•hli-h! l-ji-jatfjiffii-.-V: 
— 663.375 
— - .32550 
2038 2038 
£(•73338+ .32550) X500=£264.720=£264 14 5. 
By the 2nd formula— 
f I 4 , «(m-1, mj «(m, mi—1) | 1 f 4 , «59.37 «60.86 
2L^"‘ + -i^7 _ l^rJ —2\ a “ m+ 
2 |h (^ 00 ~^ i h7.eo)~i~ ii i9.37 Oeo.ss • J d 
I-(l-r)(l+a 37 . 6 o) = l-.0291262 x 9.1539= l-.26662=.73338 
«37.58 X “ 8.3407 X 2120 
h e 3935 
«eo.se X ■j— — 8.1917 X — 
264.720 _ 264,720 
1+«37.eo 9.1539 
216. The value A. 
= 5^28.919=^28 18 5, the annual premium, 
of an assurance payable on the failure of a ' 
life aged m, provided he die after another life aged m x is A m —A m< , 
For if there be two separate insurances, one to secure the payment 
of the sum in the event of his dying first of the two, and the other in 
the event of his dying second, the two together are evidently equal to 
an insurance on the single life : 
m, mi + A mtnil ~-A ri 
(0 (2) 
by transposition, A„’ h , 
(«) ’ (0 
If the annual premium be payable until the risk is determined, which 
8.67633 
9.40971 
8.35083 
2)1.05888 
.52944 
500 
264.720 
=£264 14 5 
(0 
-A m . 
will be on the failure of the joint existence, the divisor is 1 +a m>mi ; but 
if it be payable until the failure of the life aged m, the divisor will be 
1 ~j~ci m . 
Example 2. Let the single and annual premium be required to 
secure the sum stated in the last example on the death of the one aged 
60, provided he die after the other aged 37 ? (Northampton, 3 per 
cent.) 
A 60 = 1—(1 -r)(l+« 60 ) = 1. - .029126 x 10.7774= .68610 
By the last Example Aeo,s 7 — . 52944 
(l) .15666 
500 
78.330 =£78 6 7