Question

Derek plans to buy a $32,752.00 car. The dealership offers zero percent financing for 56.00 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 4.61%.

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

Derek decides to buy a new car. The dealership offers him a choice of paying $527.00 per month for 5 years (with the first payment due next month) or paying some $28,018.00 today. He can borrow money from his bank to buy the car. What interest rate makes him indifferent between the two options?

Answer format: Percentage Round to: 3 decimal places (Example: 9.243%, % sign required. Will accept decimal format rounded to 5 decimal places (ex: 0.09243))

I would appreciate the Help! :) would be great if you could show the steps (not in excel) for better understanding~ Thank You

Answer 1

1]	Amount payable per monthly installment = 32752/56 =	$              584.86
	Amount Derek will be planning to pay = 584.86*(1+0.0461/12)*((1+0.0461/12)^56-1)/((0.0461/12)*(*(1+0.0461/12)^56) =	$        29,531.14
	Cash back required = 32752-29531.14 =	$          3,220.86
2]	For the two options to be equal [for indifference], the PV of
	the 60 installments of $527 should be equal to $28018, when
	discounted at the required rate.
	Hence, 28018 = 527*PVIFA(r,60), where r = monthly interest
	rate.
	Solving for r.
	PVIFA(r,60) = 28018/527 = 53.1651
	Using a financial calculator, PVIFA for n = 60 and r =
	0.4 = 53.2489
	0.5 = 51.7256
	By simple interpolation, r = 0.4+0.1*(53.2489-53.1651)/(53.2489-51.7256) =	0.40550
	APR = 0.40550*12 =	4.866%