1. **State the problem:** Evaluate the expression $$P\left(1 + \frac{r}{k}\right)^{kn}$$ given $$P=6000$$, $$r=9\% = 0.09$$, $$k=2$$, and $$n=20$$. 2. **Formula used:** This is the compound interest formula where: - $$P$$ is the principal amount, - $$r$$ is the annual interest rate (decimal), - $$k$$ is the number of compounding periods per year, - $$n$$ is the number of years. The formula is: $$A = P\left(1 + \frac{r}{k}\right)^{kn}$$ 3. **Substitute the values:** $$A = 6000 \left(1 + \frac{0.09}{2}\right)^{2 \times 20}$$ 4. **Simplify inside the parentheses:** $$1 + \frac{0.09}{2} = 1 + 0.045 = 1.045$$ 5. **Calculate the exponent:** $$2 \times 20 = 40$$ 6. **Evaluate the power:** $$1.045^{40}$$ Using a calculator: $$1.045^{40} \approx 5.006$$ 7. **Multiply by the principal:** $$A = 6000 \times 5.006 = 30036$$ 8. **Round to two decimal places:** $$A \approx 30036.00$$ **Final answer:** $$\boxed{30036.00}$$