Question

Derek plans to buy a $25,614.00 car. The dealership offers zero percent financing for 53.00 months with the first payment due at signing (today). Derek would be willing to pay for the car in full today if the dealership offers him $____ cash back. He can borrow money from his bank at an interest rate of 5.26%.

Answer Format: Currency: Round to: 2 decimal places.

Answer 1

The monthly payment for the Zero Percent Financing by the dealership = 25614/53 = 483.28

If we discount this payment (outflow) over a period of 53 months at the interest rate of the bank. we will get the amount Derek would be willing to pay now. hence the difference should be the cash back required.

The equation,

Present Value of Payments = 483.28 / (1+0.0043) + 483.28 / (1+0.0043)² + ..... + 483.28 / (1+0.0043)⁵³

^{= 22811.96}

^{The Cash Back required will be = 25614 - 22811.95 = 2802.04.}