232 ESSAY ON PROBABILITIES. 



1 4- |P, gives the value of a fine of 11. in the same cir- 

 cumstances. Hence the following 



RULE. From the value of a perpetuity subtract that 

 of an annuity on A's life, and divide the remainder hy 

 the value of an annuity due on the renewal life at the 

 time of renewal. 



If there be several lives in the lease, apply the pre- 

 ceding rule to each life, and add the results: for the 

 several contingencies do not interfere with or depend 

 upon each other, nor will the case of more lives than 

 one in one lease differ from that of several leases each on 

 one life. The most convenient method is as follows : 



RULE (for several lives). Multiply the value of a 

 perpetuity by the number of the lives, and subtract the 

 sum of the values of the annuities on the different lives: 

 divide the result by the value of an annuity due on the 

 renewal life at the time of renewal. 



QUESTION. An estate of the clear annual value of 

 a per annum is to be leased on n lives, A, B, C, &c., 

 with liberty to renew at the end of each year in which 

 a life drops, the best life in the tables being P : what 

 fine should be paid, on the supposition that the pur- 

 chaser is to have a given rate of interest for his money? 



RULE. Find the value of the perpetuity of a per 

 annum; multiply it by the value of an annuity due on 

 the renewal life at the time of renewal, and divide by 

 the excess of n times the value of a perpetuity of I/, 

 over the sum of the values of annuities on the lives of 

 A, B, C, &c. : the quotient is the value of each fine 

 required. But if a sum s be paid down, and the rest 

 of the value of the estate is to be paid in fines, then 

 subtract s from the perpetuity of a per annum, before 

 using it in the preceding rule. $% 



EXAMPLE 1. The lives in possession, A, B, and C, 

 are 35, 48, and 60 years of age, and the fine paid on 

 renewal is 3007. What is the present value of all the 

 fines, using the Carlisle tables, and interest at 4 per 

 cent ? * 

 * I have taken Mr, Milne's example,.in order to show the accordance of 



