To solve this problem, we must determine both the total of the payments (denoted as [tex]\( c \)[/tex]) and the monthly payment Joe needs to make for financing his gas grill purchase. Here are the step-by-step calculations:
1. Determine the Principal (Amount Financed):
The total cost of the gas grill and accessories is [tex]$850.00. Joe makes a down payment of $[/tex]150.00. This means the amount financed (principal) can be calculated as follows:
[tex]\[
\text{Principal} = \$850.00 - \$150.00 = \$700.00
\][/tex]
2. Calculate the Interest ([tex]\( I \)[/tex]):
According to the formula:
[tex]\[
\text{Interest}(I) = \frac{2yc}{m(n+1)}
\][/tex]
Given values:
- True annual interest rate, [tex]\( y = 0.14 \)[/tex] (14%)
- Total principal amount, [tex]\( c = \$700.00 \)[/tex]
- Number of months, [tex]\( n = 12 \)[/tex]
Plugging in the values:
[tex]\[
I = \frac{2 \times 0.14 \times 700}{12 \times (12 + 1)}
\][/tex]
After performing the calculation of interest, we get:
[tex]\[
I \approx \$1.26
\][/tex]
3. Calculate the Total of Payments ([tex]\( c \)[/tex]):
The total of payments is the sum of the principal and the interest:
[tex]\[
c = \$700.00 + \$1.26 = \$701.26
\][/tex]
4. Determine the Monthly Payment:
The total of the payments is divided by the number of months to find the monthly payment:
[tex]\[
\text{Monthly Payment} = \frac{\$701.26}{12} \approx \$58.44
\][/tex]
Thus, the detailed incidentals are:
- To the nearest penny, [tex]\( c = \$701.26 \)[/tex]
- Total of payments = [tex]\( \$701.26 \)[/tex]
- Monthly payment = \[tex]$58.44
The correct answer choices are:
- \( c = \$[/tex]701.26 \)
- Total of payments = amount [tex]$+ c = \$[/tex]701.26 \)
- Monthly payment = \$58.44
