1. **State the problem:** We want to find the amount and interest earned on an investment of 500 at 9% interest compounded annually after 8 years. 2. **Formula for compound interest:** $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount after $t$ years - $P$ 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 $1.09^8$: $$1.09^8 = 1.999004$$ 6. Multiply by principal: $$A = 500 \times 1.999004 = 999.502$$ 7. Round to nearest cent: $$A = 999.50$$ 8. **Calculate interest earned:** $$\text{Interest} = A - P = 999.50 - 500 = 499.50$$ **Final answer:** - Amount after 8 years: $999.50$ - Interest earned: $499.50$