[ 7 + ] 
Jj 
Therefore - x ^ will be the value of an 
annuity on a life for the limited time. 6 ^ E. T > . 
It is obvious, that the feries denoted by J9, muft 
of necefiity have one term lefs than is the number 
of equal intervals contain’d in s\ and therefore, if 
the whole extent of life, beginning from an age 
given, be divided into feveral intervals, each having 
its own particular uniform decrements, there will be, 
in each of thefe intervals, the defeat of one pay- 
ment 5 which to remedy, the feries J^muft be cal- 
culated by problem i . 
Example. 
To find the value of an annuity for an age of 54, 
to continue 16 years, and no longer. 
TT is found, in Dr. Halleys tables of obfervations, 
**’ that a is 302, and b 172 : now n — s— 16 j and, 
by the tables of the values of annuities certain, 
^Prrrio. 8377 j alfo (by problem 1 .) 
6.1168. Hence it follows (by this problem), that 
the value of an annuity for an age of 54, to con- 
tinue during the limited time of 16 years, fuppofe- 
ing intereft at 5 per cent . per annum, will be worth 
(J^H~ ~ x p —gj=) S.3365 years purchafe. 
Prom Dr. Halleys tables of obfervations, we 
find, that from the age of 49 to 54 indufive, the 
number of perfons, exifting at thofe feveral ages, 
ate, 357, 346, 335, 324, 313, 302, which compre- 
hends a fpace of five years ; and, following the 
precepts before laid down, we fiiali find, that an 
annuity 
