Find the final monthly payment required to pay off a loan with \( \$ 800 \) remaining principal and a \( 12 \% \) annual interest rate. \[ \$[?] \] Round to the nearest cent.

To find the final monthly payment required to pay off a loan with a remaining principal of \( \$800 \) and an annual interest rate of \( 12\% \), we can use the formula for the monthly payment on a loan, which is given by: \[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \] where: - \( M \) is the monthly payment, - \( P \) is the principal (the amount of the loan), - \( r \) is the monthly interest rate (annual interest rate divided by 12), - \( n \) is the number of payments (in months). In this case, we need to determine the final payment, which typically occurs when the loan is being fully paid off. However, since we are not given the number of payments \( n \), we will assume that this is the final payment to pay off the remaining balance. 1. **Calculate the monthly interest rate**: \[ r = \frac{12\%}{12} = \frac{0.12}{12} = 0.01 \] 2. **Assuming this is the final payment, we can calculate the interest for one month**: The interest for one month on the remaining principal of \( \$800 \) is: \[ \text{Interest} = P \cdot r = 800 \cdot 0.01 = 8 \] 3. **Calculate the total amount to be paid off**: The total amount to be paid off in the final payment is the remaining principal plus the interest for that month: \[ \text{Total Payment} = \text{Principal} + \text{Interest} = 800 + 8 = 808 \] Thus, the final monthly payment required to pay off the loan is: \[ \boxed{808.00} \]