Question

Bank A offers you a loan at 7.84% compounded 5 times a year. Bank B offers to loan you the same amount at 0.10% less than the rate offered by Bank A but compounded twice as often as the Bank A rate is. Which bank's loan should you accept?

Answer 1

Bank A:

Annual interest rate, APR = 7.84%
Number of compounding period, n = 5

Effective annual rate, EAR = [(1 + (APR/n)]^n - 1
Effective annual rate, EAR = [1 + (0.0784/5)]^5 - 1
Effective annual rate, EAR = 1.01568^5 - 1
Effective annual rate, EAR = 1.0809 - 1
Effective annual rate, EAR = 0.0809 or 8.09%

Bank B:

Annual interest rate, APR = 7.74%
Number of compounding period, n = 10

Effective annual rate, EAR = [(1 + (APR/n)]^n - 1
Effective annual rate, EAR = [1 + (0.0774/10)]^10 - 1
Effective annual rate, EAR = 1.00774^10 - 1
Effective annual rate, EAR = 1.0802 - 1
Effective annual rate, EAR = 0.0802 or 8.02%

Based on above calculations, you should accept loan from Bank B