To find the final monthly payment required to pay off a loan with $900 remaining principal and a 12% annual interest rate, you can use the formula for calculating monthly payments on a loan. Here's how you can do it step-by-step:
1. Convert the annual interest rate to a monthly interest rate by dividing it by 12. In this case, 12% annual interest rate becomes 1% monthly interest rate (12% / 12 = 1%).
2. Determine the number of months remaining to pay off the loan. Since the monthly payment will pay off the remaining principal of $900, this depends on the agreed-upon loan term. Let's assume the loan term is 12 months for this example.
3. Use the formula for calculating monthly payments on a loan:
\[ \text{Monthly Payment} = \frac{P \times r}{1 - (1 + r)^{-n}} \]
Where:
- P = Principal amount (loan amount)
- r = Monthly interest rate
- n = Number of months remaining to pay off the loan
4. Plug in the values into the formula:
\[ \text{Monthly Payment} = \frac{900 \times 0.01}{1 - (1 + 0.01)^{-12}} \]
\[ \text{Monthly Payment} = \frac{9}{1 - (1.01)^{-12}} \]
5. Calculate the final monthly payment required to pay off the loan with $900 remaining principal and a 12% annual interest rate.
This calculation will give you the exact monthly payment needed to pay off the remaining principal of $900 in 12 months at a 12% annual interest rate.
