Suzanne has purchased a car with a list price of $23,860. She traded in her previous car, which was a Dodge in good condition, and financed the rest of the cost for five years at a rate of 11.62%, compounded monthly. The dealer gave her 85% of the listed trade-in price for her car. She was also responsible for 8.11% sales tax, a $1,695 vehicle registration fee, and a $228 documentation fee. If Suzanne makes a monthly payment of $455.96, which of the following was her original car?Dodge Cars in Good ConditionModel/Year20042005200620072008Viper$7,068$7,225$7,626$7,901$8,116Neon$6,591$6,777$6,822$7,191$7,440Intrepid$8,285$8,579$8,699$9,030$9,121Dakota$7,578$7,763$7,945$8,313$8,581
First find the amount financed from the monthly payments: at 11.62% ÷ 12 for 60 months, the present value of $455.96 payments is about $20,678. The car price, sales tax, registration, and documentation fee total $23,860 + ($23,860 × 0.0811) + $1,695 + $228 = $27,720. That means the trade-in allowance was about $27,720 − $20,678 = $7,042. Since the dealer offered 85% of the listed trade-in value, the list price was about $7,042 ÷ 0.85 = $8,285, matching the 2004 Intrepid.
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