ON ANNUITIES. 1^9 



under A|B will take place at the end of the year in 

 which A drops, provided B be then in existence : thus 



A|l denotes * the present value t of an annuity of I/., 

 the first (and only) payment of which is to be made at 

 the end of the year in which A drops ; while Ajl denotes 

 the present value of II. , to be paid in a year from this 

 time, if A be then dead. 



5. The last moment of a term certain is a part of 

 that term, unless the contrary be expressed by symbols: 



thus 6|1 refers to a pound payable at the end of seven 

 years, and is 6|7 But when the last moment of a 

 term is considered as having followed the end of the 

 term, a small hyphen (considered as an abridged nega- 

 tive sign) is placed after the term in question : thus, 



t-\n denotes an annuity of n payments, the first of 

 which is to be made at the end of t years ; and is the 



same with t l|n. 



6. The absence of symbols on the left of | indicates 

 that the first payment takes place in a year from the 

 present time; but -| indicates an annuity now due. 

 The absence of symbols on the right of | indicates 

 a perpetuity in reversion ; and | itself indicates a perpe- 

 tuity, the first payment of which is to be made in a 

 year ; while -| indicates a perpetuity now due. 



7. Dots between two symbols of status indicate 

 that the joint status shall be held to exist throughout 

 the year in which the first is determined, provided 

 the second remain at the end of the year; and 

 dots placed under several status denote that the 

 succeeding benefit is not due unless all those status 

 shall drop in the same year : thus |A...B denotes an 

 annuity on the joint lives of A and B, payable also 

 at the end of the year in which A dies, if B be then 



alive ; and A : B|l is the value of I/, at the end of the 

 life of the longest survivor of A and B, provided they 



* One bar may be omitted in very simple cases. 



f Remember particularly that in A 1 1, 1 means one year, not one pound. 



o 4 



