new mode of Life Insurance. 89 



nient equitably equivalent to £1 to be paid at death. In other 

 words, a table of single premiums payable to insure £1. 



On a person of any age making a payment into the office let 

 him be credited with a sum, calculated from this table, as the 

 equivalent payment to be made at death. And so for any other 

 payments he may make at regular or irregidar intervals. 



If at any time he should wish to draw any sum of money 

 from the office, let his account be charged with the correspond- 

 ing sum, calculated from same table, as the equivalent payment 

 at death. 



The series of transactions will thus partake of the character 

 of a deposit account at an ordinary bank, inasmuch as payments 

 are made into the office, and drafts made against the amount 

 standing to the insurer's credit in the office ; and it will partake 

 of the character of an insurance, inasmuch as the whole of the 

 accounts between the office and the insurer will have reference 

 to one date, viz. the death of the insurer. There will be no calcu- 

 lation of interest, but the insurer will secure for his representa- 

 tives, on any sum remaining till his death, the accumulation of 

 interest corresponding to the average duration of life. 



This system, so far as regards the payments made into the 

 office, would differ little from the system of seeming a policy 

 by a single premium. The principle of each is the same. Since, 

 however, it contemplates smaller and more frequent payments, 

 it would be necessary for arrangements to be made for effecting 

 these payments without the trouble and formality of taking out 

 a fresh policy on every occasion. 



The peculiarity consists in the proposal of one scale of prices 

 according to which the office will either sell or purchase an 

 insurance ; and by which, consequently, the depositer or insurer 

 may know precisely the amount he is entitled at any time to 

 draw without the necessity of making any bargain. 



Since the idea of buying and selling according to the same 

 scale of prices seems, at first sight, to leave nothing for expense 

 of management and profit, it will be necessary for me to enter 

 into a short calculation in order to show how this profit may be 

 seemed, while the buying and selling from one table is still 

 adhered to. 



Let, then A n be the present value of an annuity of £1 a year 

 to continue during the lifetime of a person (say John Styles), 

 whose age next birthday will be n years, the first payment being 

 due one year hence. 



r the interest of £\ for one year. 



Then, on a principle explained by De Morgan in the article 



