120 
Dr. price’s Theorems 
\ 
t 
I 
2 X If J — 2 
which va- 
lue is to i -==^x — (the value of the fame annuity pay- 
able yearly fuppofing the yearly intereft of j[. i to be r) 
i i 
as — ^ — to - , agreeably to Mr. de moivre’s deduction 
i + 
7 1 '— i 
in his Treatife on Life-annuities, p. 125. fourth edit. 
This implying, in the cafe of annuities payable half- 
yearly, a fmaller intereft than half the yearly intereft (for 
x +rV- 1 is lefs than ^ gives the difference between their 
value and the value of annuities payable yearly, greater 
than the truth. 
But to return to the inveftigation of the theorems in 
the former part this paper. 
Let us again call p the perpetuity, and^ the value of 
an annuity certain for n years and payable yearly ; it is 
well known that the value of £ . 1 payable yearly on a life 
whofe complement is n is (fuppofing an equal decrement 
of life) — — == -i — h — , 8cc. continued to n 
«xi+f wxi+n HXi+rl 
1 +r 
terms (0 
In 
(c) See Mr. de moivre’s Treatife on Life-annuities, p. 99. fourtli edit. 
Or his Do&rine of Chances, p. 31 1. third edition. Or Mr. dodson’s Mathe- 
matical Repoiitory, vol. II. p. 137. Or Mr. Simpson on Annuities and Rcvcr- 
fions, p. 14. In confuting thefe writers, care fliould be taken to remember, that 
they ul'er to denote the principal and intereft of £, 1 for a year; whereas it hath 
been 
