Evening star. [volume] (Washington, D.C.) 1854-1972, 1905-07-15

insurance companies today make their COM
putations of premiums the basis that
net premiums in their hands will earn
neither more nor less than this percentage.
Computing the Premium.
Now. let us see how the net premium is
computed.
For purposes of demonstration, suppose
there has been organized a life insurance
company with number of members equal
to the number of persons out of 100000
that the mortality table commonly in use
in this country shows viii be alive at the
age of thirty-five. This number is S1,S22,
and each member is insured for 81 900, pay
able at death, holding what Is termed
ordinary life policy, the premium to be paid
yearly until death.
If each of these members were to live
twenty years, only the simplest sort of
net premium. Or If the company could
start out on the day of its organization
with SSl SD, 900 in hand, the total face value
of all its policies. the life insurance bust
ness would be Il very simple one. But the
money is to come in in yearly installments;
therefore, 1t is necessary to know how
much money this company of 100000 MEM
bers will have to have on hand from year
to year to meet the death claims that the
mortality table shows it will be called upon
to meet each year.
According to the mortality table, all OF
these 81 ,S22 members will have died within
thirty-flve years of age. 1t is impossible TO
know when any certain member will die, or
how long he will live. The amount that
each member should pay, therefore, cannot
be determined by means Of a computation
based upon single life. as would be the
case if il were known definitely that each
of the 81, SD members would live twenty
years and then die.
But If it is not known how long any
one individual will live, it is known how
long certain groups Of members Will live
For example, the mortality table at age
thirty-five shows that 132 of the s1,S22
one year; that So will live ten years, TO
age forty-fve; lao will live fifty years to
age SIS. and that the last three Will hVe
sixty-one years, to age W. The computa-
tions must be based, therefore, upon the
aggregate number of lives-upon the length
of time the members will live as body, as
shown in the case of these several groups
of the mortality table.
Growth of the Fund on Hand.
AS So members will die during or az
the end of the tenth year, at the attained
age of forty-five, $4,000 will be needed IN
the tenth year to pay the 81 policies each
calling for s1,oO0. But as the law generally
permits life insurance companies to assume
that their funds will earn money at the
rate of 312 per cent compound interest II
is necessary to have in hand now only
ten years, at this rate.
At this rate of interest, the present worth
of SSl2, 900 due in ten years, is S515626so
With this sum In hand and safely invested,
II is mathematically certain that the COM
pany will be able to pay the losses OF the
tenth year.
The mortality table also shows that in
the twentieth year, at age ffty-four, there
will be l. 143 deaths calling for the payment
in that year of ST. $4,000. The present
worth of that sum is S514.411.S0 There
will be 49, deaths the first year, calling
for payment of s732,OO0 and the present
worth of this amount, due to be paid IN
death claims in one year, Is $l0I ,23S. 40.
In like manner, it can be determined what
the losses will be for each year to the
last the sixtyffrst, when the death claims
will aggregate $1,000. So also can be COM
puted the present worth of the amount
which will be needed in each year to pay
all the losses of each year until the very
last year, when the three surviving mem
bers will die. Three hundred and sixty
seven dollars and ninety-three cents on
hand today will amount in sxty-one years
to $1,000, sum sufficient TO pay IN full the
policies of the last three OF the original
81, 500 members of the company.
Total Losses.
The total losses in the sixty-one years.
when the last three policy holders die, will
be $S1, So, 0G0 The total present worth of
the combined losses is $30,319, 142.10. With
this amount on hand today, assuming that
the same will earn 315 per cent compound
interest, the company Will have funds suffi-
cient for the payment Of every loss that
can possibly occur in any year until the
last three members die, in the ninety-sixth
year of their age.
This amount, divided by 81 ,s22. the num-
Der of persons originally insured in the
company, gives S3T055. In other words If
each member of the company will pay in
cash the sum of 37o.55 the company will
have at date of organization a total OF
$50, 3l9, 1872 10. and this sum, plus the inter-
est 1t will earn, will be sufficient to pay
every existing policy in full as the several
deaths occur.
This s370.55 is termed the net single pre-
MUM. 1t is the net amount without pro-
vision for expenses, which man at the
age of thirty-five should pay for full-paid
ordinary life policy at $1,000.
Thus, 1t is seen that in life insurance The
larger part of the money used in paying
losses comes from interest.
The net single premium having been de-
posted no further payments would ever be
required. Most men, however, would find
1t inconvenient to pay for their life insur-
ance in lump sum; that is, to take out
full-paid or paid-up policies. But by means
of a comparatively simple mathematical
process the net single premium may be ap-
portioned into equivalent yearly payments
to be made by the insured during life
The Net Annual Premium.
annual premium is to compute the value
of life annuity.
An annuity is specified sum OF money
to be paid yearly to some designated per-
son. The one to whom the money is to be
paid Is termed the annuitant. If the pay
ment Is to be made every year until the
annuitant dies 1t is termed a life annuity.
The amount of yearly income or annuity
which can be purchased with $1,000, say.
viii naturally depend upon the age of the
annuitant. One thousand dollars will buy
o larger income for man of sixty than for
one Of thirty-five years. because the for
mer has on an average a much shorter
time to live. The net cost OF an annuity
the amount to be paid therefor In one sum-
Is termed the value of the annuity Like
the net single premium of life insurance 1t
is determined by means Of the mortality
table.
Suppose each of 1882 persons. each
thirty-fve years of age, wishes to take out a
life annuity of 81 and the first payment
Is to be made Immediately on Issuance CT
the contract. The first step Is to ascer-
tain the net amount that the company
should charge for life annuity of 81 in
order that its funds would be sufficient
to pay every annuity until the last three
members die In the sixty-frst year.
Z On the day the contracts are made the
company must pay out $91.S22 In annnittes.