Questions: In order to start a small business, a student takes out a simple interest loan for 6000 for 9 months at a rate of 8.75%. a. How much interest must the student pay? b. Find the future value of the loan. a. The amount of interest is . (Round to the nearest cent as needed.) b. The future value of the loan is (Round to the nearest cent as needed.)

Solution Steps

We are given the following information for a simple interest loan:

• Principal amount (\(P\)) = \$6000
• Time (\(t\)) = 9 months = \(\frac{9}{12}\) years = 0.75 years
• Interest rate (\(r\)) = 8.75\% = 0.0875

The formula for simple interest is:

\[ I = P \times r \times t \]

Substituting the given values:

\[ I = 6000 \times 0.0875 \times 0.75 \]

\[ I = 393.75 \]

The future value (\(FV\)) of the loan is the sum of the principal and the interest:

\[ FV = P + I \]

Substituting the values we have:

\[ FV = 6000 + 393.75 = 6393.75 \]

Final Answer