new mode of Life Insurance. 91 



number of cases were taken, would exactly make up these 

 losses, leaving no margin for expense of management, loss by 

 bad investment of money, depreciation of interest, or profit. 



With the view of supplying this margin, let A (1 — x) be used 

 instead of A throughout the previous calculations, i.e., let the 



accurately calcxdated present value of Annuities be all reduced 

 in the ratio 1 : 1 — x before they are used to form the table referred 

 to ; we shall then have the following sums corresponding to a 

 policy of £\ payable at the death of John Styles : — 



Original deposit — — J -A, (1 — x) \ 



Increase or profit on that ,-. . 



deposit when withdrawn after r ^ x ) ( A A _i_ j 



m years l + r x 



True risk incurred ^— — T , 

 by office i + r i ~ L — JL.S a TTh— A \ 



as before, and 



Margin to cover expense of management, profit, &c, 



r x ( 

 T+r\ 



A l + r \—A , 



n 1 n -f- , 



To this profit must be added any that may be derived from 

 investing the 'money at a higher rate of interest than that 

 assumed for the basis of the table. 



The table which would be required is a table of the value of 



l+r \ r nK J j 



or all values of n. 



The most obvious objection to the plan is the trouble arising 

 from the necessity of a medical examination, which, since every 

 deposit is, strictly speaking, the opening of a new policy, should 

 precede every such deposit. I think, however, that sufficient 

 security might be obtained for the office without this. 



The object of the plan is to afford a ready, secure and highly 

 unspecidative investment for savings, which furnishes a certain 

 and easily calculable but small profit thereon, in case of with- 

 drawal ; and some of the security of a life insurance, in case of 

 death. 



