Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Let's walk through the process step-by-step to determine which Dodge car Suzanne traded in.
1. Calculate the total cost of the new car:
- The list price of the car is \[tex]$23,860. - Sales tax is 8.11% of the list price. - Registration fee is \$[/tex]1,695.
- Documentation fee is \[tex]$228. First, calculate the sales tax: \[ \text{Sales Tax} = \$[/tex]23,860 \times 0.0811 = \[tex]$1,935.146 \] Now, calculate the total cost: \[ \text{Total Cost} = \$[/tex]23,860 + \[tex]$1,935.146 + \$[/tex]1,695 + \[tex]$228 = \$[/tex]27,718.146
\]
Rounding, we get:
[tex]\[ \text{Total Cost} \approx \$27,718 \][/tex]
2. Determine the trade-in value:
- She receives 85% of the listed trade-in price for her Dodge car.
We'll consider each possible car and calculate the trade-in value:
- For the 2004 Intrepid (\[tex]$8,285): \[ \text{Trade-in Value} = \$[/tex]8,285 \times 0.85 = \[tex]$7,042.25 \] - For the 2008 Neon (\$[/tex]7,440):
[tex]\[ \text{Trade-in Value} = \$7,440 \times 0.85 = \$6,324 \][/tex]
- For the 2005 Viper (\[tex]$7,225): \[ \text{Trade-in Value} = \$[/tex]7,225 \times 0.85 = \[tex]$6,141.25 \] - For the 2007 Dakota (\$[/tex]8,313):
[tex]\[ \text{Trade-in Value} = \$8,313 \times 0.85 = \$7,066.05 \][/tex]
3. Calculate the amount to be financed:
- Subtract the trade-in value from the total cost.
- For the 2004 Intrepid:
[tex]\[ \text{Financing Amount} = \$27,718 - \$7,042.25 = \$20,675.75 \][/tex]
- For the 2008 Neon:
[tex]\[ \text{Financing Amount} = \$27,718 - \$6,324 = \$21,394 \][/tex]
- For the 2005 Viper:
[tex]\[ \text{Financing Amount} = \$27,718 - \$6,141.25 = \$21,576.75 \][/tex]
- For the 2007 Dakota:
[tex]\[ \text{Financing Amount} = \$27,718 - \$7,066.05 = \$20,651.95 \][/tex]
4. Calculating the Monthly Payment using the Annuity Formula:
The formula for calculating the monthly payment is:
[tex]\[ \text{Monthly Payment} = \frac{P \times r}{1 - (1 + r)^{-n}} \][/tex]
Where:
- [tex]\( P \)[/tex] is the financing amount.
- [tex]\( r \)[/tex] is the monthly interest rate.
- [tex]\( n \)[/tex] is the number of total payments (months).
Given:
[tex]\[ r = \frac{0.1162}{12}, \quad n = 5 \times 12 = 60 \text{ months} \][/tex]
We'll use this formula to check which financing amount gives a monthly payment close to \[tex]$455.96: - For the 2004 Intrepid: \[ P = 20,675.75 \] Calculated Monthly Payment: \[ \approx \$[/tex]455.44
\]
- For the 2007 Dakota:
[tex]\[ P = 20,651.95 \][/tex]
Calculated Monthly Payment:
[tex]\[ \approx \$455.44 \][/tex]
Both cars give a monthly payment of around \[tex]$455.44, which is very close to \$[/tex]455.96.
After reconciling all conditions, it turns out:
- The 2004 Intrepid (a)
- 2007 Dakota (d)
Both satisfy Suzanne's requirements. Thus, both are correct.
1. Calculate the total cost of the new car:
- The list price of the car is \[tex]$23,860. - Sales tax is 8.11% of the list price. - Registration fee is \$[/tex]1,695.
- Documentation fee is \[tex]$228. First, calculate the sales tax: \[ \text{Sales Tax} = \$[/tex]23,860 \times 0.0811 = \[tex]$1,935.146 \] Now, calculate the total cost: \[ \text{Total Cost} = \$[/tex]23,860 + \[tex]$1,935.146 + \$[/tex]1,695 + \[tex]$228 = \$[/tex]27,718.146
\]
Rounding, we get:
[tex]\[ \text{Total Cost} \approx \$27,718 \][/tex]
2. Determine the trade-in value:
- She receives 85% of the listed trade-in price for her Dodge car.
We'll consider each possible car and calculate the trade-in value:
- For the 2004 Intrepid (\[tex]$8,285): \[ \text{Trade-in Value} = \$[/tex]8,285 \times 0.85 = \[tex]$7,042.25 \] - For the 2008 Neon (\$[/tex]7,440):
[tex]\[ \text{Trade-in Value} = \$7,440 \times 0.85 = \$6,324 \][/tex]
- For the 2005 Viper (\[tex]$7,225): \[ \text{Trade-in Value} = \$[/tex]7,225 \times 0.85 = \[tex]$6,141.25 \] - For the 2007 Dakota (\$[/tex]8,313):
[tex]\[ \text{Trade-in Value} = \$8,313 \times 0.85 = \$7,066.05 \][/tex]
3. Calculate the amount to be financed:
- Subtract the trade-in value from the total cost.
- For the 2004 Intrepid:
[tex]\[ \text{Financing Amount} = \$27,718 - \$7,042.25 = \$20,675.75 \][/tex]
- For the 2008 Neon:
[tex]\[ \text{Financing Amount} = \$27,718 - \$6,324 = \$21,394 \][/tex]
- For the 2005 Viper:
[tex]\[ \text{Financing Amount} = \$27,718 - \$6,141.25 = \$21,576.75 \][/tex]
- For the 2007 Dakota:
[tex]\[ \text{Financing Amount} = \$27,718 - \$7,066.05 = \$20,651.95 \][/tex]
4. Calculating the Monthly Payment using the Annuity Formula:
The formula for calculating the monthly payment is:
[tex]\[ \text{Monthly Payment} = \frac{P \times r}{1 - (1 + r)^{-n}} \][/tex]
Where:
- [tex]\( P \)[/tex] is the financing amount.
- [tex]\( r \)[/tex] is the monthly interest rate.
- [tex]\( n \)[/tex] is the number of total payments (months).
Given:
[tex]\[ r = \frac{0.1162}{12}, \quad n = 5 \times 12 = 60 \text{ months} \][/tex]
We'll use this formula to check which financing amount gives a monthly payment close to \[tex]$455.96: - For the 2004 Intrepid: \[ P = 20,675.75 \] Calculated Monthly Payment: \[ \approx \$[/tex]455.44
\]
- For the 2007 Dakota:
[tex]\[ P = 20,651.95 \][/tex]
Calculated Monthly Payment:
[tex]\[ \approx \$455.44 \][/tex]
Both cars give a monthly payment of around \[tex]$455.44, which is very close to \$[/tex]455.96.
After reconciling all conditions, it turns out:
- The 2004 Intrepid (a)
- 2007 Dakota (d)
Both satisfy Suzanne's requirements. Thus, both are correct.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
