

A neio Method for computing Interest. 53 



The usual formula for compound interest is 



a=P(l+r)< (5), 



where r=rate per cent per annum. 



(5) 



Pe*=P(l+r)« (6). 



This is readily reduced to 



e^l-fr (7). 



Taking the logarithm of both members of (7), we have by a 



] cr n_[-r) 



slight reduction ^= -4342944819^: < 8 > 



Equation (8) gives the rate per cent, per annum r', so that the 



interest being compounded at every instant shall be the same as 

 yearly compound interest at r per cent, per annum. 



By giving to r successively the values 003; 0*03£; 004; 

 0-04J; 005; 0'05£ ; 0-06; 0'06£; 0-07; we find the following 

 values for r' : 



When r=003 we have r'=0-0295587 



<c 



a 





« 



u 



03 \ 



04 



004£ 



005 



0-05£ 



0-06 



0-06J 



007 



per 



00344013 

 0392206 

 00440169 

 0-0487902 

 00535408 

 0-0582690 

 0629748 

 0-0676587 ' 

 otts compou 

 fear on $1, 





If 



WhenP=l, equation (4) 



a = e 



^ (9). 



Putting this into logarithms, we have 



log. a = ft log. e (10). 



If for / we write ?^> this will become 



r'd 

 • log.a=3g- 5 log.e (UJ. 



Substituting 0-0676587 for r 7 , and using the well known value 

 0I * «, equation (11) becomes 



log. a = 000008050353 xd (12), 

 w here d expresses the time in days. 





