142 
LIFE ANNUITIES. 
The divisor for the annual premium which is payable so long as P is 
in existence with either of the lives A or B, is 
1 + 2 r n (p m ,„+p m\,n ) Pr*2, n 
1 S ? P(mi, m2), n — P(jn,m\,msO,n) 1 "t" «12 J 
Examples. 
166. Required the present value of an annuity of £40 during the joint 
existence of two lives, A and B, respectively aged 66 and 33, and seven 
years after the death of B, provided A shall live so long. (Northampton 
3 per cent.) 
Art. 158. a (m s 4 1 
t1 
4673.1637 
1552 
7.9947- 
7.9947-3.0111=4.9836 
4.9836 + 2.7209=7.7045 
40 
308.1800 =£308 3 7 
(By Davies’s Tables). Here m is greater than m x — t. 
N e6 -N 78 _ 1763.756-664.293 _ J 
_ A nOO/? 
What is the present value of an annuity of £40, to be entered 
upon after the failure of the joint existence of two lives, aged 29 and 30, 
and then to continue during the life of a person now aged 18? (North 
ampton 3 per cent.) 
®18 — ^18.29.30 (Art. 162.) 
a, 8 = 19.0131 
a i8.s9.3o = 10.7472 = cf 18i 49 — .05 (Art. 145) 
8.2659 
40 
330.636 = £330 12 9 
What is the present value of an annuity of ¿£40, to revert to a person