Sarah is on her way to the local Chevrolet dealership to buy a new car. The list, or “sticker,” price of the car is $24,000. Sarah has $3,000 in her checking account that she can use as a down payment toward the purchase of a new car. Sarah has carefully evaluated her finances, and she has determined that she can afford payments that total $4,800 per year on a loan to purchase the car. Sarah can borrow the money to purchase the car either through the dealer’s “special financing package,” which is advertised as 4 percent financing, or from a local bank, which has automobile loans at 12 percent interest. Each loan would be outstanding for a period of five years, and the payments would be made quarterly (every three months). Sarah knows the dealer’s “special financing package” requires that she will have to pay the “sticker” price for the car. But if she uses the bank financing, she thinks she can negotiate with the dealer for a better price. Assume Sarah wants to pay $1,200 per payment regardless of which loan she chooses, and the remainder of the purchase price will be a down payment that can be satisfied with the money Sarah has in her checking account. Ignoring charges for taxes, tag, and title transfer, how much of a reduction in the “sticker price” must Sarah negotiate to make the bank financing more attractive than the dealer’s “special financing package”?
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