[ *75 1 ' 
ages refpe&ively for n years, by n. Now .pT 
-j-r, &c. (continued to n terms) is the value of an 
annuity on the given life B for n years. And ~ r - i r i 
~yri, &c. (continued to n terms) is the value of an 
annuity certain for n years, divided by 2 b. 
The general rule, therefore, is this. 
“ Find (by problem 23. in M. de Moivre’s 
“ Treatife on Annuities, fourth edition) the value of 
“ an annuity on the life of B for n years. To this 
“ value add the quotient arifing from dividing by 2 b y 
“ the value of an annuity certain for n years, taken 
<c out of M. de Moivre’s tables in the treatife juft 
“ mentioned, or out of table III. in Mr. Simpfon’s 
S 
“ Seledl Exercifes : and the fum multiplied by ~ 
“ will be the required value.” 
Example. Let the rate of intereft be 3 per cent. 
or r— 1.03. 
The table of obfervations, Mr. Simpfon’s in his 
Seledt Exercifes, p. 254. 
Let the age of A be feven years. B, 30. 77—14 anc * 
S— 1 00 /. 
The fum of the decrements in the table for four- 
teen years from feven years of age, is 73 ; which 
divided by 14 is 5.2. The number alive at feven is 
430 j and this, divided by 5.2, gives 82.6 for the 
value of a. In like manner the value of b may be 
found to be 41.7. The value of an annuity for 14 
years on a life of 30, is 9.5. The value of an an- 
nuity certain for 14 years is 11.296, which divided 
N n 2 by 
