Your bank offers you a $100,000 line of credit with an interest rate of 2.5% per quarter. The loan agreement also requires that 4% of the unused portion of the credit line be deposited in a non-interest bearing account as a compensating balance. Your short-term investments are paying 1.25% per quarter. What is your effective annual interest rate on this arrangement if you do not borrow any money on this credit line during the year? Assume that both the funds you borrow and the funds you invest use compound interest.

Question

Quizplus · Accepted Answer

First, calculate the amount of the compensating balance: 4% x $100,000 = $4,000.
Since the compensating balance does not earn any interest, the amount available for investment is $96,000 ($100,000 - $4,000).
Next, calculate the interest earned on the short-term investment: $96,000 x (1 + 0.0125)^4 - $96,000 = $4,138.70
Now, calculate the interest you would have to pay if you were to use the entire credit line: $100,000 x 0.025 x 4 = $10,000
Therefore, the effective annual interest rate is: ($10,000 - $4,000 + $4,138.70) / $96,000 = 0.0509 or 5.09%.

Your Bank Offers You a $100,000 Line of Credit with an Interest