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