1.0440 | 1.0329 | 1.0274 | 1.0237 | 1.0223 |
| 4.6 | 1.0460 | 1.0344 | 1.0286 | 1.0247 | 1.0233 |
| 4.8 | 1.0480 | 1.0359 | 1.0298 | 1.0258 | 1.0243 |
| 5.0 | 1.0500 | 1.0373 | 1.0311 | 1.0269 | 1.0253 |
| 5.2 | 1.0520 | 1.0388 | 1.0323 | 1.0279 | 1.0263 |
| 5.4 | 1.0540 | 1.0403 | 1.0335 | 1.0290 | 1.0273 |
| 5.6 | 1.0560 | 1.0418 | 1.0348 | 1.0301 | 1.0283 |
| 5.8 | 1.0580 | 1.0433 | 1.0360 | 1.0311 | 1.0293 |
| 6.0 | 1.0600 | 1.0448 | 1.0372 | 1.0322 | 1.0303 |
| 6.2 | 1.0620 | 1.0463 | 1.0385 | 1.0333 | 1.0313 |
| 6.4 | 1.0640 | 1.0478 | 1.0397 | 1.0343 | 1.0323 |
| 6.6 | 1.0660 | 1.0492 | 1.0409 | 1.0354 | 1.0333 |
| 6.8 | 1.0680 | 1.0507 | 1.0422 | 1.0365 | 1.0343 |
| 7.0 | 1.0700 | 1.0522 | 1.0434 | 1.0375 | 1.0353 |
| 7.2 | 1.0720 | 1.0537 | 1.0446 | 1.0386 | 1.0363 |
| 7.4 | 1.0740 | 1.0552 | 1.0458 | 1.0396 | 1.0373 |
| 7.6 | 1.0760 | 1.0567 | 1.0471 | 1.0407 | 1.0383 |
| 7.8 | 1.0780 | 1.0581 | 1.0483 | 1.0418 | 1.0393 |
| 8.0 | 1.0800 | 1.0596 | 1.0495 | 1.0428 | 1.0403 |
| 8.2 | 1.0820 | 1.0611 | 1.0507 | 1.0439 | 1.0413 |
| 8.4 | 1.0840 | 1.0626 | 1.0520 | 1.0449 | 1.0422 |
| 8.6 | 1.0860 | 1.0641 | 1.0532 | 1.0460 | 1.0432 |
| 8.8 | 1.0880 | 1.0655 | 1.0544 | 1.0471 | 1.0442 |
| 9.0 | 1.0900 | 1.0670 | 1.0556 | 1.0481 | 1.0452 |
| 9.2 | 1.0920 | 1.0685 | 1.0569 | 1.0492 | 1.0462 |
| 9.4 | 1.0940 | 1.0700 | 1.0581 | 1.0502 | 1.0472 |
| 9.6 | 1.0960 | 1.0715 | 1.0593 | 1.0513 | 1.0482 |
| 9.8 | 1.0980 | 1.0729 | 1.0605 | 1.0523 | 1.0492 |
| 10.0 | 1.1000 | 1.0744 | 1.0618 | 1.0534 | 1.0502 |
| 10.2 | 1.1020 | 1.0759 | 1.0630 | 1.0544 | 1.0512 |
| 10.4 | 1.1040 | 1.0774 | 1.0642 | 1.0555 | 1.0521 |
| 10.6 | 1.1060 | 1.0788 | 1.0654 | 1.0565 | 1.0531 |
| 10.8 | 1.1080 | 1.0803 | 1.0666 | 1.0576 | 1.0541 |
| 11.0 | 1.1100 | 1.0818 | 1.0679 | 1.0586 | 1.0551 |
| 11.2 | 1.1120 | 1.0833 | 1.0691 | 1.0597 | 1.0561 |
| 11.4 | 1.1140 | 1.0847 | 1.0703 | 1.0607 | 1.0571 |
| 11.6 | 1.1160 | 1.0862 | 1.0715 | 1.0618 | 1.0581 |
| 11.8 | 1.1180 | 1.0877 | 1.0727 | 1.0628 | 1.0590 |
| 12.0 | 1.1200 | 1.0892 | 1.0739 | 1.0639 | 1.0600 |
| 12.2 | 1.1220 | 1.0906 | 1.0752 | 1.0649 | 1.0610 |
| 12.4 | 1.1240 | 1.0921 | 1.0764 | 1.0660 | 1.0620 |
| 12.6 | 1.1260 | 1.0936 | 1.0776 | 1.0670 | 1.0630 |
| 12.8 | 1.1280 | 1.0950 | 1.0788 | 1.0681 | 1.0639 |
| 13.0 | 1.1300 | 1.0965 | 1.0800 | 1.0691 | 1.0649 |
| 13.2 | 1.1320 | 1.0980 | 1.0812 | 1.0701 | 1.0659 |
| 13.4 | 1.1340 | 1.0994 | 1.0824 | 1.0712 | 1.0669 |
| 13.6 | 1.1360 | 1.1009 | 1.0836 | 1.0722 | 1.0679 |
| 13.8 | 1.1380 | 1.1024 | 1.0849 | 1.0733 | 1.0688 |
| 14.0 | 1.1400 | 1.1039 | 1.0861 | 1.0743 | 1.0698 |

Table J—Adjustment Factors for Term Certain Annuities Payable at the Beginning of Each Interval Applicable After April 30, 1989

[Frequency of payments]

| Interest Rate | Annually | Semiannually | Quarterly | Monthly | Weekly |
| --- | --- | --- | --- | --- | --- |
| 4.2 | 1.0000 | 1.0104 | 1.0156 | 1.0191 | 1.0205 |
| 4.4 | 1.0000 | 1.0109 | 1.0164 | 1.0200 | 1.0214 |
| 4.6 | 1.0000 | 1.0114 | 1.0171 | 1.0209 | 1.0224 |
| 4.8 | 1.0000 | 1.0119 | 1.0178 | 1.0218 | 1.0234 |
| 5.0 | 1.0000 | 1.0123 | 1.0186 | 1.0227 | 1.0243 |
| 5.2 | 1.0000 | 1.0128 | 1.0193 | 1.0236 | 1.0253 |
| 5.4 | 1.0000 | 1.0133 | 1.0200 | 1.0245 | 1.0262 |
| 5.6 | 1.0000 | 1.0138 | 1.0208 | 1.0254 | 1.0272 |
| 5.8 | 1.0000 | 1.0143 | 1.0215 | 1.0263 | 1.0282 |
| 6.0 | 1.0000 | 1.0148 | 1.0222 | 1.0272 | 1.0291 |
| 6.2 | 1.0000 | 1.0153 | 1.0230 | 1.0281 | 1.0301 |
| 6.4 | 1.0000 | 1.0158 | 1.0237 | 1.0290 | 1.0311 |
| 6.6 | 1.0000 | 1.0162 | 1.0244 | 1.0299 | 1.0320 |
| 6.8 | 1.0000 | 1.0167 | 1.0252 | 1.0308 | 1.0330 |
| 7.0 | 1.0000 | 1.0172 | 1.0259 | 1.0317 | 1.0339 |
| 7.2 | 1.0000 | 1.0177 | 1.0266 | 1.0326 | 1.0349 |
| 7.4 | 1.0000 | 1.0182 | 1.0273 | 1.0335 | 1.0358 |
| 7.6 | 1.0000 | 1.0187 | 1.0281 | 1.0344 | 1.0368 |
| 7.8 | 1.0000 | 1.0191 | 1.0288 | 1.0353 | 1.0378 |
| 8.0 | 1.0000 | 1.0196 | 1.0295 | 1.0362 | 1.0387 |
| 8.2 | 1.0000 | 1.0201 | 1.0302 | 1.0370 | 1.0397 |
| 8.4 | 1.0000 | 1.0206 | 1.0310 | 1.0379 | 1.0406 |
| 8.6 | 1.0000 | 1.0211 | 1.0317 | 1.0388 | 1.0416 |
| 8.8 | 1.0000 | 1.0215 | 1.0324 | 1.0397 | 1.0425 |
| 9.0 | 1.0000 | 1.0220 | 1.0331 | 1.0406 | 1.0435 |
| 9.2 | 1.0000 | 1.0225 | 1.0339 | 1.0415 | 1.0444 |
| 9.4 | 1.0000 | 1.0230 | 1.0346 | 1.0424 | 1.0454 |
| 9.6 | 1.0000 | 1.0235 | 1.0353 | 1.0433 | 1.0463 |
| 9.8 | 1.0000 | 1.0239 | 1.0360 | 1.0442 | 1.0473 |
| 10.0 | 1.0000 | 1.0244 | 1.0368 | 1.0450 | 1.0482 |
| 10.2 | 1.0000 | 1.0249 | 1.0375 | 1.0459 | 1.0492 |
| 10.4 | 1.0000 | 1.0254 | 1.0382 | 1.0468 | 1.0501 |
| 10.6 | 1.0000 | 1.0258 | 1.0389 | 1.0477 | 1.0511 |
| 10.8 | 1.0000 | 1.0263 | 1.0396 | 1.0486 | 1.0520 |
| 11.0 | 1.0000 | 1.0268 | 1.0404 | 1.0495 | 1.0530 |
