Question

Kelly takes out a loan with the stated rate of 12% interest. If the interest is calculated weekly, how much greater is Kelly’s effective rate (The growth rate of compounded amount) Then her stated rate (the “stated” 12%)? Does the difference in effective rate and stated rate change depending on 1 year or 10 years ?

Please answer this step if you can! Greatly appreciate it.

Answer 1

12.73%

Explanation:

Given the annual rate is 12% compounded weekly.

Let's assume 1 yr=52weeks.

The effective interest rate is calculated as:

`i_m=(1+r/m)^m-1, r=annual\ rate\\\\i_(52)=(1+0.12/52)^(52)-1\\\\i_(52)=0.1273`

Hence, the effective rate for 12% compounded weekly is 12.73%

-The effective rate will be different when the number of compounding times is less than or more than 1 year.

- the effective rate is equal to the stated rate if the compounding number of times is once per year.