1. **State the problem:** Calculate the future value of 10,000 with 9% annual interest compounded monthly. 2. **Formula used:** The future value $FV$ with compound interest is given by: $$FV = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $P$ is the principal amount (10,000), - $r$ is the annual interest rate (0.09), - $n$ is the number of compounding periods per year (12 for monthly), - $t$ is the time in years. 3. **Important rules:** Interest compounds monthly, so divide the annual rate by 12 and multiply the number of years by 12. 4. **Intermediate work:** Since the time $t$ is not given, the problem is incomplete to find a numeric answer. If you provide $t$, we can calculate $FV$. For example, if $t=1$ year: $$FV = 10000 \left(1 + \frac{0.09}{12}\right)^{12 \times 1} = 10000 \left(1 + 0.0075\right)^{12} = 10000 \times (1.0075)^{12}$$ Calculate $(1.0075)^{12}$: $$ (1.0075)^{12} \approx 1.0938 $$ So, $$FV \approx 10000 \times 1.0938 = 10938$$ 5. **Answer:** The future value after 1 year is approximately 10938. Please provide the time period $t$ if you want the exact future value for a different duration.