Question

You have saved $3,000 for a down payment on a new car. The largest monthly payment you can afford is $300. The loan will have a 10% APR based on end-of-month payments.

A.What is the most expensive car you can afford if you finance it for 48 months? Do not round intermediate calculations. Round your answer to the nearest cent.

B. What is the most expensive car you can afford if you finance it for 60 months? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

	P =	Regular Payments
	PV =	Loan Amount
	r =	rate of interest
	n =	no of periods
A)	P =	r (PV)
		1 - (1 + r )-n
	300 =	(10%/12)*X
		1 - (1 / (1 + 10%/12)^48))
	300 =	0.00833333333333333 X
		0.328568001
	X =	300 * 0.328568001 / 0.0083333333333333
	X =	11828.45
	LOAN AMOUNT =	$ 11828.45
	CAR VALUE =	DOWNPAYMENT+ LOAN AMOUNT
		3000 + 11828.45
		14828.45
B)	P =	r (PV)
		1 - (1 + r )-n
	300 =	(10%/12)*X
		1 - (1 / (1 + 10%/12)^60))
	300 =	0.00833333333333333 X
		0.392211409
	X =	300 * 0.392211409 / 0.0083333333333333
	X =	14119.61
	LOAN AMOUNT =	$ 14119.61
	CAR VALUE =	DOWNPAYMENT+ LOAN AMOUNT
		3000 + 14119.61
		$ 17119.61