REVERSIONS. 
139 
#83.25 — 13.5308 
«2S.30 = 13.0978 
#23,30 = 12.9661 s= a i8 
#23.25.30'— #23.48 .05 = 10.7184 
2 
21.4368 
39.5947 
21.4368 
”18.1579 
80 
1452.632 =: £1452 12 8 
REVERSIONS. 
158. To find the value of an annuity on a life A aged m, after the 
extinction of another P aged m x . 
The chance of the life A receiving the annuity in any year, as the wth 
from the present time, depends on his being alive at the end of that 
time, the life P having failed previously, the probability of which is 
Pnj.nCl Pm\,ii) “ Pm, n Pins, ntl), Il 
and 2 r n (2 } m,n ), n ) - a m - a m , , the value of the reversion. 
Rule. From the value of the annuity on the life in expectation sub 
tract the value of the annuity on the two joint lives. 
Example. What sum should be paid to secure an annuity of £55 to 
a male aged 35, during his life, after the death of a female aged 40 ? 
(Chester 5 per cent.) 
a 35 = 13.1892 
#35.40 — 10.6690 
2.5202 
55 
126010 
12601 
138.611 = £138 12 3 
159. If the reversion be secured by an annual premium the whole 
amount of payments will .consist of the premium paid down at the 
present time, and of an annuity during the joint existence of the two 
lives; the annual premium will therefore be found by dividing the single 
premium by unity added to the present value of an annuity of £l during 
the joint lives. 
The annual premium for the above reversion will be