Get comprehensive solutions to your questions with the help of IDNLearn.com's experts. Our Q&A platform is designed to provide quick and accurate answers to any questions you may have.
Sagot :
Let's break down Sally Seair's sailboat financing step by step:
1. Purchase Price and Down Payment:
- The price of the sailboat, including tax, is \[tex]$5,275. - The down payment Sally makes is \$[/tex]500.
2. Amount Financed:
- The amount Sally finances is the purchase price minus the down payment.
- [tex]\(\$5,275 - \$500 = \$4,775\)[/tex]
3. Annual Interest Rate and Loan Term:
- The true annual interest rate is 15%.
- The loan term is 36 months.
4. Monthly Interest Rate:
- The annual interest rate is 15%, so the monthly interest rate is [tex]\(\frac{15\%}{12} = 1.25\%\)[/tex].
5. Monthly Payment Calculation:
- We need to use the formula for the monthly payment of an installment loan:
[tex]\[ M = P \frac{r(1+r)^n}{(1+r)^n - 1} \][/tex]
where:
- [tex]\( M \)[/tex] is the monthly payment,
- [tex]\( P \)[/tex] is the loan amount (\[tex]$4,775), - \( r \) is the monthly interest rate (0.0125), - \( n \) is the number of payments (36). 6. Calculating Monthly Payment: - Using the given values, we find the monthly payment to be approximately \$[/tex]165.53.
7. Total of Payments:
- The total amount paid over the course of the loan can be calculated by multiplying the monthly payment by the number of payments:
[tex]\[ c = M \times n \][/tex]
- Substituting the values, we get:
[tex]\[ c = \$165.53 \times 36 \approx \$5,958.97 \][/tex]
8. Total of Payments and Amount Financed:
- The total of payments consists of the down payment and [tex]\( c \)[/tex]:
[tex]\[ \text{Total of payments} = \$500 + c \][/tex]
- Substituting [tex]\( c \)[/tex], we get:
[tex]\[ \text{Total of payments} = \$500 + \$5,958.97 = \$6,458.97 \][/tex]
Summarizing the solutions:
- To the nearest penny, [tex]\( c = \$5,958.97 \)[/tex].
- Total of payments = \[tex]$4,775 (amount financed) + \$[/tex]5,958.97 = \[tex]$10,733.97. - Monthly payment = \$[/tex]165.53.
1. Purchase Price and Down Payment:
- The price of the sailboat, including tax, is \[tex]$5,275. - The down payment Sally makes is \$[/tex]500.
2. Amount Financed:
- The amount Sally finances is the purchase price minus the down payment.
- [tex]\(\$5,275 - \$500 = \$4,775\)[/tex]
3. Annual Interest Rate and Loan Term:
- The true annual interest rate is 15%.
- The loan term is 36 months.
4. Monthly Interest Rate:
- The annual interest rate is 15%, so the monthly interest rate is [tex]\(\frac{15\%}{12} = 1.25\%\)[/tex].
5. Monthly Payment Calculation:
- We need to use the formula for the monthly payment of an installment loan:
[tex]\[ M = P \frac{r(1+r)^n}{(1+r)^n - 1} \][/tex]
where:
- [tex]\( M \)[/tex] is the monthly payment,
- [tex]\( P \)[/tex] is the loan amount (\[tex]$4,775), - \( r \) is the monthly interest rate (0.0125), - \( n \) is the number of payments (36). 6. Calculating Monthly Payment: - Using the given values, we find the monthly payment to be approximately \$[/tex]165.53.
7. Total of Payments:
- The total amount paid over the course of the loan can be calculated by multiplying the monthly payment by the number of payments:
[tex]\[ c = M \times n \][/tex]
- Substituting the values, we get:
[tex]\[ c = \$165.53 \times 36 \approx \$5,958.97 \][/tex]
8. Total of Payments and Amount Financed:
- The total of payments consists of the down payment and [tex]\( c \)[/tex]:
[tex]\[ \text{Total of payments} = \$500 + c \][/tex]
- Substituting [tex]\( c \)[/tex], we get:
[tex]\[ \text{Total of payments} = \$500 + \$5,958.97 = \$6,458.97 \][/tex]
Summarizing the solutions:
- To the nearest penny, [tex]\( c = \$5,958.97 \)[/tex].
- Total of payments = \[tex]$4,775 (amount financed) + \$[/tex]5,958.97 = \[tex]$10,733.97. - Monthly payment = \$[/tex]165.53.
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is committed to providing accurate answers. Thanks for stopping by, and see you next time for more solutions.