Questions: In order to start a small business, a student takes out a simple interest loan for 9000 for 9 months at a rate of 12.25%. a. How much interest must the student pay? b. Find the future value of the loan. a. The amount of interest is 826.88. (Round to the nearest cent as needed.) b. The future value of the loan is 9826.88. (Round to the nearest cent as needed.)

Solution Steps

To calculate the simple interest, we use the formula:

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

where:

• \( P = 9000 \) is the principal amount,
• \( r = 0.1225 \) is the annual interest rate (converted from percentage),
• \( t = \frac{9}{12} = 0.75 \) is the time in years (since 9 months is 0.75 years).

Substituting the values into the formula:

\[ I = 9000 \times 0.1225 \times 0.75 \]

\[ I = 826.875 \]

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

\[ F = P + I \]

Substituting the known values:

\[ F = 9000 + 826.875 \]

\[ F = 9826.875 \]

Final Answer