A car company is offering a choice of deals. You can receive $600 cash back on the purchase, or a 2 percent APR, 4-year loan. The price of the car is $18,900 and you could obtain a 4-year loan from your credit union at 6 percent APR. What is the monthly payment of each deal?

Question

Quizplus · Accepted Answer

To find the monthly payment for each deal, we need to use the formula for the present value of an annuity:

PMT = PV * (r / (1 - (1 + r)^(-n)))

where PV is the present value (the price of the car), r is the monthly interest rate, and n is the number of payments (48 for a 4-year loan).

For the cash back deal, the present value is $18,900 - $600 = $18,300. The monthly interest rate is 6% / 12 = 0.005, and the number of payments is 48. Plugging these values into the formula gives:

PMT = $18,300 * (0.005 / (1 - (1 + 0.005)^(-48))) = $429.78

For the 2 percent APR deal, the present value is $18,900. The monthly interest rate is 0.02 / 12 = 0.00167, and the number of payments is 48. Plugging these values into the formula gives:

PMT = $18,900 * (0.00167 / (1 - (1 + 0.00167)^(-48))) = $410.04

Comparing these two monthly payments, we see that the 2 percent APR deal has a lower payment, so it is the better choice.

A Car Company Is Offering a Choice of Deals