234 



ESSAY ON PROBABILITIES. 



This is evidently the present value of 11. to be re- 

 ceived upon the failure of the joint existence of A, B, 

 and C, and is to be found (page 214.) by subtracting 

 (ABC, the value of an annuity on the joint lives, from 

 that of a perpetuity, and dividing by the present value 

 of a perpetuity due. 



QUESTION. If the tenant wish to exchange one life 

 for another and a better, how much should he pay to be 

 allowed to do so ? 



RULE. If the fine be I/., subtract the value of the 

 inferior life from that of the better one, and divide the 

 difference by the value of a perpetuity due on the re- 

 newal life at the time of renewal. To exchange two 

 lives, or three lives, use the sums of the values of the 

 better lives, diminished by that of the inferior ones. 



QUESTION-* If the lessor have only a life interest in 

 the estate on which he grants leases for lives, what is the 

 value of his interest ? 



In strict justice to future holders, it ought not to be 

 worth more than the rental calculated in the last ques- 

 tion but three, continued for his life. But it is the 

 nature of this species of property, that the life interest 

 of the holder is subject to considerable fluctuations of 

 value, the preceding annuity being at one time less and 

 at another greater. A lessor, for instance, who enters 

 when the lives in possession are very old, himself being 

 very young, has nearly a certainty of one fine on account 

 of each, and riot much less than an even chance of a 

 second, while his prospect of a third may be worth 

 calculating. But a lessor who enters at an advanced 

 age, against lives which are very young, has a present 

 interest in each coming fine, which may be determined 

 by finding the present value on/., to be paid when the life 

 drops,on condition the lessor survives(page 223). Indeed, 

 whatever may be the lives in the lease, provided the 

 lessor enters at an advanced age, his interest is deter- 



* This problem, properly treated, would be of extreme complication, and 

 I do not remember having seen it proposed. The method in the text is an 

 approximation. 



