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