for the Valuation of Life-annuities . 1 1 7 
or the number of lives, a fifth of a year’s purchafe will 
be generally more than a fufhcient addition, if the value 
of the annuity is defired payable half-yearly ; and three- 
tenths of a year’s purchafe, if the value of the annuity is 
defired payable quarterly. Mr. de moivre’s rules, in p. 
85 of his Book on Life-annuities, for finding the values 
of life-annuities payable half-yearly and quarterly from 
their values payable yearly, are ftill lefs correct ; for they 
fuppofe the difference between thefe values the fame, 
whether the annuities are life -annuities, or annuities 
certain. 
Mr. dodson, in the firft queftion in the third volume 
of his Mathematical Repofitory, hath given a rule for find- 
ing the value of an annuity fecuredby land and payable 
yearly, which coincides with that here given ; and Mr. 
de moivre, in p. 338. of his Treatife on the Docffrine of 
Chances, hath given a theorem for this purpofe, which 
alfo brings out nearly the fame anfwers. But Mr. simp- 
son, in prob. 1. p. 3 23. of his Select Exerciles, makes the 
excefs of the value of fuch an annuity above the value 
of an annuity payable yearly, but not fecured by land, dou- 
ble to the fame excefs derived from Mr. dodson’s and Mr. 
de moivre’s rules. The truth is, that Mr. dodson’s rule 
gives the exadt value ; and that Mr. simpson’s problem 
gives the value, not of an annuity fecured by land and 
payable yearly, but of an annuity fecured by land and 
payable momently ; and alfo, that his method of folution 
implies a rate of intercft fomewhat lefs when the annuity 
is payable momently than when it is payable yearly. 
But 
