ON THE VALUE OF REVERSIONS. 



215 



status, to insure II at the end of the year in which that 

 status drops. 



RULE I. From the quotient of a perpetuity divided 

 by a perpetuity due, subtract that of an annuity on the 

 status divided by an annuity due. 



34-3) 33-3 ('9708 

 9441 



17-9) 16-9 (-9441 



0267 Answer, as before. 



RULE II. Divide 1 by the value of an annuity due, 

 and by that of a perpetuity due, the difference of the 

 quotients is the premium required. 



34 -3)1 (-0292 



17 '9)1 ('0559 

 0292 



0267 Answer, as before. 



A perpetuity divided by a perpetuity due, is the 

 present value of II. to be received a year hence, and 

 may be taken from the following table : 



From the preceding rule an illustration of the reason 

 of it may be derived, which I give professedly as an 

 exercise of ingenuity to those who may be beginners in 

 the subject. Let there be two persons, one of whom 

 holds a perpetuity and the other a life annuity, each of 

 I/. Both the perpetuitant * and the annuitant desire 



* If the holder of an annuity be an annuitant, the extension of lan- 

 guage is justifiable, by which the holder of a perpetuity may be called a 

 perpetuitant. 



p 4 



