To find the solution to the given finance problem, let’s break it down step-by-step:
1. Price with tax of the TV is [tex]$1,950.00.
2. A down payment of $[/tex]200.00 is made.
First, calculate the amount to be financed:
[tex]\[
\text{Amount financed} = \text{Price with tax} - \text{Down payment} = \$1950.00 - \$200.00 = \$1750.00
\][/tex]
Next, we need to consider the annual interest rate of [tex]\(16\%\)[/tex], which needs to be converted to a monthly interest rate:
[tex]\[
\text{Monthly interest rate} = \frac{\text{Annual interest rate}}{12} = \frac{0.16}{12} \approx 0.01333
\][/tex]
The financing is spread over 24 months. We use the formula for monthly payment on an installment loan, which is:
[tex]\[
\text{Monthly Payment} = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}
\][/tex]
where:
- [tex]\( P \)[/tex] = amount financed = [tex]$1750.00
- \( r \) = monthly interest rate = 0.01333
- \( n \) = number of months = 24
After computing using the formula, the monthly payment is approximately:
\[
\text{Monthly Payment} \approx \$[/tex]85.69
\]
To find the total amount of payments:
[tex]\[
\text{Total of payments} = (\text{Monthly Payment} \times \text{Number of months}) + \text{Down Payment}
\][/tex]
[tex]\[
\text{Total of payments} \approx (\$85.69 \times 24) + \$200.00 \approx \$2256.45
\][/tex]
Now, the total amount to be financed [tex]\( c \)[/tex], after interest, is:
[tex]\[
c = \text{Total of payments} - \text{Down payment} = \$2256.45 - \$200.00 = \$2056.45
\][/tex]
Thus, the answers, to the nearest penny, are:
- [tex]\( c = \$2056.45 \)[/tex]
- Total of payments = \[tex]$2256.45
- Monthly payment = \$[/tex]85.69
