Answer :
Let’s analyze the problem step by step to determine which Dodge model and year Suzanne's original car was. Here’s how we can solve this:
1. List Price and Trade-in Value Calculation:
Suzanne purchased a car for \[tex]$23,860. The dealer gave her 85% of the listed trade-in price for her Dodge car. - Let the trade-in price of Suzanne’s Dodge be \(P\). - Trade-in value \( = 0.85 \times P\) 2. Additional Costs: Besides the car price, Suzanne has to pay other fees: - Sales tax \(= 8.11\% \) of the car price. - Vehicle registration fee \( = \$[/tex]1,695\).
- Documentation fee [tex]\( = \$228\)[/tex].
3. Total Cost Calculation:
Total cost including the car price, sales tax, registration fee, and documentation fee:
- Sales tax amount [tex]\(= 0.0811 \times 23,860\)[/tex]
- Total cost [tex]\(= \$23,860 + (\$23,860 \times 0.0811) + \$1,695 + \$228\)[/tex]
4. Financed Amount:
The financed amount is given by subtracting the trade-in value from the total cost.
5. Calculating Monthly Payments:
Suzanne is financing this amount over 5 years at an annual interest rate of 11.62%, compounded monthly.
6. Monthly Payment Information:
We know her monthly payment is \[tex]$455.96. 7. Identify the Car: We are provided with a table of the trade-in prices of Dodge cars in good condition for different models and years. We need to find which car and year corresponds to the trade-in value. By summarizing these steps and performing the calculations based on the given result: - \(P\) is the trade-in price we need to find. - Trade-in value \( = 0.85 \times P\). From the result, we know that Suzanne's trade-in value correctly matches one of the values in the provided table. We examined the trade-in values from the table: \[ \text{Trade-in values for each vehicle model/year:} \] - \$[/tex]7,068, \[tex]$7,225, \$[/tex]7,626, \[tex]$7,901, \$[/tex]8,116 (for Viper from 2004-2008)
- \[tex]$6,591, \$[/tex]6,777, \[tex]$6,822, \$[/tex]7,191, \[tex]$7,440 (for Neon from 2004-2008) - \$[/tex]8,285, \[tex]$8,579, \$[/tex]8,699, \[tex]$9,030, \$[/tex]9,121 (for Intrepid from 2004-2008)
- \[tex]$7,578, \$[/tex]7,763, \[tex]$7,945, \$[/tex]8,313, \$8,581 (for Dakota from 2004-2008)
Considering these values and knowing the final result, one of these values should match with [tex]\(0.85 \times P\)[/tex].
Among the values provided, none equate to a trade-in value.
Therefore, the Python code returns the result `None`, indicating no exact match was found for any given car model and year for the values in the table.
However, for purposes of answering multiple choice questions, the given options must contain the right combination, where Suzanne's original car:
[tex]\[ \boxed{\text{None of the above}} \][/tex]
1. List Price and Trade-in Value Calculation:
Suzanne purchased a car for \[tex]$23,860. The dealer gave her 85% of the listed trade-in price for her Dodge car. - Let the trade-in price of Suzanne’s Dodge be \(P\). - Trade-in value \( = 0.85 \times P\) 2. Additional Costs: Besides the car price, Suzanne has to pay other fees: - Sales tax \(= 8.11\% \) of the car price. - Vehicle registration fee \( = \$[/tex]1,695\).
- Documentation fee [tex]\( = \$228\)[/tex].
3. Total Cost Calculation:
Total cost including the car price, sales tax, registration fee, and documentation fee:
- Sales tax amount [tex]\(= 0.0811 \times 23,860\)[/tex]
- Total cost [tex]\(= \$23,860 + (\$23,860 \times 0.0811) + \$1,695 + \$228\)[/tex]
4. Financed Amount:
The financed amount is given by subtracting the trade-in value from the total cost.
5. Calculating Monthly Payments:
Suzanne is financing this amount over 5 years at an annual interest rate of 11.62%, compounded monthly.
6. Monthly Payment Information:
We know her monthly payment is \[tex]$455.96. 7. Identify the Car: We are provided with a table of the trade-in prices of Dodge cars in good condition for different models and years. We need to find which car and year corresponds to the trade-in value. By summarizing these steps and performing the calculations based on the given result: - \(P\) is the trade-in price we need to find. - Trade-in value \( = 0.85 \times P\). From the result, we know that Suzanne's trade-in value correctly matches one of the values in the provided table. We examined the trade-in values from the table: \[ \text{Trade-in values for each vehicle model/year:} \] - \$[/tex]7,068, \[tex]$7,225, \$[/tex]7,626, \[tex]$7,901, \$[/tex]8,116 (for Viper from 2004-2008)
- \[tex]$6,591, \$[/tex]6,777, \[tex]$6,822, \$[/tex]7,191, \[tex]$7,440 (for Neon from 2004-2008) - \$[/tex]8,285, \[tex]$8,579, \$[/tex]8,699, \[tex]$9,030, \$[/tex]9,121 (for Intrepid from 2004-2008)
- \[tex]$7,578, \$[/tex]7,763, \[tex]$7,945, \$[/tex]8,313, \$8,581 (for Dakota from 2004-2008)
Considering these values and knowing the final result, one of these values should match with [tex]\(0.85 \times P\)[/tex].
Among the values provided, none equate to a trade-in value.
Therefore, the Python code returns the result `None`, indicating no exact match was found for any given car model and year for the values in the table.
However, for purposes of answering multiple choice questions, the given options must contain the right combination, where Suzanne's original car:
[tex]\[ \boxed{\text{None of the above}} \][/tex]
