To determine Seth's approximate monthly payment, we will use the formula for the monthly payment to pay off a loan or credit card balance. The balance, interest rate, compounding frequency, and payment duration are all factors to consider.
Given:
- Credit card balance [tex]\( P = \)[/tex] [tex]$18,875
- Annual interest rate \( r = 11.6\% \) or \( r = 0.116 \)
- Number of months to pay off \( n = 24 \)
First, we need to convert the annual interest rate to a monthly interest rate, since Seth will be making monthly payments.
\[
i = \frac{r}{12} = \frac{0.116}{12} \approx 0.009667
\]
Next, we use the formula for the monthly payment of an amortizing loan:
\[
M = P \times \frac{i \times (1 + i)^n}{(1 + i)^n - 1}
\]
Where:
- \( M \) is the monthly payment.
- \( P \) is the principal balance (initial amount of the loan).
- \( i \) is the monthly interest rate.
- \( n \) is the number of payments (months).
Substitute the known values into the formula:
\[
M = 18875 \times \frac{0.009667 \times (1 + 0.009667)^{24}}{(1 + 0.009667)^{24} - 1}
\]
By performing the calculations:
1. Calculate \((1 + i)^n\):
\[
(1 + 0.009667)^{24} \approx 1.260864
\]
2. Calculate the numerator:
\[
0.009667 \times 1.260864 \approx 0.0121858
\]
3. Calculate the denominator:
\[
1.260864 - 1 \approx 0.260864
\]
4. Finally, calculate the monthly payment:
\[
M = 18875 \times \frac{0.0121858}{0.260864} \approx 884.99
\]
Thus, Seth's approximate monthly payment will be \( \$[/tex] 884.99 \).
Therefore, the answer is:
C. Seth's approximate monthly payment will be $884.99.
