What is the present value of an annuity of ¿£*40, to revert from the
present possessor, at the death of a person aged 30, to another individual
during the joint lives of two persons, aged 18 and 29 ? (Northampton
3 per cent.)
«18.29 <2l8.29.30 (Art. 164.)
«18.29
«18.29.30
13.5452
10.7472
2.7980
40
111.920 = £111 18 5
1G7. Those problems in survivorships which involve several of the
preceding cases are next to be considered.
Example. An annuity of £20 is granted on the life of the survivor
of A and B, aged 15 and 20 years, to be divided equally between them
while they are both living, and after the death of either of them the
survivor is to receive the whole of the annuity for the remainder of his
life : what is the value of A’s share therein ? (Northampton 3 per cent.)
A’s share consists of two separate parts; one entitling him to half
the annuity during the joint existence of himself and B, the other
entitling him to the annuity during the remainder of his life after the
decease of B.
The value of the 1st part is . . ^ «15.20
of the 2nd . . a l5 — «15.20 (Art. 158.)
the sum of the two . .
the value of A’s share.
4 « 15 .2o is the formula for finding
By substituting the value of the annuity on the life of B for that on
the life of A, we have the value of B’s share, a 20 — i a 15 .2o >
= 19.6577
= 7.3299
12.3278
20
246.556 =£246 11 1
A’s share
«20
h a
= 18.6385
= 7.3299
11.3086
20
2267172 =
£226 3 5
B’s share.