Question

Consider two​ investments, one earning simple interest and one earning compound interest. If both start with the same initial deposit​ (and you make no other deposits or​ withdrawals) and earn the same annual interest​ rate, how will the balance in the simple interest account compare to that of the compound​ interest?

Answer 1

Ratio between balances will be:

`(x*(1+i)*n)/(x*(1+i)^n)`

Where;

x = deposit

%i = interest rate annual

n = years

Explanation:

Lets say first deposit is x$ for both investment and annual interest rate for both investment are %i. Also, they stayed under i interest in n years:

Total balance for simple interest is:

`Total balance=x*(1+i)*n`

How ever total balance for compound interest is:

`Total balance=x(1+i)^n`