Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To solve this problem, we need to calculate the monthly payments for both the new car and the used car using the provided loan formula:
[tex]\[ PMT = \frac{P \left(\frac{r}{n}\right)}{1 - \left(1 + \frac{r}{n}\right)^{-nt}} \][/tex]
Here:
- [tex]\(P\)[/tex] is the principal loan amount (the cost of the car).
- [tex]\(r\)[/tex] is the annual interest rate.
- [tex]\(n\)[/tex] is the number of payments per year.
- [tex]\(t\)[/tex] is the loan term in years.
For the new car:
- Principal, [tex]\(P_{\text{new}}\)[/tex] = \[tex]$ 28,000 - Annual interest rate, \(r_{\text{new}}\) = 0.0522 - Loan term, \(t_{\text{new}}\) = 5 years - Number of payments per year, \(n = 12\) Plug these values into the formula: \[ PMT_{\text{new}} = \frac{28000 \left(\frac{0.0522}{12}\right)}{1 - \left(1 + \frac{0.0522}{12}\right)^{-12 \times 5}} \] For the used car: - Principal, \(P_{\text{used}}\) = \$[/tex] 14,000
- Annual interest rate, [tex]\(r_{\text{used}}\)[/tex] = 0.0786
- Loan term, [tex]\(t_{\text{used}}\)[/tex] = 4 years
- Number of payments per year, [tex]\(n = 12\)[/tex]
Plug these values into the formula:
[tex]\[ PMT_{\text{used}} = \frac{14000 \left(\frac{0.0786}{12}\right)}{1 - \left(1 + \frac{0.0786}{12}\right)^{-12 \times 4}} \][/tex]
After calculating these monthly payments, we can find the difference between the monthly payment for the new car and the used car.
Performing the calculations:
1. For the new car, the monthly payment (PMT_new) is approximately [tex]$531.22. 2. For the used car, the monthly payment (PMT_used) is approximately $[/tex]340.86.
To find the difference in monthly payments:
[tex]\[ \text{Difference} = PMT_{\text{new}} - PMT_{\text{used}} = 531.22 - 340.86 = 190.36 \][/tex]
So, the difference in monthly payments between financing the new car and financing the used car is [tex]\(\$ 190.36\)[/tex].
[tex]\[ PMT = \frac{P \left(\frac{r}{n}\right)}{1 - \left(1 + \frac{r}{n}\right)^{-nt}} \][/tex]
Here:
- [tex]\(P\)[/tex] is the principal loan amount (the cost of the car).
- [tex]\(r\)[/tex] is the annual interest rate.
- [tex]\(n\)[/tex] is the number of payments per year.
- [tex]\(t\)[/tex] is the loan term in years.
For the new car:
- Principal, [tex]\(P_{\text{new}}\)[/tex] = \[tex]$ 28,000 - Annual interest rate, \(r_{\text{new}}\) = 0.0522 - Loan term, \(t_{\text{new}}\) = 5 years - Number of payments per year, \(n = 12\) Plug these values into the formula: \[ PMT_{\text{new}} = \frac{28000 \left(\frac{0.0522}{12}\right)}{1 - \left(1 + \frac{0.0522}{12}\right)^{-12 \times 5}} \] For the used car: - Principal, \(P_{\text{used}}\) = \$[/tex] 14,000
- Annual interest rate, [tex]\(r_{\text{used}}\)[/tex] = 0.0786
- Loan term, [tex]\(t_{\text{used}}\)[/tex] = 4 years
- Number of payments per year, [tex]\(n = 12\)[/tex]
Plug these values into the formula:
[tex]\[ PMT_{\text{used}} = \frac{14000 \left(\frac{0.0786}{12}\right)}{1 - \left(1 + \frac{0.0786}{12}\right)^{-12 \times 4}} \][/tex]
After calculating these monthly payments, we can find the difference between the monthly payment for the new car and the used car.
Performing the calculations:
1. For the new car, the monthly payment (PMT_new) is approximately [tex]$531.22. 2. For the used car, the monthly payment (PMT_used) is approximately $[/tex]340.86.
To find the difference in monthly payments:
[tex]\[ \text{Difference} = PMT_{\text{new}} - PMT_{\text{used}} = 531.22 - 340.86 = 190.36 \][/tex]
So, the difference in monthly payments between financing the new car and financing the used car is [tex]\(\$ 190.36\)[/tex].
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.