Question

Paula is considering the purchase of a new car. She has narrowed her search to two cars that are equally appealing to her. Car A costs $23,000, and Car B costs $23,200. The manufacturer of Car A is offering 0% financing for 48 months with zero down, while the manufacturer of Car B is offering a rebate of $2000 at the time of purchase plus financing at the rate of 3%/year compounded monthly over 48 months with zero down. If Paula has decided to buy the car with the lower net cost to her, which car should she purchase? (Round numerical values to the nearest cent.)

net cost of Car A	$
net cost of Car B	$
car she should purchase		---Select--- Car A Car B

Answer 1

Cost ouflow for Car A:

Monthly EMI with Zero Financing = $23000/ 48 months = $479.1667

Total cash outflow after 4 years = $479.1667 * 48 months = $23,000

Cost ouflow for Car B:

Cost of car after rebate = $23200 - $2000 = $21,000

Interest rate per month = 0.03 / 12 months = 0.25%

Monthly EMI computation:

= [cost of car after rebate *r * (1+r)^n] / [(1+r)^n - 1]

= [21000*0.25% * (1+0.0025)^48] / [(1+0.0025)^48 - 1]

= [ 52.50 * 1.12733] / [1.12733 - 1]

= 59.1847 / 0.12733

= $464.814

Therefore, Total cash outflow for 4 years = $464.814 * 48 = $22,311.00

Hence,

Car A = $23,000.00

Car B = $22,311.00

Therefore, Car B will be purchases because of least cost.