[ 75 ] 
annuity for a life of 49, to continue for the limited 
time of 5 years, intereft being at 5 per cent, per 
annum , is worth 4.0374 years purchafe. 
And, in the fame manner, we fhail find, that the 
value of an annuity on life, for the limited time 
comprehended between the ages of 42 and 49, is 
worth 5.3492 years purchafe. 
Now, if it were required to determine the value of 
an annuity on life, to continue from the age of 
42 to 70, we muff proceed thus : 
It has been- -proved, that an annuity on life, reach- 
ing from the age of 54 to 70, is worth 8.3365 years 
purchafe j but this value, being eflimated from the age 
of 49, ought to be diminifhed on two accounts : Firff, 
becaufeof the probability of the life’s reaching from 
49 to 54, which probability is to be deduced from the 
table of obfervations, and is proportional to the num- 
ber of people living at the end and beginning of that 
interval, which, in this cafe, will be found 302 and 
357 : The fecond diminution proceeds from a dis- 
count that ought to be made, becaufe the annuity, 
which reaches from 54 to 70, is eflimated 5 years 
fooner, viz. from the age of 49, and therefore that 
diminution ought to be expreffed by -^5 fo that the 
total diminution of the annuity of 16 years will be 
expreffed by the fra&ion fhi— , 
which will reduce it 
from 8-3365 years purchafe to 5 • 5 2 5 9 > this being 
added to the value of the annuity to continue from 
49 to 54, viz. 4.0374, will give 9.5633, the value 
of an annuity to continue from the age of 49 to 70. 
For the fame reafon, the value 9.56 33, eflimated 
K 2 from 
