1. **Problem Statement:** Ivanna places 6000 in an account with 9% interest compounded annually. We need to find the amount in the account after 1 year and after 2 years. 2. **Formula for compound interest:** $$ A = P \left(1 + \frac{r}{n}\right)^{nt} $$ where: - $A$ is the amount after time $t$, - $P$ is the principal (initial amount), - $r$ 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:** - $P = 6000$ - $r = 0.09$ (9% as decimal) - $n = 1$ (compounded yearly) 4. **Calculate amount after 1 year ($t=1$):** $$ A = 6000 \left(1 + \frac{0.09}{1}\right)^{1 \times 1} = 6000 \times (1 + 0.09)^1 = 6000 \times 1.09 $$ 5. **Intermediate step showing cancellation:** $$ A = 6000 \times \cancel{1.09} = 6540 $$ 6. **Amount after 1 year:** $$ A = 6540 $$ 7. **Calculate amount after 2 years ($t=2$):** $$ A = 6000 \left(1 + \frac{0.09}{1}\right)^{1 \times 2} = 6000 \times (1.09)^2 $$ 8. **Calculate $(1.09)^2$:** $$ (1.09)^2 = 1.09 \times 1.09 = 1.1881 $$ 9. **Calculate amount after 2 years:** $$ A = 6000 \times 1.1881 $$ 10. **Intermediate step showing cancellation:** $$ A = 6000 \times \cancel{1.1881} = 7128.6 $$ 11. **Amount after 2 years:** $$ A = 7128.6 $$