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?

a. 2004 intrepid
b. 2008 neon
c. 2005 viper
d. 2007 dakota

Question

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?

a. 2004 intrepid
b. 2008 neon
c. 2005 viper
d. 2007 dakota

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Car Financing", "Sales Tax Calculation", "Trade-in Valuation", "Table Reading", "Loan Monthly Payment" ], "new_concepts": [], "current_concepts": [ "Car Financing", "Sales Tax Calculation", "Trade-in Valuation", "Table Reading", "Loan Monthly Payment" ] } ## Calculate the loan principal from the monthly payment Using the *Loan Monthly Payment* and *Car Financing* knowledge points $$ \begin{aligned} &PMT = 455.96\ &r = \frac{0.1162}{12} \approx 0.00968333\ &n = 5 \times 12 = 60\ &P = PMT \times \frac{1 - (1 + r)^{-n}}{r}\ &P = 455.96 \times \frac{1 - (1 + 0.00968333)^{-60}}{0.00968333} \approx 20,750.00 \end{aligned} $$ ## Determine total purchase cost before trade-in credit Using the *Sales Tax Calculation* knowledge point $$ \begin{aligned} &\text{List Price} = 23,860\ &\text{Sales Tax} = 23,860 \times 0.0811 \approx 1,935.05\ &\text{Fees} = 1,695 + 228 = 1,923\ &\text{Total Cost} = 23,860 + 1,935.05 + 1,923 = 27,718.05 \end{aligned} $$ ## Calculate the trade-in allowance and value Using the *Trade-in Valuation* knowledge point $$ \begin{aligned} &\text{Trade-in Allowance} = \text{Total Cost} - P\ &\text{Trade-in Allowance} = 27,718.05 - 20,750.00 = 6,968.05\ &\text{Trade-in Value} = \frac{6,968.05}{0.85} \approx 8,197.71 \end{aligned} $$ ## Identify the matching car from the table Using the *Table Reading* knowledge point $$ \begin{aligned} &\text{Target Value} \approx \$8,197.71\ &\text{Option (a): 2004 Intrepid} ightarrow \$8,285 \times 0.85 = \$7,042.25 \quad (\text{Value: } \$8,285)\ &\text{Option (b): 2008 Neon} ightarrow \$7,440 \times 0.85 = \$6,324.00 \quad (\text{Value: } \$7,440)\ &\text{Option (c): 2005 Viper} ightarrow \$7,225 \times 0.85 = \$6,141.25 \quad (\text{Value: } \$7,225)\ &\text{Option (d): 2007 Dakota} ightarrow \$8,313 \times 0.85 = \$7,066.05 \quad (\text{Value: } \$8,313) \end{aligned} $$ Comparing the options, the 2004 Intrepid value of \$8,285 is the closest match to the calculated trade-in value of \$8,197.71.

a. 2004 Intrepid

b. 2008 Neon

c. 2005 Viper

d. 2007 Dakota

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

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QUESTION IMAGE

Question

Explanation:

Calculate the loan principal from the monthly payment

Determine total purchase cost before trade-in credit

Calculate the trade-in allowance and value

Identify the matching car from the table

Answer: