90 On a Suggestion for a 



" Keversion," in the Penny Cyclopaedia, the present value oi £\ 

 payable at the settling day next after the death of John Styles is 



iT^Ct- — A)po^ids. 



John Styles, therefore, on paying -i . ( — — «/ ™*° e 



office, will be credited with £1 payable to his representatives at 

 his death. 



After m years from this transaction, the present value of ^l 

 payable at the death of John Styles, who will then be n + m 

 years old, will be 



r s 1 



T+i\ r 





and, in the event of John Styles wishing to draw the £1 standing 

 to his credit as payable at his death, this is the sum to which he 

 will be entitled. 



This exceeds his original payment by 



which represents the profit he derives from the investment of 

 his original deposit during m years. 



The accumulation of interest on the original deposit during 

 these m years, which will be obtained by the office, is 



i^(7-^)(^r-o 



and if from this we deduct the increase obtained by John Styles 

 there remains to the office a balance of 



1+r | — 1 r / - m \ 



"TT^ I+A4. l+r I ~ A n+ m ) 



Now supposing that the tables of the duration of life adopted 

 itfcalculating the value of A n could be strictly depended on, and 

 supposing also that the assumed rate of interest could always 

 be obtained, and no higher rate, then this balance would exactly 

 represent the risk of loss to the office during the m years which 

 would accrue by the death of John Styles ; and, if a sufficient 



t 



