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 ?
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Answer 1

Answer:

12.73%

Step-by-step 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.