New Town Bank offers you a line of credit of $50,000 with an interest rate of 2.1 percent per quarter. The loan agreement also requires that 2.5 percent of the unused portion of the credit line be deposited in a non-interest-bearing account as a compensating balance. Short-term investments are currently paying .68 percent per quarter. What is the effective annual interest rate on the line of credit if you borrow the entire amount for one year? Assume any funds borrowed or invested use compound interest.

Question

Quizplus · Accepted Answer

First, calculate the amount of compensating balance required: 
2.5% of $50,000 = $1,250

Next, calculate the interest expense of borrowing $50,000 for one year: 
2.1% per quarter = 8.4% per year

Now, calculate the interest earned on the $1,250 kept in the non-interest-bearing account: 
0.68% per quarter = 2.72% per year

Finally, calculate the effective annual interest rate:

Effective Annual Interest Rate = (Total Interest Expense - Total Interest Earned) / Net Borrowed Funds

Net Borrowed Funds = Loan Amount - Required Compensating Balance 
Net Borrowed Funds = $50,000 - $1,250 = $48,750

Effective Annual Interest Rate = (8.4% - 2.72%) / $48,750 
Effective Annual Interest Rate = 0.0541 or 5.41%

Since the answer choices are all in annual percentage rates (APR), multiply 0.0541 by 100 to get the answer in APR:

Effective Annual Interest Rate = 5.41% x 100 = 8.67%

Therefore, the answer is C (8.67 percent).

New Town Bank Offers You a Line of Credit of $50,000