Question

Tangshan Mining borrowed $100,000 for one year under a line of credit with a stated interest rate of 7.5 percent and a 15 percent compensating balance. Normally, the firm keeps almost no money in its checking account. Based on this information, the effective annual interest rate on the loan is ________.

Answer 1

The effective annual interest rate for Tangshan Mining, which borrowed $100,000 at a stated interest rate of 7.5% with a 15% compensating balance, is approximately 8.82%.

Step-by-step explanation:

To calculate the effective annual interest rate on a loan with a compensating balance, you need to consider the actual amount of loan funds available for use. For Tangshan Mining, which borrowed $100,000 with a compensating balance of 15%, this means $85,000 is available ($100,000 less the 15% compensating balance of $15,000). The stated interest rate is 7.5%, but since the company must maintain a 15% compensating balance, the effective interest rate is higher. The effective interest rate can be calculated by dividing the annual interest by the available funds. The annual interest amount is the product of the total loan amount and the stated interest rate, which is $100,000 * 7.5% = $7,500. To find the effective annual interest rate, divide $7,500 by $85,000 and multiply by 100 to convert to a percentage. This gives us an effective annual interest rate of approximately 8.82%.

Answer 2

Effective annual interest rate = 8.8% (Approx)

Step-by-step explanation:

Given:

Nominal interest rate = 7.5% = 7.5 / 100 = 0.075

Compensating balance rate = 15% = 15 / 100 = 0.15

Effective annual interest rate = ?

Computation of effective annual interest rate:

Effective annual interest rate = [Nominal interest rate / (1 - Compensating balance rate)] x 100

Effective annual interest rate = [0.075 / (1 - 0.15)] x 100

Effective annual interest rate = [0.075 / (0.85)] x 100

Effective annual interest rate = [0.0882352941] x 100

Effective annual interest rate = 8.82352941

Effective annual interest rate = 8.8% (Approx)