Annual interest rate

Question

Sally invests $4000 in a savings account which compounds interest monthly. After 10 years, she has a balance of $4,491.73. What is the annual interest rate of the account, rounded to the nearest 0.01%?

Answer 1

Hi Tara,

The question doesn't specify whether it wants the APR (annual percentage rate) or the EAIR (effective annual interest rate). I will give you both answers. What they are probably looking for is the APR.

 

4000 * (1+i)^(10*12) = 4491.73, where i is the monthly interest rate

 

Dividing both sides of the equation by 4000 gives us: (1+i)^120 = (4491.73/4000.00) = 1.122933

Taking the 120th root of both sides of the equation (using a calculator or Excel) gives us: 1+i = 1.122933^(1/120) = 1.000967. Subtracting 1 from both sides give us i = .000967 = .0967%.

 

That's the monthly interest rate, The APR is 12 times this value = 1.16%.

 

The EAIR is (1.000967)^12 -1 = 1.1662% (rounded = 1.17%).

Bill