Venus Inc. recently borrowed $750,000 from its bank at a simple interest rate of 10 percent. The loan is for six months. The loan agreement requires the interest to be added to the amount borrowed and the total amount to be repaid in monthly installments. What is the loan's effective annual rate (EAR)?

Question

Venus Inc. recently borrowed $750,000 from its bank at a simple interest rate of 10 percent. The loan is for six months. The loan agreement requires the interest to be added to the amount borrowed and the total amount to be repaid in monthly installments. What is the loan's effective annual rate (EAR)?

Quizplus · Accepted Answer

First, we need to calculate the amount to be repaid in monthly installments:

The loan amount with added interest = $750,000 + ($750,000 x 0.10 x 6/12) = $825,000

Monthly installment = $825,000 / 6 = $137,500

To find the EAR, we need to use the following formula:

EAR = (1 + i/n)^n - 1

where i is the annual interest rate, and n is the number of compounding periods per year.

For this loan, i = 0.10 and n = 2 (since the loan is for six months and the interest is added to the balance monthly).

EAR = (1 + 0.10/2)^2 - 1 = 0.1832 or 18.32%

Therefore, the answer is choice C.

Venus Inc Recently Borrowed $750,000 from Its Bank at a Simple