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Find the final monthly payment required to pay off a loan with a remaining principal of [tex]$700 and an annual interest rate of 18%.
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.
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