Tangshan Mining borrowed $10,000 for one year under a revolving credit agreement that authorized and guaranteed the firm access to $20,000. The revolving credit agreement had a stated interest rate of 8 percent and charged the firm a half percent commitment fee on the unused portion of the agreement. Based on this information, the effective annual interest rate on the loan was 8.50 percent.

Question

Quizplus · Accepted Answer

The effective annual interest rate on the loan is calculated as follows:

Effective Annual Interest Rate = (1 + Stated Interest Rate / Number of Compounding Periods) ^ Number of Compounding Periods - 1

In this case, the stated interest rate is 8 percent and the loan is for one year, so there is only one compounding period. Therefore:

Effective Annual Interest Rate = (1 + 0.08 / 1) ^ 1 - 1 = 0.08 or 8%

However, the loan also had a commitment fee of 0.5 percent on the unused portion of the agreement. Since the firm only used $10,000 out of the authorized $20,000, it had an unused portion of $10,000. Therefore, the firm paid a commitment fee of:

Commitment Fee = 0.5% * $10,000 = $50

The total cost of the loan (including the interest and commitment fee) was:

Total Cost = $10,000 + $50 = $10,050

The effective annual interest rate on this total cost is:

Effective Annual Interest Rate = ($10,050 / $10,000) ^ 1/1 - 1 = 0.085 or 8.5%

Therefore, the correct answer is A) True.

Tangshan Mining Borrowed $10,000 for One Year Under a Revolving