Answer :
To determine the final monthly payment required to pay off a loan with [tex]$1,300 remaining principal and a 9% annual interest rate, we need to follow these steps:
### Step 1: Determine the monthly interest rate
The annual interest rate is given as 9%. We need to convert this to a monthly interest rate by dividing by 12 (the number of months in a year).
\[ \text{Monthly Interest Rate} = \frac{9\%}{12} = \frac{0.09}{12} = 0.0075 \]
### Step 2: Calculate the monthly payment
Since we want to pay off the loan in one month, the payment should include the entire remaining principal as well as the interest for that one month.
The formula to calculate this is:
\[ \text{Monthly Payment} = \text{Remaining Principal} \times (1 + \text{Monthly Interest Rate}) \]
Substitute the given values into the formula:
\[ \text{Monthly Payment} = 1300 \times (1 + 0.0075) \]
### Step 3: Perform the calculation
First, compute the term inside the parentheses:
\[ 1 + 0.0075 = 1.0075 \]
Next, multiply the remaining principal by this value:
\[ 1300 \times 1.0075 = 1309.75 \]
### Step 4: Round to the nearest cent
The final monthly payment required to pay off the loan should be rounded to the nearest cent:
\[ \boxed{1309.75} \]
Thus, the final monthly payment required to pay off the loan is $[/tex]1309.75.
