If $10,000 is invested for 9 months at 5% annual interest,
compute:
a. The simple interest earned at the end of 9 months.
b. The Future Value of the original investment at the end
of the 9 months.

Let's solve the problem in two steps.

### Given Data
- Principal $ P = 10,000 $ USD
- Time $ t = 9 $ months, which is $ \frac{9}{12} = 0.75 $ years
- Annual interest rate $ r = 5\% $ or $ 0.05 $

### (a) Simple Interest Earned
The formula for simple interest $ I $ is:
\[
I = P \cdot r \cdot t
\]
Substitute the values:
\[
I = 10,000 \times 0.05 \times 0.75 = 375
\]
Thus, the simple interest earned at the end of 9 months is **$375**.

### (b) Future Value
The future value $ A $ of the investment, or the amount at the end of the investment period, is given by:
\[
A = P + I
\]
Or equivalently:
\[
A = P \cdot (1 + r \cdot t)
\]
Substitute the values:
\[
A = 10,000 \times (1 + 0.05 \times 0.75) = 10,000 \times 1.0375 = 10,375
\]
Thus, the future value of the original investment at the end of 9 months is **$10,375**.

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### Related Questions
1. How would the future value change if the investment period was extended to one year?
2. What is the formula for future value with compound interest?
3. How does changing the interest rate affect the future value?
4. Can we find the future value if interest is compounded monthly instead of annually?
5. How can simple interest be calculated if the time period is given in days instead of months?

### Tip:
When calculating interest over partial years, always express the time in years to align with the annual interest rate.

If $10,000 is invested for 9 months at 5% annual interest, compute: a. The simple interest earned at the end of 9 months. b. The Future Value of the original investment at the end of the 9 months.

Calculate the simple interest and future value of a $10,000 investment over 9 months at a 5% annual interest rate. This solution includes step-by-step formulas for interest and future value, providing valuable insight into financial math concepts suitable for Grades 9-10.

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