Question

What is the APR if your bank wants to earn an EAR of 7.90% on the loans, compounding quarterly?

Answer 1

APR = 7.676% per annum compounded quarterly

Concept

Effective Annual Rate = [1 + (APR / Number of compounding in a year)]^Number of compounding in a year - 1

Solution

We are given the following information

EAR = 7.9% or 0.079

No of compounding in a year = 4

Putting this two information in the equation

Effective Annual Rate = [1 + (APR / Number of compounding in a year)]^Number of compounding in a year - 1

0.079 = [1 + (APR/4)]^4 - 1

1.079^(1/4) = 1 + (APR/4)

1.01919  = 1 + (APR/4)

0.01919 = APR / 4

APR = 0.07676 or 7.676% per annum compounded quarterly