Question

You're about to buy a new car for $10,000. The dealer offers you a one-year loan where you pay $860.66 every month for the next 12 months. Since you pay $860.66 * 12 = $10,328 in total, the dealer claims that the loan's annual interest rate is (10,328-10,000)/10,000 = 3.28%. What is the actual effective annual rate?

Answer 1

The actual effective annual rate is 3.33%.

Step-by-step explanation:

Effective Annual Rate (EAR) refers to an interest rate has been adjusted for compounding over specified period of time.

Effective annual rate can therefore be described as the interest rate that paid to an investor in a year after compounding has been adjusted for.

Effective annual rate can be computed using the following formula:

EAR = [(1 + (i / n))^n] - 1 .............................(1)

Where;

i = Annual interest rate claimed by the dealer = 3.28%, or 0.0328

n = Number of compounding periods or months = 12

Substituting the values into equation (1), we have:

EAR = [(1 + (0.0328 / 12))^12] - 1 = 0.0332976137123635

EAR = 0.0333, or 3.33% approximately.

Therefore, the actual effective annual rate is 3.33%.