Question

Kangaroo Autos is offering free credit on a new $12,500 car. You pay $500 down and then $400 a month for the next 30 months. Turtle Motors next door does not offer free credit but will give you $1,190 off the list price. a. If the rate of interest is 0.83% a month, calculate the present value of the payments to Kangaroo Autos. (Do not round Intermediate calculations. Round your answer to 2 decimal places.) Answer is complete but not entirely correct. Present value $ 10,584.02 b. Which company is offering the better deal? Kangaroo Autos Turtle Motors

Answer 1

1). The better deal is the one with a lower present value.

Offer from Kangaroo Autos:

PV = Downpayment + [Monthly payment * {1 - (1 + r)^-n} / r]

= $500 + [$400 * {1 - (1 + 0.0083)^-30} / 0.0083]

= $500 + [$400 * {0.2196 / 0.0083}]

= $500 + [$400 * 26.4601]

= $500 + $10,584.02 = $11,084.02

Offer from Turtle Motors:

PV = Cost of Car - Discount = $12,500 - $1,190 = $11,310

b). As the Kangaroo Autos have a lower PV, which means they are offering a better deal.

2-24). Annual Income = [Amount Invested * r] / [1 - (1 + r)^-n]

= [$18,500 * 0.10] / [1 - (1 + 0.10)^-10]

= $1,850 / 0.6145

= $3,010.79