To determine the final monthly payment required to pay off a loan with a remaining principal of [tex]$1,700 and an annual interest rate of 6%, we can follow these steps:
1. Convert the annual interest rate to a monthly interest rate:
- The annual interest rate is 6%. To find the monthly interest rate, we divide the annual rate by 12 (since there are 12 months in a year).
- Monthly interest rate = \( \frac{6\%}{12} \) = \( \frac{6}{12 \times 100} \) = 0.005.
2. Calculate the monthly payment amount:
- We'll use the formula for calculating the payment when the loan term is just 1 month, which simply means adding the interest for one month to the principal.
- Monthly payment = Principal amount \( \times \) (1 + Monthly interest rate).
- Here, the principal amount is $[/tex]1,700, and the monthly interest rate is 0.005.
- Monthly payment = [tex]$1,700 \( \times \) (1 + 0.005) = $[/tex]1,700 [tex]\( \times \)[/tex] 1.005.
3. Perform the multiplication:
- Monthly payment = [tex]$1,700 \( \times \) 1.005 = $[/tex]1,708.5.
4. Round to the nearest cent:
- As the result is already rounded, the final monthly payment required to pay off the loan is [tex]$1,708.50.
So, the final monthly payment required to pay off the loan is $[/tex]1,708.50.
