To find the simple interest owed for the loan, we can use the formula for simple interest:
[tex]\[ \text{Simple Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
Let's break down the steps with the given information:
1. Principal (P): This is the initial amount of money borrowed. In this case, the principal is [tex]$2650.
2. Rate (R): This is the annual interest rate expressed as a decimal. The given rate is 4.82%, which we convert to decimal form by dividing by 100:
\[ \text{Rate} = \frac{4.82}{100} = 0.0482 \]
3. Time (T): This is the duration for which the money is borrowed. Since the rate is given annually, we need to convert the time into years. Here, the time is given in months, specifically 31 months. We convert months to years by dividing by 12:
\[ \text{Time} = \frac{31}{12} \approx 2.5833 \text{ years} \]
Now, we can plug these values into the simple interest formula:
\[ \text{Simple Interest} = 2650 \times 0.0482 \times 2.5833 \]
Performing the multiplication:
\[ \text{Simple Interest} \approx 2650 \times 0.0482 \times 2.5833 \approx 329.9692 \]
4. Rounding to the Nearest Cent: Since monetary values are usually represented to two decimal places, we need to round the calculated interest to the nearest cent:
\[ 329.9692 \approx 329.97 \]
Therefore, the interest charged on a principal of $[/tex]2650 at an interest rate of 4.82% over 31 months is approximately $329.97.
