John is shopping for a used car and has found one being offered by Alice for $12,000, based on $2,000 down and a $10,000 balance to be paid to Alice over 36 months at 6% (annual) simple interest paid monthly on the unpaid balance (John’s monthly payments would be $10,000/36 + unpaid balance x 0.06/12).

However, if he pays cash, he can get a reduction of D dollars so the cash payment would be $12,000 - D.

Although Alice will finance the car at 6%, she believes she can better invest her money at 10% elsewhere.

If the 36 monthly payments are discounted to the present at a rate of 10%, how big a reduction in the cash price (to the nearest dollar) can Alice afford to give John so that buying the car for a single cash payment and the net present value of financing over 36 months (plus $2,000 added to account for the down payment), are equivalent propositions?

Assume all months have 30 days, and a year is 360 days.

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Posted by Francis Ramirez on 2025-05-19 01:19:16