To find the final monthly payment required to pay off a loan with a [tex]$700 remaining principal and an 18% annual interest rate, follow these steps:
1. Identify the given values:
- Remaining principal: \$[/tex]700
- Annual interest rate: 18%
2. Convert the annual interest rate to a monthly interest rate:
- The annual interest rate is converted by dividing it by 12 (since there are 12 months in a year).
- So, the monthly interest rate [tex]\( r \)[/tex] is:
[tex]\[
r = \frac{0.18}{12} = 0.015
\][/tex]
3. Calculate the monthly payment:
- The formula for the monthly payment (PMT) when paying off the loan in one month is:
[tex]\[
\text{Monthly Payment} = \text{Principal} \times (1 + \text{Monthly Interest Rate})
\][/tex]
- Plugging in the values we have:
[tex]\[
\text{Monthly Payment} = 700 \times (1 + 0.015) = 700 \times 1.015 = 710.4999999999999
\][/tex]
4. Round the result to the nearest cent:
- The final step is to round the calculated monthly payment to the nearest cent.
[tex]\[
\text{Monthly Payment (Rounded)} = \$710.50
\][/tex]
Therefore, the final monthly payment required to pay off the loan is \$710.50.