| 11.2 | 1.0000 | 1.0273 | 1.0411 | 1.0503 | 1.0539 |
| 11.4 | 1.0000 | 1.0277 | 1.0418 | 1.0512 | 1.0549 |
| 11.6 | 1.0000 | 1.0282 | 1.0425 | 1.0521 | 1.0558 |
| 11.8 | 1.0000 | 1.0287 | 1.0432 | 1.0530 | 1.0568 |
| 12.0 | 1.0000 | 1.0292 | 1.0439 | 1.0539 | 1.0577 |
| 12.2 | 1.0000 | 1.0296 | 1.0447 | 1.0548 | 1.0587 |
| 12.4 | 1.0000 | 1.0301 | 1.0454 | 1.0556 | 1.0596 |
| 12.6 | 1.0000 | 1.0306 | 1.0461 | 1.0565 | 1.0605 |
| 12.8 | 1.0000 | 1.0310 | 1.0468 | 1.0574 | 1.0615 |
| 13.0 | 1.0000 | 1.0315 | 1.0475 | 1.0583 | 1.0624 |
| 13.2 | 1.0000 | 1.0320 | 1.0482 | 1.0591 | 1.0634 |
| 13.4 | 1.0000 | 1.0324 | 1.0489 | 1.0600 | 1.0643 |
| 13.6 | 1.0000 | 1.0329 | 1.0496 | 1.0609 | 1.0652 |
| 13.8 | 1.0000 | 1.0334 | 1.0504 | 1.0618 | 1.0662 |
| 14.0 | 1.0000 | 1.0339 | 1.0511 | 1.0626 | 1.0671 |

Table K—Adjustment Factors For Annuities Payable At The End Of Each Interval Applicable After April 30, 1989

[Frequency of Payments]

(7) *Actuarial Table S and Table 2010CM where the valuation date is on or after June 1, 2023* —

(i) *Determination of required factors.* Except as provided in § 20.7520-3(b) (pertaining to certain limitations on the use of prescribed tables), for determination of the present value of a remainder interest that is dependent on the termination of a life interest, where the valuation date is on or after June 1, 2023, actuarial remainder factors computed to at least five decimal places directly by using the formula in paragraph (d)(2)(ii)(B) of this section, Table 2010CM, and the section 7520 rate are used in the application of the provisions of this section. For the convenience of taxpayers, the actuarial factors, when the section 7520 interest rate component is from 0.2 to 20 percent, inclusive, have been computed by the IRS and can be found in Table S. Table S currently is available, at no charge, electronically via the IRS website at *https://www.irs.gov/retirement-plans/actuarial-tables.* Table S is also referenced and explained by IRS Publication 1457, *Actuarial Valuations Version 4A,* which will be available within a reasonable time after June 1, 2023.

