In order to start a small business, a student takes out a simple interest loan for \( \$ 6000 \) for 3 months at a rate of \( 7.25 \% \). a. How much interest must the student pay? b. Find the future value of the loan. a. The amount of interest is \( \$ \square \). (Round to the nearest cent as needed.)

To calculate the interest on the loan, we use the formula for simple interest: \[ I = P \times r \times t \] Where: - \( I \) is the interest, - \( P \) is the principal amount (\$6000), - \( r \) is the annual interest rate (7.25% or 0.0725 as a decimal), - \( t \) is the time in years (3 months or \( \frac{3}{12} = 0.25 \) years). Plugging in the values: \[ I = 6000 \times 0.0725 \times 0.25 \] Calculating the interest: \[ I = 6000 \times 0.0725 \times 0.25 = 108.75 \] So, the amount of interest is \( \$108.75 \). To find the future value of the loan: \[ \text{Future Value} = P + I = 6000 + 108.75 = 6108.75 \] Thus, the future value of the loan is \( \$6108.75 \). The amount of interest is \( \$108.75 \). The future value of the loan is \( \$6108.75 \).