204 ARITHMETIC. 



COMPOUND INTEREST BY DECIMALS, 



RULE.* 



I. Find the amount of iL for one year at the given rate 

 per cent, 



* 2. Involve 



* Demonstration. Let r = amount of il. for one year, 

 and p = principal or given sum ; then since r is the amount of 

 il. for one year, r* will be its amount for two years, r' for 3 

 j^ears, and so on ; for, when the rate and time are the same, all 

 principal sums are necessarily as their amounts ; and consequently 

 as r is the principal for the second year, it will be as i : r : : r 

 : r^-=. amount for the second year, or principal for the third j and 

 again, as i : r :: r* : r'r= amount for the third year, or prin- 

 cipal for the fourth, and so on to any number of years. And if 

 the number of years be denoted by t, the amount of il. for t 

 years will be K Hence it will appear, that .the amount of any 

 other principal sum p for t years is pr^ ; -for as i : r' i : /» : pr\ 

 the sarai^ as in the rule. 



If the rste of interest be determined to any other time than a 



year, as f, -4-, &c. the rule is the same, and then t will represent 



that stated time. 



r r = amount of il. for one year, at the given rate 



j per cent. 



p zz principal, or sum put out to interest. 

 Let { . .- \ 



' t =r mtertst- 



t r= time. 



r,i = amount for the time i. 

 Then the following theorems will exhibit the solutions of all 

 /i:e cases in compound interest, 



I. p/zzm. II. pr^ — pzz'i^ 



III. --=:/, IV. — I = f\ 



The 



