1. **State the problem:** Find the future value of an ordinary annuity with payment $R=800$, monthly deposits and compounding ($m=12$), annual interest rate $r=0.09$, and time $t=3$ years. 2. **Formula for future value of an ordinary annuity:** $$FV = R \times \frac{(1 + \frac{r}{m})^{mt} - 1}{\frac{r}{m}}$$ 3. **Substitute the given values:** $$R=800, \quad r=0.09, \quad m=12, \quad t=3$$ 4. **Calculate the periodic interest rate:** $$\frac{r}{m} = \frac{0.09}{12} = 0.0075$$ 5. **Calculate the total number of payments:** $$mt = 12 \times 3 = 36$$ 6. **Calculate the growth factor:** $$\left(1 + \frac{r}{m}\right)^{mt} = (1 + 0.0075)^{36} = 1.0075^{36}$$ 7. **Evaluate $1.0075^{36}$:** $$1.0075^{36} \approx 1.308$$ 8. **Calculate the numerator:** $$1.308 - 1 = 0.308$$ 9. **Calculate the denominator:** $$\frac{r}{m} = 0.0075$$ 10. **Calculate the fraction:** $$\frac{0.308}{0.0075} = \cancel{\frac{0.308}{0.0075}} = 41.0667$$ 11. **Calculate the future value:** $$FV = 800 \times 41.0667 = 32853.33$$ **Final answer:** The future value of the annuity after 3 years is approximately **32853.33**.