Question

c. Your company needs to borrow funds and has several options available to it, Loans A, B and C. The interest rates (APR) for these options are 5.45%, monthly, 5.50% semi-annually, 5.40% daily . What is the EAR of the loan option the company should choose?

Answer 1

Effective rate of loan formula = (1+ i/m )^m -1

i = Interest rate

m= no. of times compounding in year

Loan A

Interest rate = 5.45% or 0.0545

compounding= monthly = 12 times in year

So, EAR = (1 + (0.0545/12 )) ^ 12 - 1

1.055882 -1

= 0.05582 or 5.582%

Loan B

Interest rate = 5.50% or 0.055 Compounding = semiannually = 2 times in a year So, EAR = (1 + (0.055/2) )^2 - 1 =1.055756 - 1 = 0.055756 or 5.5756% Loan C Interest rate = 5.40% or 0.054 compounding = daily = 365 days in a year So,EAR = (1 + (0.054/365) ) ^365 -1 = 1.05548 - 1 =0.05548 or 5.548% Least Annual Effective interest rate is of Loan C 5.548% or 5.55%. So,it will be chosen. EAR of loan C is 5.55%