40 Mr. Morgan on Survivorships. 



" failed ; and also the value of the same sum, should B be the 

 " first, C the second, and A the third, that failed :" but the 

 foregoing rules, in being more simple, are preferable. 



In the particular case of the equality of the three lives, the 



value, by these problems, will be = S into x V — CCC -f- 



r -=± x V — 3C + 3CC - CCC = Sr ~ l x V-C+CC-CCC, 

 as before. Q. E. D. 



PROBLEM VII. 



To determine the value of a given sum, payable on the death 

 of A, B, and C, provided C shall die after one life in parti- 

 cular, (A). 



Solution. 



In the 1st year, the value of the given sum will be = 



s 1 — — _ - g 



— r — x6 — m .c — d .a'\ in the 2d year, it will be = — 7 — r- 



aocr ' J ' abcr* 



2 



. m — n.d — e . a" , , , , , c—d-tn — n . a' , ——^—— 



into \- — m . a — e . a' -j \- m — n . 



b — m.d — e a" • ,i , S n — o.e — f.a" 



e . a' -\ ; in the 3d year = , r3 into 



c — e . n — & . a'-\-a" 



j r b — n.e—f.a'+a"+ z ^ +n —0 .e—f.a'+a" 

 , ~ ~ ; ' • e -> a t an( j so on j n t ne other years ; whence the 



r — \ 



whole value may at last be found = S into — — x BC —• B — 



ABC + -5£---^-+^- x i+AP- tl±SL - 



1 2 zr ■ 2br ' c 



2C 



BK— ABK -f R, (R denoting the value of S, by the 3d problem 



