Question

Derek plans to buy a $27,043.00 car. The dealership offers zero percent financing for 51.00 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 5.12%.

Answer 1

Calculating Present Value of amount to be paid in case we purchase on installments

Lets consider 51 installments beginning today as 1 down payment and 50 installments starting from end of 1st month

Down payment = $27043 / 51 = 530.255

Equal monthly payments starting from end of (PMT) = - $ 530.255

No of monthly payments (N) = 50

Interest rate per month (I) = 5.12/12 = 0.4267% p.m.

Present value of installments paid (PV) = ??

Using financial calculator or PV function in excel,

Present value of installments paid (PV) = $23,829.96

Present Value of amount to be paid in case we purchase on installments = Down payment + PV of installments

Present Value of amount to be paid in case we purchase on installments = 530.25 + 23829.96

Present Value of amount to be paid in case we purchase on installments = $ 24,360.22

Derek would be willing to pay for the car in full today if the dealership offers him $ 2,682.78 cash back (27,043-24,360.22)

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