ON THE VALUE OF REVERSIONS. 21? 



or status ; that is, what is the value of an annuity on 

 that status, which is such that the office must be ruined 

 if the truth falls below it ? 



RULE. Take the rate of interest which money 

 really makes *, and subtract the premium for II. from 

 the present value of I/, to be received at the end of a 

 year (see last table) : divide the remainder by the 

 excess of unity over the remainder, and the quotient is 

 the number of years' purchase in the present value of 

 the annuity. 



EXAMPLE. A society professes to insure lives of 

 35 at a premium of 3 per cent, on the nominal sum 

 insured ; what is the lowest value of the annuity on 

 such lives at which this can be done ? 



At 4 per cent. |l = -9615 



(page 200.), A||l ='0300 



0685)-9315(13-6 -0685 



ANSWER. Such an office cannot permanently stand 

 (as far as this one species of bargain is concerned), 

 unless the value of an annuity on lives of 35 (at 4 per 

 cent.) be more than 13'6 years' purchase. 



Generally speaking, contracts of insurance are not made 

 for the end of the year in which the party dies, but for 

 payment at a given number of months after the parties' 

 death is proved and the claim made. If this agreement 

 were always made for six months after the real death, 

 the office would, one party with another, neither gain 

 nor lose, while for every month less than six, the office 

 gives that month's interest to the parties' executor, while 

 for every month more than six by which payment is 

 deferred, the office takes a month's interest. I believe 

 no office defers its payments more than six months after 

 the claim is made ; and the difference is rendered im- 

 material by the probable errors of the tables, which 

 require too large a covering profit to make it worth 

 while to take such a circumstance into account. 



* This is an essential element, but cannot be very accurately determined : 

 something above the truth should be assumed. 



