COMPOUND INTEREST BY DECIMALS. 205 



2. Involve the amount thus fcund to such a power, as is 

 denoted by the number of years. 



3. Mukiply this power by the principal, on given sum, 

 and the product i^ill be the amount required. 



^ ■ 4. Subtract 



The mbsfj convenient way of giving the theorem for the /;W, 

 as well as for all the other cases, will be by logarithms, as follows : 



I. tX^og. r-\-Iog. p:=:Iog.m. II. log.m — ty.log.rzzlog. p, 



III. % m-l o g.p _^ j^^ h'm —log.p _j^^^ 



log. r t "^ 



If the compound interest, or amount of any sum, be required 

 for the parts of a year, it may be determined as foUov^s : 



I. When the time is any aliquot part cf a year, 



RULE. 



1. Find the amount of il. for one year, as before, and that 

 root of it, which is denoted by the aliquot part, will be the 

 amount sought* 



2. Multiply the amount thus found by the principal, and it wi'I 

 be the amount of the given sum required. 



II. When the time is not an aliquot part of a year. 



RULE. 



1. Reduce the tirtie into days, and the ^^^\.h 1001 ol i_,c 

 amount of il. for one year is the amount for one day. 



2. Raise this amount to that power, v/hose index is equal i-c 

 die number of days, and it will be the amount of il. for the giv 

 en time. 



3. Multiply this amount by the principal, and it will be li.f 

 amount of the given sum required. 



To avoid extracting very high roots, the same may be done by 

 logarithms thus : divide the logarli'im of the rate, or amount oi 

 il. for one year, b,y the denominator of the given aliquot part, 

 and the quotient will be the logarithm of the root sough^. 



