Question

Derek plans to buy a $33,328.00 car. The dealership offers zero percent financing for 58.00 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 4.86%

Answer 1

Given that,

Derek plan to buy car at price = $33328

The dealership offers zero percent financing for 58.00 months with the first payment due at signing (today)

=> Monthly payment PMT = 33328/58 = $574.62

bank offer a rate of r = 4.86% compounded monthly

Based on the bank rate, PV of the annuity can be calculated using PV formula of annuity due

=> PV = PMT*(1 - (1+r/n)^-N)*(1+r/n)/(r/n) = 574.62*(1 - (1+0.0486/12)^-58)*(1+0.0486/12)/(0.0486/12) = $29769.79

So, if company give a cashback of 33328 - 29770 = $3558, Derek will be willing to pay for the car in full today.