ON THE VALUE OF REVERSIONS. 



225 



consider this question independently of the double risk, 

 and as if it were certain that both parties would not die 



in the same year. Instead of A) IB, we then employ 

 A|fB (page- 222). Mr. Milne (in his page 352. &c.) 

 has given three examples, which I here repeat by the 

 latter formula, taking the data from the work cited : 

 1. A is aged 1 7, B is aged 57 : Carlisle Tab., 4 per cent. 



A...B = 10-009 

 |AB = 9-923 



1 B= -086, which in work cited 

 ["is -08656. 



( 0-086 



2. A is aged 45, B is aged 35 ; do. do. 5 per cent. 



= 10-912 



0-260 



Ajl B = -260, which in work cited 

 [is -266331. 



3. A is aged 64, B is aged 19; do. do. 5 per cent. 



7-593 

 0-522 



1 B = -522, which in work cited 

 [is -52556. 



The present value of a pound, to be received at the 

 end of the year in which A dies, provided he survives 



B, or B:A 



1, is readily found from the preceding: 



for since A must either die before or after B, the sum 

 of the two must be the present value of II. to be received 

 at the death of A, independently of B. That is, 



7 A 



FB rz A 



T Al B very nearly. 



The present value of an insurance is also that of the 



reversion of a fixed sum ; since it is the same thing whe- 



ther I/, is to be received from an office, or conditionally 



under a will, or in any other way. The reversion of a 



Q 



