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 if you borrow the whole £100,000 for the
Entire year? Assume that both the funds you borrow and the funds you invest use compound
Interest.

Question

Quizplus · Accepted Answer

First, let's calculate the amount of compensating balance required:

Compensating balance = 4% x £100,000 = £4,000

So, when we borrow the full £100,000, we will receive only £96,000 (due to the compensating balance requirement).

Now, let's calculate the interest we will pay for the borrowed amount:

Interest per quarter = 2.5% x £96,000 = £2,400

And the interest we will earn from our short-term investments:

Interest per quarter = 1.25% x £4,000 = £50

Our net interest cost per quarter is:

Net interest cost per quarter = £2,400 - £50 = £2,350

To calculate the effective annual interest rate, we need to use the following formula for compound interest:

Effective annual interest rate = (1 + (interest rate per period / n))^n - 1

Where n is the number of compounding periods in a year (in this case, 4 since we have quarterly compounding).

Plugging in the numbers, we get:

Effective annual interest rate = (1 + (0.0235 / 4))^4 - 1 = 0.1038 or 10.38%

Therefore, the best choice is C with an effective annual interest rate of 10.38%.

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