Mr. Morgan on Survivorships . 
HS 
SOLUTION. 
In the first year the payment of the given sum will depend 
upon either of two events ; ist, that all the three lives shall 
b — m . c — d . a ,, 
2dly f 
— d . ma' 
zabc 
drop (B having survived A) which is = 
That B shall live, and only A and C die, which is 
The value therefore of the given sum in the first year will be 
In the second and following years 
abc 
S 
abcr 
bc-\-mc — bd — md 
the payment of S will depend upon either of seven events ; 
ist. that all the three lives drop in the year, B having survived 
A. sdly, That B lives, and only A and C die in the year. 3 dly, 
that A dies in the year, C dies in any of the foregoing years, 
and B lives. 4 thly, That B dies after A in the year, and C 
dies in any of the foregoing years. 5 thly, That C dies in the 
year, and B dies after A in any of the foregoing years, bthly, 
That B and C both die in the year, and A dies in any of the 
foregoing years. And 7 thly, That C dies in the year, A in any 
of the foregoing years, and B lives. From the several frac- 
tions expressing these contingencies the value of the given 
s 
sum will be found = 
2 ab 
X a + ^ + £ 
+ &C. + 
2 ab 
" + + &c. - A X i ^ ^ + &c. _ 
s 
zabc 
a'md . 
x-r + 
+$?H-&c.+S f .x7 ? + 
a'd 
a' -\-a" 
+ &C. + 
S a'md , a'-f-c 
2 abcr X r * ] 
S 
zabcr 
+ &c. 
a' me , a'-fa" . nf 
BC — ABC — S —I 
zb 
+ &c. = E -f 
FC — AFC + 
I i 2 
s. d 
m . PT— APT 
