ON THE VALUE OF REVERSIONS. 



begin after n years, signified by n\n + t, or by n\t, is de- 

 termined by the same formula as an annuity on the life 

 of B, to begin after the death of A, signified by A|B. 

 n|n + *=|n + *-|(n + A|B = |B-|AB 



but in the first I write \n instead of \(n n-\-i) since 

 the joint continuance of n and n+t years must be n 

 years. 



The only difficulty of this notation is the necessity of 

 remembering the distinction by which it appears whether 

 n\n-Jrt means that a payment is to be made at the end 

 of the nth year or of the (n-hl)th. In the case of 

 A|B the first payment is to be made at the end of the 

 year in which A dies, which is always intelligible, 

 since it is considered as an infinitely small probability 

 that A should die at the moment which divides two 

 years. But since the term of n years does expire at 

 such a moment, the analogy which connects the symbols 

 of terms certain and contingencies points out no rule. 

 Let n | stand for a perpetuity of I/., the first payment to 

 be due at the end of n+ 1 years, then n 1 1 stands for a 

 similar perpetuity due at the end of n years. But since 

 the introduction of a new figure may turn the attention 

 off n, the datum of the problem, and since analogy 

 does not require us to strike off a whole year from the 

 term, let -| signify a perpetuity deferred for a term 

 (no matter how little) short of n years, that is, payable 

 in n years. And by analogy -| A will signify an annuity 

 due on the life of A. The symbol n-\n + t must be 

 treated as if it were 



n l\n + t or n 1\ t+I 



The symbol of a perpetuity of II to commence 

 from the present time (that is, payment at the end of 

 a year), is simply | . This is found as in p. 1 84., 

 and by subtracting | A, the value of an annuity on the 

 life of A, we obtain | | A, the value of the reversion 

 of a perpetuity, of which payment is made at the end 

 of the year in which A dies. At the end of that year, 

 the holder of the reversion will have in possession and 

 p 3 



