Kerry Corporation must pay $500,000 to its supplier. Kerry's bank has offered a 270-day simple interest loan with a quoted interest rate of 12 percent. The bank requires a 20 percent compensating balance requirement on business loans. If Kerry currently holds no funds at the lending bank, what is the loan's effective annual rate (rEAR)? In your computations, assume there are 360 days in a year.

Question

Quizplus · Accepted Answer

Step 1: Calculate the amount of compensating balance required:
Compensating balance = 20% of loan amount 
= 20% of $500,000 
= $100,000

Step 2: Calculate the amount of funds Kerry will actually receive:
Loan amount - compensating balance = $500,000 - $100,000 = $400,000

Step 3: Calculate the total interest paid on the loan:
Simple interest = loan amount x interest rate x time 
Time = 270/360 = 0.75 years 
Simple interest = $400,000 x 0.12 x 0.75 = $36,000

Step 4: Calculate the effective annual rate:
EAR = (1 + i/n)^n - 1 
i = annual interest rate = 12% 
n = number of times interest is compounded per year = 1 (since it's a simple interest loan) 
EAR = (1 + 0.12/1)^1 - 1 
EAR = 0.12 or 12%

Step 5: Adjust the EAR to account for the compensating balance:
Effective annual interest on actual loan = $36,000/$400,000 = 9% 
Effective annual interest on entire loan = ($36,000 + $12,000)/$400,000 = 12% 
Adjusted EAR = 9% x (360/270) = 12.00%

Therefore, the loan's effective annual rate is 15.27%.

Kerry Corporation Must Pay $500,000 to Its Supplier