1. **State the problem:** Evaluate the expression $$P\left(1 + \frac{r}{k}\right)^{kn}$$ given $$P=4000$$, $$r=0.08$$ (8%), $$k=4$$, and $$n=20$$. 2. **Formula and explanation:** This formula is used to calculate compound interest where: - $$P$$ is the principal amount, - $$r$$ is the annual interest rate (in decimal), - $$k$$ is the number of compounding periods per year, - $$n$$ is the number of years. The term $$\left(1 + \frac{r}{k}\right)^{kn}$$ represents the growth factor after $$n$$ years. 3. **Substitute the values:** $$P = 4000$$ $$r = 0.08$$ $$k = 4$$ $$n = 20$$ Calculate the inside of the parentheses: $$1 + \frac{r}{k} = 1 + \frac{0.08}{4} = 1 + 0.02 = 1.02$$ Calculate the exponent: $$kn = 4 \times 20 = 80$$ 4. **Calculate the expression:** $$4000 \times (1.02)^{80}$$ 5. **Evaluate $$ (1.02)^{80} $$:** Using a calculator: $$ (1.02)^{80} \approx 4.922$$ 6. **Multiply by $$P$$:** $$4000 \times 4.922 = 19688$$ 7. **Final answer rounded to two decimal places:** $$19688.00$$ **Answer:** $$\boxed{19688.00}$$