tation of enjoying after a given period is found by multiplying the ex
pectation at the advanced age by the chance the individual has of
attaining that age.
How many years has a male aged 50 the expectation of enjoying after
the expiration of 10 years by the Chester rate?
10.55.
126. Since the expectation for the whole of life is made up of the
expectation during the next t years, and of the expectation after that
term, “the expectation for the next t years only is evidently equal to the
difference between the expectation for the whole term of life and the
expectation deferred for t years.”
&m “ i X e,n+<
v-r,
Example. How many years has a male aged 50 the expectation of
enjoying during the’next 10 years by the Chester rate ?
p — v P
. -A
im
■ ■ - X e 60
'27*78
19.32 - r^r X 13.96 = 19.32 — 10.55 = 8.77.
127. Many persons who have but an imperfect knowledge of the
subject, erroneously suppose that the value of an annuity payable during
the life of an individual is found by calculating the value of an annuity
certain for a number of years equal to the expectation of life of the
individual.
By Art. 112 it appears, that if the probability of an individual sur
viving 1, 2, 3, &c. years to the extremity of life, be respectively mul
tiplied by the present value of £l due 1, 2, 3, &c. years, the sum
of the several values thus found will be the value of an annuity on the
life of that individual.
The expectation shows the number of payments received on an ave
rage by every person of the same age; if an annuity certain be calcu
lated therefore for a term equal to the expectation, the longest period of
discount introduced in the calculation will be the number of years’
expectation; but in valuing a life annuity at the same age, although
each individual receives on an average the same number of payments as
are made upon an annuity certain, yet some of the probabilities are
discounted for a longer term than is represented by the expectation ; at
the age of 30, for instance, the expectation is 30.80, which is the term
for which the last payment of the annuity certain is discounted, while,
in finding the true value of a life annuity, the probability of completing
each year is discounted for every year a life may complete according to