To find the simple interest owed for the given loan, you can use the formula for simple interest:
[tex]\[ \text{Simple Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
Here's a detailed step-by-step solution:
1. Principal (P): The principal amount is the initial amount of money borrowed or invested. In this case, the principal [tex]\( P \)[/tex] is \[tex]$2825.
2. Rate (R): The rate of interest is given as a percentage. Here, the rate \( R \) is 10.5%. To use this in the formula, you need to convert the percentage to a decimal by dividing by 100:
\[ R = \frac{10.5}{100} = 0.105 \]
3. Time (T): The time period for which the interest is calculated is given in years. Here, the time \( T \) is 2 and a half years. As a decimal, this is:
\[ T = 2 + \frac{1}{2} = 2.5 \]
4. Calculate Simple Interest:
Substitute \( P = 2825 \), \( R = 0.105 \), and \( T = 2.5 \) into the simple interest formula:
\[ \text{Simple Interest} = 2825 \times 0.105 \times 2.5 \]
5. Multiplying the values:
\[ 2825 \times 0.105 = 296.625 \]
\[ 296.625 \times 2.5 = 741.5625 \]
Therefore, the simple interest owed for the loan is \$[/tex]741.5625.
