one time The one time good deal CashForClunkere program offe

The \"one time good deal\" Cash-For-Clunkere program offered by the federal government proved a temporary boon for ear dealers. In addition to this program, dealers were eager to add their own incentives. Bill Mitselfik was considering two different deals he could make for his new car. He can finance the purchase price, $25,000, entirely through the dealer at a 1.9% APR (compounded monthly) for 5 years, with payments monthly. Alternatively, the dealer will give Bill a cash rebate and provide financing at 9% APR (compounded monthly) for 5 years, with monthly payments. What is the value of the rebate for which Bill would be indifferent between the two financing options?

Solution

1.9% APR = (1.9 / 12)%, or 0.1583% per month.

9% APR = (9 / 12)%, or 0.75% per month.

Number of months = 12 x 5 = 60

If entire $25,000 is financed,

$25,000 = Monthly payment x PVIFA (0.1583%, 60 periods)

$25,000 = Monthly payment x 57.1956 [From PVIFA Table]

Monthly payment = $25,000 / 57.1956 = $437.0966

If Bill pays $437.0966 each month for 5 years at 0.75% per month,

Present value of this payment = $437.0966 x PVIFA (0.75%, 60 periods)

= $437.0966 x 48.1734 [From PVIFA Table]

= $21,056.43

So, Discount = $(25,000 - 21,056.43)

= $3,943.57