Question

An auto dealership is advertising that a new car with a sticker price of $34,128 is on sale for $25,995 if payment is made in full, or it can be financed at 0% interest for 72 months with a monthly payment of $474. Note that 72 payments × $474 per payment = $34,128, which is the sticker price of the car. By allowing you to pay for the car in a series of payments (starting one month from now) rather than $25,995 now, the dealer is effectively loaning you $25,995. If you choose the 0% financing option, what is the effective interest rate that the auto dealership is earning on your loan? (Hint: Discount the payments back to current dollars, and use Goal Seek to find the discount rate that makes the net present value of the payments = $25,995.)

Answer 1

Answer:

effective annual rate = 9.77%

monthly rate = 0.78%

Explanation:

we can solve this by using a financial calculator or an excel spreadsheet:

our initial outlay = -25,995

then we have 72 cash flows = 474

I prefer to use excel, since all you need to do is use the IRR formula to determine the interest rate at which the NPV = 0. The interest rate at which NPV = 0 is the effective monthly interest rate. IRR = 0.78% monthly

In order to determine the effective annual rate:

EAR = (1 + 0.0078)¹² - 1 = 1.0977 - 1 = 0.0977 = 9.77%