54 



A new Metliod for computing Interest. 



By means of formula (12) I have computed the values in the 

 third coUimn of the following table. The first column gives the 

 time in days; the second is the simple interest of $1, at 7 per 

 cent, per annum ; the fourth column gives the difference between 

 the simple interest and the instantaneous compound in<terest. 



By the foregoing table we see that the greatest difference, as 

 given in the fourth column, is $0.000587, which corresponds to 

 200 days. If we wish to know the exact time when this differ- 

 ence is a maximum, we proceed as follows : The amount at sim- 

 ple interest of $1 for t number of years at r per cent, per annum 

 is l-\-tr. 



The amount at instantaneous compound interest at r' per cent, 

 per annum for $1, for the same time, is 

 e^'K 



The difference is therefore expressed by 

 l+^r-e*-'' 

 In this expression t is the only variable. 



(13). 



