Basic Value of the Car = $30,976.
No of months for which zero percent financing is offered = 53 months
Since, the first payment is due at signing (today) , we will calculate the PVIFA for 52 months to arrive at the present value of the car
Monthly payment required to be made = 30,976/53 = $584.4528
Interest rate per month = 5.04%/12 = 0.42%
Present Value of the Car at zero cost financing for 53 months with the first payment due at signing (today) = Monthly payment required to be made*PVIFA(0.42%,52)
= 584.45288*46.6258
= $27,250.58
.
Derek would be willing to pay for the car in full today if the dealership offers him the following cash back:
Basic Value of the Car - Present Value of the Car at zero cost financing for 53 months with the first payment due at signing (today)
= 30,976 - 27,250.58
= $3,725.42
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