Question

Problem 5-48 Low Financing or Cash Back? (LG5-4, LG5-9)

A car company is offering a choice of deals. You can receive $3,000 cash back on the purchase, or a 4.0 percent APR, 4-year loan. The price of the car is $30,000 and you could obtain a 4-year loan from your credit union, at 9.0 percent APR.

Since the cash back is used to reduce the size of the loan, the cost of the car is entirely paid for with the debt. Therefore, the true cost of each deal can be compared through the monthly payment. Compute the monthly payment of each deal. Which one is cheaper?

• $3,000 cash back offer

• 4 percent APR offer

Answer 1

Deal 1: $3,000 cash back offer:

Annuity = [Loan x r] / [1 - (1 + r)^-n]

= [($30,000 - $3,000) x (0.09/12)] / [1 - {1 + (0.09/12)}^-(4*12)]

= $202.50 / 0.3014 = $671.90

Deal 2: 4% APR offer:

Annuity = [Loan x r] / [1 - (1 + r)^-n]

= [$30,000 x (0.04/12)] / [1 - {1 + (0.04/12)}^-(4*12)]

= $100 / 0.1476 = $677.37

As the monthly payment of cash back offer is cheaper, hence, it is cheaper.