Questions: In order to start a small business, a student takes out a simple interest loan for 3000 for 9 months at a rate of 9.25%. a. How much interest must the student pay? b. Find the future value of the loan.

In order to start a small business, a student takes out a simple interest loan for 3000 for 9 months at a rate of 9.25%. a. How much interest must the student pay? b. Find the future value of the loan.
Transcript text: In order to start a small business, a student takes out a simple interest loan for $\$ 3000$ for 9 months at a rate of $9.25 \%$. a. How much interest must the student pay? b. Find the future value of the loan.
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Solution

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Solution Steps

Step 1: Calculate the Interest (I)

To calculate the interest, we use the formula: $I = P \times \left( \frac{T}{12} \right) \times \left( \frac{R}{100} \right)$. Substituting the given values: $I = 3000 \times \left( \frac{9}{12} \right) \times \left( \frac{9.25}{100} \right) = 208.12$.

Step 2: Calculate the Future Value (FV)

The future value is calculated using the formula: $FV = P + I$. Substituting the values: $FV = 3000 + 208.12 = 3208.12$.

Final Answer:

The interest on the loan is $208.12, and the future value of the loan after 9 months is $3208.12.

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