Question

Alexis Martin has just graduated from college and needs to buy a car to commute to work. She estimates that she can afford to pay about $450 per month for a loan or lease and has about $2,000 in savings to use for a down payment. Develop a plan to guide her through her first car-buying experience, including researching car type, deciding whether to buy a new or used car, negotiating the price and terms, and financing the transaction. If she gets a 3 year loan for 5% how much car can she afford

	A.	17,000
	B.	18,000
	C.	19,000
	D.	20,000
	E.	21,000

Answer 1

A.$17,000.

First let us know the present value of $450 monthly payments, that can be made over 3 year period.

present value of annuity = A*[1-(1+r)^(-n)]/r

here,

A=$450.

r=5% per year =>5%*1/12 =>0.416667%=>0.00416667.

n=3 years*12 months=>36 months.

=>$450*[1-(1.00416667)^(-36)]/0.00416667

=>$450*[0.1390239/0.00416667]

=>$15,015.

The cost of car she can afford = present value of loan payments + down payment

=>$15,015 +2000

=>$17,015.

=>$17,000 ...(closest to ) (minor differences arise due to rounding off of present value factors).