2©8 ARITHMETIC. 



2. Multiply this sum by one years interest of the an- 

 nuity, and the product will be the whole interest due upon 

 the annuity.^ 



3. To .this product add the product of the annuity and 

 time, and the sum will be the amount sought. .. ■. 



. Note. When the annuity is to be paid half-yearly or 

 quarterly ; then take, in the former case,^ -f the ratio, half 

 the annuity, and twice the number of year& j and, in the 

 latter case, ■^- the ratio, -J the annuity, and 4 times the 

 number of years, and proceed as before. 



EXAMPLES. 



I. What is the amount of an annuity of 50I. for 7 

 years, allowing simple interest at 5 per cent. ? 

 1 + 2+3+4+5+6=21=^:3X7 

 2I. 10s. zi I year's interest of 50!. 

 3 



10 

 7 



52 10 

 350 o =r 50I. X 7 



402I. 10s. = amount required. 



2. I£ 



2a 



III. tZ—=n, IV. ~ +- 



t^r — tr-{-2t rn 4 



2 ~~ * 



In the last theorem J= , and in theorem first, if a sum 



rn 



cannot be found equal to tfie amount, the problem is impossible in 

 whole years. 



Note. Some writers look upon this method of finding the 

 amount of an annuity as a species of compound interest ; the annui^ 

 ty itself, they say, being properly the simple interest, and the cap- 

 ital, whence it arises, the principal. 



