Let's solve this step-by-step.
1. Calculate the principal amount financed:
- The total cost including tax is [tex]$850.00.
- The down payment made is $[/tex]150.00.
- Therefore, the principal amount financed is [tex]\(850.00 - 150.00 = 700.00\)[/tex].
2. Calculate the monthly interest rate:
- The annual interest rate is 14%.
- The monthly interest rate is [tex]\( \frac{14\%}{12} = 0.014 / 12 = 0.011666666666666667\)[/tex].
3. Calculate [tex]\(c\)[/tex]:
- Using the formula [tex]\(c = \frac{\text{Principal} \times \text{Monthly Interest Rate} \times \text{Loan Term in Months}}{\text{Loan Term in Months} + 1}\)[/tex]:
- Here, \text{Principal} is [tex]$700.00.
- \text{Loan Term in Months} is 12.
- Monthly Interest Rate is 0.011666666666666667.
- Plugging in the numbers: \(c = \frac{700.00 \times 0.011666666666666667 \times 12}{12 + 1}\).
- \(c = \frac{700.00 \times 0.011666666666666667 \times 12}{ 13} = 7.54\).
4. Calculate the total of the payments:
- The total of the payments is the amount financed plus \(c\).
- Therefore, the total of the payments is \(700.00 + 7.54 = 707.54\).
5. Calculate the monthly payment:
- The monthly payment is the total of the payments divided by the number of payments (loan term in months).
- Therefore, the monthly payment is \( \frac{707.54}{12} = 58.96\).
Now let's fill in the blanks:
- \( c = \$[/tex]\ 7.54 \)
- [tex]\( \text{Total of payments} = \text{amount financed} + c = \$ 700.00 + \$ 7.54 = \$ 707.54\)[/tex]
- [tex]\( \text{Total of payments} \div \text{number of payments} = \text{monthly payment} = \frac{707.54}{12} = \$ 58.96\)[/tex]
Thus:
- [tex]\( c = \$ 7.54 \)[/tex]
- Total of payments [tex]$= \$[/tex] 707.54 \)
- Monthly payment [tex]$= \$[/tex] 58.96 \)
