charles is going to purchase a new car that has a list price of $21,450. he is planning on trading in his good-condition 2004 dodge neon and financing the rest of the cost over three years, paying monthly. his finance plan has an interest rate of 12.28%, compounded monthly. charles will also be responsible for 6.88% sales tax, a $1,089 vehicle registration fee, and a $124 documentation fee. if the dealer gives charles 80% of the listed trade-in price on his car, once the financing is paid off, what percent of the total amount paid will the interest be? (consider the trade-in to be a reduction in the amount paid.)

a. 17.64%
b. 15.67%
c. 16.70%
d. 12.86%

Question

charles is going to purchase a new car that has a list price of $21,450. he is planning on trading in his good-condition 2004 dodge neon and financing the rest of the cost over three years, paying monthly. his finance plan has an interest rate of 12.28%, compounded monthly. charles will also be responsible for 6.88% sales tax, a $1,089 vehicle registration fee, and a $124 documentation fee. if the dealer gives charles 80% of the listed trade-in price on his car, once the financing is paid off, what percent of the total amount paid will the interest be? (consider the trade-in to be a reduction in the amount paid.)

a. 17.64%
b. 15.67%
c. 16.70%
d. 12.86%

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Car Financing", "Sales Tax Calculation", "Trade-in Valuation", "Table Reading", "Total Interest Percentage" ], "new_concepts": [], "current_concepts": [ "Car Financing", "Sales Tax Calculation", "Trade-in Valuation", "Table Reading", "Total Interest Percentage" ] } ## Find trade-in value and calculate total purchase cost $$ \begin{aligned} &\text{Trade-in Value (2004 Dodge Neon)} = \$6,591 \ &\text{Actual Trade-in Credit} = 0.80 \times \$6,591 = \$5,272.80 \ &\text{Sales Tax} = 0.0688 \times \$21,450 = \$1,475.76 \ &\text{Total Cost} = \$21,450 + \$1,475.76 + \$1,089 + \$124 - \$5,272.80 = \$18,865.96 \end{aligned} $$ ## Calculate monthly payment and total amount paid $$ \begin{aligned} &P = \$18,865.96, \quad r = \frac{0.1228}{12} \approx 0.0102333, \quad n = 36 \ &M = P \frac{r(1+r)^n}{(1+r)^n - 1} \approx \$18,865.96 \times 0.0333475 \approx \$629.13 \ &\text{Total Payments} = 36 \times \$629.13 = \$22,648.68 \ &\text{Total Amount Paid (including trade-in reduction)} = \$22,648.68 \end{aligned} $$ ## Calculate total interest and its percentage $$ \begin{aligned} &\text{Total Interest} = \$22,648.68 - \$18,865.96 = \$3,782.72 \ &\text{Interest Percentage} = \frac{\$3,782.72}{\$22,648.68} \times 100\% \approx 16.70\% \end{aligned} $$

a. 17.64%

b. 15.67%

c. 16.70%

d. 12.86%

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Car Financing" ] }

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Question

Explanation:

Find trade-in value and calculate total purchase cost

Calculate monthly payment and total amount paid

Calculate total interest and its percentage

Answer: