ON ANNUITIES. 185 



interest. This is also said to be 20 years' purchase, 

 meaning the sum which would buy at once the annual 

 payments of twenty years. 



3. The present value of an annuity certain of 11. 

 (so called to distinguish it from a life annuity.) By an 

 annuity of II. is meant, a right to receive II. at the 

 expiration of every complete year after the creation of 

 the annuity,, which is said to commence a year before 

 any payment is made; (or a term before payment is made, 

 whether the term be yearly, half-yearly, &c.) Thus 

 an annuity certain of five years, commencing January 1, 

 1838, is paid on the first days of 1839, 1840, 1841, 



4 1842, and 1843. 



When an annuity is to be designated which makes 

 one payment immediately, I shall call it an annuity 

 due; and a perpetuity of which one payment is to 

 be made immediately, a perpetuity due. Thus on 

 January 1, 1839, the preceding annuity becomes an 

 annuity due of four years, comprising an immediate 

 payment of II. and a commencing annuity of four 

 years. To find the present value of an annuity of I/., 

 use the following 



RULE. Multiply the perpetuity (present value of 

 the perpetuity) by the excess of one pound over the 

 present value of the last payment. Thus, for an 

 annuity of five years, at 4 per cent, multiply 25 by the 

 excess of 1 over '822, or by -178; the result is 

 4-45/., nearly 



4. The amount of II. at compound interest, meaning 

 the sum to which II. with its interest will amount in 

 any number of years. It is found by dividing 1 by 

 the present value of II. due that number of years hence. 

 Thus II in 25 years, at 6 per cent., will amount to 

 (11. -s- -233), or 4-29/. 



5. The amount of an annuity at compound interest, 

 meaning the sum of which the annuitant would be 

 possessed immediately after receiving the last annual 

 payment, if he had made compound interest upon every 

 preceding payment. This amount is found by multi- 



