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, we can use the formula for simple interest: \[ I = P \times r \times t \] where: - \( I \) is the interest, - \( P \) is the principal amount (loan amount), - \( r \) is the interest rate (as a decimal), and - \( t \) is the time in years. Given: - \( P = 6000 \), - \( r = 7.25\% = \frac{7.25}{100} = 0.0725 \), - \( t = 3 \text{ months} = \frac{3}{12} = 0.25 \text{ years} \). Plugging in the values: \[ I = 6000 \times 0.0725 \times 0.25 \] \[ I = 6000 \times 0.0725 \times 0.25 = 108.75 \] So, the amount of interest is \( \$ 108.75 \). To find the future value of the loan, we can use: \[ FV = P + I \] Calculating the future value: \[ FV = 6000 + 108.75 = 6108.75 \] Thus, the future value of the loan is \( \$ 6108.75 \). The amount of interest is \( \$ 108.75 \).