ON THE VALUE OP REVERSIONS. 233 



= 25 |A = 16-041 |P=19-792 



3 |B = 13-419 1 



|C= 9-663 



75 20-792)35 '877(1 -7255 



39-123 39-123 300 



35-877 517-65 



In Milne 517-6296 



The present value of every single pound of the fine is 

 1'7255L, which,, multiplied by 300, gives 517'65L 



EXAMPLE 2. All things remaining as above, the pre- 

 ceding lease, worth 120/. per annum, is purchased for 

 2500/. and a contract for fines on renewal. What 

 should the fine be ? 



|= 25 l + |P = 20-792 



120 500 



3000 35-877)10396(289-77 



2500 289-782 in Milne. 



500 



The answer is 289'77/. 



QUESTION. What yearly rental should the fines be 

 considered as amounting to ; and what should be paid 

 by the lessee annually to an insurance office which would 

 undertake to pay all the fines as they become due ? 



These two questions are the same, and the answer to 

 both is, the yearly interest upon the present value of 

 the fines. Thus, in the first preceding example, the 

 lessor's interest, at 4 per cent., is worth 20'7/. per 

 annum for ever ; which the lessee might either pay to 

 his landlord, as a commutation of fines, or to an insur- 

 ance office, which should take them upon itself. 



QUESTION. What is the present value of the next 

 fine upon the renewal of the first life which drops of 

 the three, A, B, C ? 



the rules. The slight difference arises from Mr. Milne's rule requiring an 

 interpolation, which he has very properly thought it not worth while to 

 make. I have taken more decimal places than those previously given, iw 

 order to show the accordance more clearly. (Milne, page 365.) 



