To determine the final monthly payment required to pay off a loan with a remaining principal of [tex]$1,100 and an annual interest rate of 15%, follow these steps:
1. Determine the annual interest rate: The given annual interest rate is 15%, which can be expressed as a decimal for calculations by dividing by 100:
\[
\text{Annual Interest Rate} = \frac{15}{100} = 0.15
\]
2. Calculate the monthly interest rate: Since interest is compounded monthly, we need the monthly interest rate. There are 12 months in a year, so divide the annual interest rate by 12:
\[
\text{Monthly Interest Rate} = \frac{0.15}{12} \approx 0.0125
\]
3. Calculate the interest for the month: To find the interest for the month on the principal, multiply the principal by the monthly interest rate. The remaining principal is $[/tex]1,100:
[tex]\[
\text{Monthly Interest} = 1100 \times 0.0125 = 13.75
\][/tex]
4. Determine the final monthly payment: To find the total monthly payment, add the calculated monthly interest to the remaining principal:
[tex]\[
\text{Monthly Payment} = 1100 + 13.75 = 1113.75
\][/tex]
Hence, the final monthly payment required to pay off a loan with $1,100 remaining principal and a 15% annual interest rate is:
[tex]\[
\boxed{1113.75}
\][/tex]
