To find the final monthly payment required to pay off a loan with a remaining principal of [tex]$1600 and an annual interest rate of 6%, follow these steps:
1. Understand the key terms:
- Remaining Principal: The amount left to be paid on the loan, which is $[/tex]1600.
- Annual Interest Rate: The yearly interest rate, which is 6%.
2. Convert the annual interest rate to a monthly interest rate:
- Since there are 12 months in a year, divide the annual interest rate by 12 to get the monthly interest rate.
- Monthly interest rate = 6% / 12 = 0.5%.
3. Calculate the interest for one month:
- Convert the percentage to a decimal for calculation purposes. Thus, 0.5% becomes 0.005.
- Multiply the remaining principal by the monthly interest rate to get the interest for one month:
- Interest = [tex]$1600 * 0.005 = $[/tex]8.
4. Determine the total final amount:
- The final amount due at the end of the period is the sum of the remaining principal and the interest for one month.
- Final amount = Remaining Principal + Monthly Interest = [tex]$1600 + $[/tex]8 = [tex]$1608.
5. Ensure the result is rounded to the nearest cent (in this case, it already is):
- Final Monthly Payment = $[/tex]1608.00.
Thus, the final monthly payment required to pay off the loan is $1608.00.
