Newbie Business Center has borrowed $12,000 from its bank. The loan is for three years and requires the firm to make equal monthly payments of $398.57. Each payment is comprised of
Both interest and principal repayment, and the payments will begin one month after the loan
Agreement. What effective annual rate is the bank charging Newbie for this loan? Round your
Answer to the nearest tenth of a percent.

Question

Quizplus · Accepted Answer

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

Effective annual rate = (1 + i/n)^n - 1

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

In this case, we know that Newbie has borrowed $12,000 at an equal monthly payment of $398.57 for three years. Therefore, the total number of payments will be:

Total number of payments = 3 years x 12 months/year = 36

The monthly interest rate can be calculated as follows:

Monthly interest rate = (total payment - loan amount) / loan amount x 1 / total number of payments
Monthly interest rate = ($398.57 - $12,000) / $12,000 x 1 / 36
Monthly interest rate = -0.00973

Note that the monthly interest rate is negative because Newbie is paying back more than the amount borrowed.

Now, we can calculate the effective annual rate using the formula above:

Effective annual rate = (1 - 0.00973/12)^12 - 1
Effective annual rate = 0.1270 or 12.7% (rounded to the nearest tenth)

Therefore, the bank is charging Newbie an effective annual rate of 12.7%. The answer is D.

Newbie Business Center Has Borrowed $12,000 from Its Bank