on Survivorjhips. 347 
$ 
reafoning as in p. 335. the value of the fumS, when the ages are 
equal, will be = Sx^x- — c -f -f i- x C — 1 + + &c. rr 
1 br b 
2 di>r br‘ 
2 bbt 
S bb cc dd q S 
- x 77- + 7— 2 + nr * + &c * — x 
2 bbr bb) bbr 3 2 
K i-Ji + jL 4-&C =l+i_i 
bbr bbr 1 * Ur* 2»' 2 r 
bbr 3 2 ££/■' £6/" i^ 3 2>' 2r 2 
x BB (putting BB for the value of the two equal joint lives) = 
1 1 the 
S t r — I 
“ X - — 
xBB= (fince the perpetuity P is - — and 
intereft of any fum is that fum multiplied by r— i) 
F • — 7.1 — LR ‘ which is Mr. Simpson’s rule with Dr. 
— x 
2 
Price’s correction ; that is, “ half the fum multiplied by the 
“ difference between the perpetuity and the value of the equal 
joint lives, and divided by yf. i increafed by its intereft for a 
a 
year 
>» 
PROBLEM III. 
The ages of A and B being given ; to determine the value 
of the fum S, payable on the extinction of one life in particu- 
lar, fhould that happen after the extinction of the other life. 
SOLUTION. 
Suppofing B to be the oldeft of the two lives and the fum 
S to become payable on his deceafe, it is evident that this 
payment at the end of the firft year mu ft depend on the con- 
tingency of both lives being extinCt before this period and of 
B’s dying laft. Retaining the fame fymbols, and reafoning as 
I have done in the folution of the firft problem, this value 
Vol. LXXVIII. A a a will 
