A company obtained a short-term bank loan of $250,000 at an annual interest rate of 6%. As a condition of the loan, the company is required to maintain a compensating balance of $50,000 in its checking account. The checking account earns interest at an annual rate of 2%. Ordinarily, the company maintains a balance of $25,000 in its account for transaction purposes. What is the effective interest rate of the loan?
Question
A company obtained a short-term bank loan of 50,000 in its checking account. The checking account earns interest at an annual rate of 2%. Ordinarily, the company maintains a balance of $25,000 in its account for transaction purposes. What is the effective interest rate of the loan?
Solution 1
To calculate the effective interest rate of the loan, we need to consider the interest earned on the compensating balance in the checking account.
Step 1: Calculate the interest earned on the compensating balance: Interest earned on the compensating balance = Compensating balance * Interest rate Interest earned on the compensating balance = 1,000
Step 2: Calculate the interest expense on the loan: Interest expense on the loan = Loan amount * Interest rate Interest expense on the loan = 15,000
Step 3: Calculate the net interest expense: Net interest expense = Interest expense on the loan - Interest earned on the compensating balance Net interest expense = 1,000 = $14,000
Step 4: Calculate the effective interest rate: Effective interest rate = Net interest expense / Average loan balance Average loan balance = (Loan amount - Compensating balance) / 2 + Compensating balance Average loan balance = (50,000) / 2 + 225,000
Effective interest rate = 225,000 = 0.0622 or 6.22%
Therefore, the effective interest rate of the loan is 6.22%.
Solution 2
To calculate the effective interest rate of the loan, we need to consider the interest earned on the compensating balance in the checking account.
Step 1: Calculate the interest earned on the compensating balance: Interest earned on the compensating balance = Compensating balance * Interest rate Interest earned on the compensating balance = 1,000
Step 2: Calculate the interest expense on the loan: Interest expense on the loan = Loan amount * Interest rate Interest expense on the loan = 15,000
Step 3: Calculate the net interest expense: Net interest expense = Interest expense on the loan - Interest earned on the compensating balance Net interest expense = 1,000 = $14,000
Step 4: Calculate the effective interest rate: Effective interest rate = Net interest expense / Average loan balance Average loan balance = (Loan amount - Compensating balance) / 2 + Compensating balance Average loan balance = (50,000) / 2 + 225,000
Effective interest rate = 225,000 = 0.0622 or 6.22%
Therefore, the effective interest rate of the loan is 6.22%.
Similar Questions
if a company borrows $100,000 at a 10% stated interest rate and is required to maintain a 15% compensating balance ($15,000), the effective interest rate would be:
A company’s bank requires a compensating balance of 20% on a $100,000 loan. If the stated interest on the loan is 7%, what is the effective cost of the loan?
14. Holland Construction Co. has an outstanding 180-day bank loan of $400,000 at an annualinterest rate of 9.5%. The company is required to maintain a 15% compensating balance in itschequing account. What is the annual interest cost on the loan? Assume the company wouldnot normally maintain this average amount.A. 11.18%
The interest rate on a personal loan is 4% per month. What is the effective rate? Group of answer choices 60.10% p.a. compounded monthly 160.1% p.a. compounded annually 60.1% p.a. compounded yearly 48% p.a. compounded monthly
A $50 perpetuity paid monthly has a present value of $7500 on the date of the first payment. What is the annual effective rate of interest?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.