(ii)

| Age x | *l*
x | Age x | *l*
x | Age x | *l*
x |
| --- | --- | --- | --- | --- | --- |
| 0 | 100,000.00 | 37 | 97,193.66 | 74 | 71,177.55 |
| 1 | 99,382.28 | 38 | 97,058.84 | 75 | 69,174.83 |
| 2 | 99,341.16 | 39 | 96,915.25 | 76 | 67,044.59 |
| 3 | 99,313.80 | 40 | 96,761.20 | 77 | 64,773.93 |
| 4 | 99,292.72 | 41 | 96,595.51 | 78 | 62,366.05 |
| 5 | 99,276.45 | 42 | 96,416.30 | 79 | 59,795.50 |
| 6 | 99,261.55 | 43 | 96,220.61 | 80 | 57,080.84 |
| 7 | 99,248.33 | 44 | 96,005.41 | 81 | 54,213.71 |
| 8 | 99,236.50 | 45 | 95,768.60 | 82 | 51,205.27 |
| 9 | 99,226.09 | 46 | 95,509.98 | 83 | 48,059.88 |
| 10 | 99,217.03 | 47 | 95,229.06 | 84 | 44,808.51 |
| 11 | 99,208.80 | 48 | 94,923.45 | 85 | 41,399.79 |
| 12 | 99,199.98 | 49 | 94,589.88 | 86 | 37,895.25 |
| 13 | 99,188.21 | 50 | 94,225.50 | 87 | 34,313.98 |
| 14 | 99,170.64 | 51 | 93,828.33 | 88 | 30,700.82 |
| 15 | 99,145.34 | 52 | 93,398.01 | 89 | 27,106.68 |
| 16 | 99,111.91 | 53 | 92,934.52 | 90 | 23,586.75 |
| 17 | 99,070.69 | 54 | 92,438.08 | 91 | 20,198.02 |
| 18 | 99,021.50 | 55 | 91,907.95 | 92 | 16,996.17 |
| 19 | 98,964.16 | 56 | 91,342.02 | 93 | 14,032.08 |
| 20 | 98,898.61 | 57 | 90,737.24 | 94 | 11,348.23 |
| 21 | 98,824.20 | 58 | 90,090.97 | 95 | 8,975.661 |
| 22 | 98,741.32 | 59 | 89,401.06 | 96 | 6,931.559 |
| 23 | 98,652.16 | 60 | 88,665.95 | 97 | 5,218.261 |
| 24 | 98,559.87 | 61 | 87,883.66 | 98 | 3,823.642 |
| 25 | 98,466.80 | 62 | 87,051.88 | 99 | 2,722.994 |
| 26 | 98,373.71 | 63 | 86,167.86 | 100 | 1,882.108 |
| 27 | 98,280.09 | 64 | 85,226.77 | 101 | 1,261.083 |
| 28 | 98,185.51 | 65 | 84,221.59 | 102 | 818.2641 |
| 29 | 98,089.05 | 66 | 83,142.34 | 103 | 513.7236 |
| 30 | 97,989.90 | 67 | 81,978.28 | 104 | 311.8784 |
| 31 | 97,887.47 | 68 | 80,728.83 | 105 | 183.0200 |
| 32 | 97,781.58 | 69 | 79,387.95 | 106 | 103.8046 |
| 33 | 97,672.13 | 70 | 77,957.53 | 107 | 56.91106 |
| 34 | 97,559.20 | 71 | 76,429.84 | 108 | 30.17214 |
| 35 | 97,442.53 | 72 | 74,797.63 | 109 | 15.47804 |
| 36 | 97,321.14 | 73 | 73,049.33 | 110 | 0.000000 |

Table 4 to Paragraph (d)(7)(ii)

(e) *Applicability date.* This section applies on and after June 1, 2023.

[T.D. 8540, 59 FR 30152, June 10, 1994, as amended by T.D. 8819, 64 FR 23212, Apr. 30, 1999; T.D. 8886, 65 FR 36929, June 12, 2000; T.D. 9448, 74 FR 21484, May 7, 2009; T.D. 9540, 76 FR 49612, Aug. 10, 2011; T.D. 9974, 88 FR 37439, June 7, 2023]