Dennis has just made the final monthly payment necessary for paying off his car financing. When he purchased the car three years ago, it had a list price of $23,878. Dennis traded in his good-condition 2001 Honda Odyssey and financed the rest of the cost at an interest rate of 11.82%, compounded monthly. The dealer gave Dennis 85% of the trade-in value of his car, listed below. Dennis was also responsible for paying 9.05% sales tax, a $1,474 vehicle registration fee, and a $225 documentation fee. Sales tax was calculated after subtracting the trade-in credit from the vehicle price. All told, how much did Dennis pay in interest? (Round all dollar values to the nearest cent, and consider the trade-in to be a reduction in the amount paid.) Honda Cars in Good Condition Model/Year 2000 2001 2002 2003 Element $5,887 $6,080 $6,225 $6,622 Odyssey $8,450 $8,693 $8,928 $9,224 Insight $4,384 $4,661 $5,006 $5,440 Accord $6,356 $6,626 $6,817 $7,114
The trade-in credit is 85% of $8,693, or $7,389.05. After subtracting that credit, Dennis’s taxable price is $16,488.95, so sales tax is $1,492.25; adding the $1,474 registration fee and $225 documentation fee gives a financed amount of $19,680.20. At 11.82% annually compounded monthly, the monthly rate is 0.985%, and 36 monthly payments are about $651.97. The total interest is 36($651.97) − $19,680.20 = $3,790.72, choice A.
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