In order to start a small business, a student takes out a simple interest loan for \( \$ 2000 \) for 9 months at a rate of \( 6.75 \% \). 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 find the interest on a simple interest loan, you can use the formula: \[ \text{Interest} = P \times r \times t \] Where: - \( P \) is the principal amount (the initial loan amount), - \( r \) is the annual interest rate (as a decimal), - \( t \) is the time in years. For this loan, \( P = 2000 \), \( r = 6.75\% = 0.0675 \), and \( t = \frac{9}{12} \) years (or 0.75 years). Plugging in these values: \[ \text{Interest} = 2000 \times 0.0675 \times 0.75 = 101.25 \] So, the amount of interest is \( \$101.25 \). To find the future value of the loan, you calculate the total amount that needs to be paid back, which includes the principal and the interest: \[ \text{Future Value} = P + \text{Interest} \] Thus, \[ \text{Future Value} = 2000 + 101.25 = 2101.25 \] The future value of the loan is \( \$2101.25 \). Now for your answer: a. The amount of interest is \( \$101.25 \). b. The future value of the loan is \( \$2101.25 \).