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.