Algebra

 

Chuck deposits $2000 into a bank account that compounds weekly at an annual interest rate of 15% Assuming there are no other transactions, what will the balance be after 10 years, in dollars?  

 

Since the yearly interest rate for Chuck's account is 15% (same as 0.15) and there  

are 52 weeks in a year, then the amount earned the first week is (2000)(0.15 / 52)  

 

I'm going to change (0.15 / 52) to its decimal equal.  I'll round that value to 0.00288   

only for the convenience in writing it in this post.  In my calculator I will not round it,  

but maintain the entire 15-digit decimal in the calculations.  

 

Since the bank is adding (0.00288) of the current balance to the account each week,  

the total in the account (principal plus interest) after the first week is (2000)(1.00288).  

Then each week, the balance is (1.00288) times what it was the week before.  

 

Let's make a little tabulation, to demonstrate clearly the progression of the balance.   

 

Balance at end of 1^st week      (2000)(1.00288)  

Balance at end of 2^nd week     (2000)(1.00288)(1.00288)  

Balance at end of 3^rd week      (2000)(1.00288)(1.00288)(1.00288)   

Balance at end of 4^th week      (2000)(1.00288)(1.00288)(1.00288)(1.00288)   

Balance at end of n^th week      (2000)(1.00288)ⁿ   

 

Balance at end of 520^th week   (2000)(1.00288)⁵²⁰ =  8944.04 dollars   

_.