To determine Seth's approximate monthly payment, we can start by identifying the necessary components from the given scenario and applying the formula provided for the sum of a finite geometric series.
The formula to find the monthly payment [tex]\( P \)[/tex] is given by:
[tex]\[ P = \frac{P_p \cdot i}{1 - (1 + i)^{-\pi}} \][/tex]
Where:
- [tex]\( P_p \)[/tex] is the present value (balance), which is \[tex]$18,875.
- \( i \) is the monthly interest rate.
- \( \pi \) is the number of payment periods (months).
First, let's find \( i \), the monthly interest rate:
\[ \text{Annual Interest Rate} = 11.6\% \]
\[ i = \frac{11.6\%}{12} = \frac{11.6}{100 \times 12} = \frac{0.116}{12} \approx 0.0096667 \]
Next, we know the number of payment periods \( \pi \) is 24 months.
Substituting these values into the formula, we get the monthly payment \( P \):
\[ P = \frac{18,875 \cdot 0.0096667}{1 - (1 + 0.0096667)^{-24}} \]
This calculation involves:
1. Calculating the monthly interest rate \( i \).
2. Raising \( 1 + i \) to the power of \( -24 \).
3. Computing the denominator \( 1 - (1 + i)^{-24} \).
4. Finally, dividing the product of \( P_p \) and \( i \) by this denominator.
Upon calculation, the approximate monthly payment value we obtain is:
\[ P \approx 884.99 \]
Therefore, the correct answer is:
A. Seth's approximate monthly payment will be \$[/tex] 884.99.
