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Find [tex]\( c \)[/tex], the total of the payments, and the monthly payment. Choose the correct answers.

[tex]\[
\operatorname{Interest}(I)=\frac{2yc}{m(n+1)}
\][/tex]

Joe Summers buys a gas grill and accessories. The cost, including tax, amounts to [tex]\(\$850.00\)[/tex]. Joe finances the grill over 12 months after making a [tex]\(\$150\)[/tex] down payment. The true annual interest rate is [tex]\(14\%\)[/tex]. What are Joe's monthly payments (principal plus interest)?

To the nearest penny:
[tex]\[ c = \$ \boxed{58.15} \][/tex]

Total of payments:
[tex]\[ \text{amount financed} + c = \$ \boxed{} \][/tex]

Total of payments [tex]\(\div\)[/tex] number of payments:
[tex]\[ \text{monthly payment} = \$ \boxed{} \][/tex]



Answer :

GinnyAnswer
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 \)

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