REVERSIONS. 
147 
5 • 5492 — î ^18.23.28 
17.2890 = a 28 
22.8382 
20.2826 
13.6424 :— $18.28 
6.6402 = £«28. 
20.2826 
2.5556 . \ 
40 
102,2240 '= ¿£102 4 6 C’s sliare 
172. An annuity certain of £50 for tlie term of 15 years is to be 
enjoyed by P and his heirs during the joint existence of two lives, A 
and B, aged 14 and 19 years, and if that joint existence fail before the 
expiration of 8 years the annuity is to go to Q and his heirs for the 
remainder of the term of 15 years. To determine the value of Q’s in 
terest in the annuity. Northampton 3 per cent. 
Q’s interest may be divided into two parts : 
1st. The chance of enjoying the annuity during the first 8 years. 
2nd. The chance of enjoying it after the expiration of that term. 
The amount of the interests of P and Q together for the first 8 years 
is evidently equal to the present value of an annuity certain for that 
of P’s interest for the same term is the present value of a temporary 
annuity for 8 years on the lives of A and B; the expression for which, 
by Art. 136 and 137, is 
if this be subtracted from the value of the annuity certain, it will leave 
the value of Q’s interest for the term; i. e. 
Q’s interest after the expiration of 8 years will be the present value 
of an annuity for 7 years after the expiration of 8 years, provided the 
joint existence of A and B shall have failed within that time, the chance 
of which is by Art. 109, 1 •— ~ X ~ ; the present value of the second 
l U l 19 
part of Q’s interest is therefore 
this, added to the value of Q’s interest for the first 8 years, will give the 
value of his interest in the annuity ; viz., 
h 2