1. **Problem Statement:** We have an initial investment of $500 at an interest rate of 9% compounded annually. We want to find the amount after 8 years and the interest earned. 2. **Formula Used:** The compound interest formula is: $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount after time $t$, - $P$ is the principal (initial investment), - $r$ is the annual interest rate (decimal), - $n$ is the number of times interest is compounded per year, - $t$ is the number of years. 3. **Given Values:** - $P = 500$ - $r = 0.09$ - $n = 1$ (compounded annually) - $t = 8$ 4. **Calculate the amount:** $$A = 500 \left(1 + \frac{0.09}{1}\right)^{1 \times 8} = 500 (1.09)^8$$ 5. **Calculate $(1.09)^8$:** $$ (1.09)^8 \approx 1.999004$$ 6. **Calculate $A$:** $$A = 500 \times 1.999004 = 999.502$$ 7. **Round to nearest cent:** $$A \approx 999.50$$ 8. **Calculate interest earned:** $$\text{Interest} = A - P = 999.50 - 500 = 499.50$$ **Final answer:** - Amount after 8 years: $999.50$ - Interest earned: $499.50$