LIFE ANNUITIES. 
■ ■ 
168. An annuity of ¿£30 is granted on the longest of three lives, A, 
JB, and C, respectively aged 16, 21, and 26 years, which is to he 
equally divided between them whilst they are all living, and on the 
decease of either of them it is to be equally divided between the sur 
vivors during their joint lives, and then to belong entirely to the last 
survivor during his life. Required the value of A’s interest therein. 
(Northampton 3 per cent.) 
A’s interest consists, 1°, of one-third of the annuity on the joint 
lives ( -\aie.2i.2o) j 2°, of one-half the annuity during the joint existence 
of A and B after the death of C ; 3°, of one-half of the annuity during 
the joint existence of A and C after the death of B; 4°, of the entire 
annuity during the remainder of his life after the death of the other two. 
The following table shows the separate values, the sum of which is 
the value of A’s interest therein ; 
the sum a u — a 16iS!1 — ^ a 16-26 -J- i cti6.21.2e — value of A’s interest. 
7.2285 = ^cti C21 
7.0149 =: 
14.2434 
3)11.5641 — ^ig.21.26 — CI16.45 —" 
3.8547 “ cho.2i.26 
19.4358 — a ie 
23.2905 
14.2434 
9.0471 
30 
271.413 — ¿£271 8 3 
value of A’s 
interest. 
Alive. 
Dead. 
Value of the Annuity to be received. 
ABC 
none 
i Cfi6.21.2g 
( 
A B 
C 
h («16.21 “ Cfi6.2l.se) 
Art. 164. 
A C 
B 
i (cfl6.26 — «16.21.20 ) 
do. 
A 
B c 
«16 Cf 16 . s i «16.26 "h Cf l 6.21.20 
Art. 163, 
169. An annuity of ¿£30 on the longest of three lives, A, B, and C, 
aged respectively 18, 28, and 33 years, is to be divided equally between 
A and B during their joint lives, but on the decease of either of them to 
be divided equally between the two remaining lives, and afterwards to 
be wholly enjoyed by the survivor. Required the value of A’s share 
therein. (Northampton 3 per cent.) 
The following table shows the different parts of which A’s interest is 
composed, and the corresponding values :