1. **State the problem:** We want to find the annual deposit amount made at the beginning of each year into an account with 5% annual interest, compounded annually, so that after 9 years the account balance is 32000. 2. **Formula used:** Since deposits are made at the beginning of each year, this is an annuity due problem. The future value of an annuity due is given by: $$FV = P \times \frac{(1 + r)^n - 1}{r} \times (1 + r)$$ where: - $FV$ is the future value (32000), - $P$ is the annual deposit, - $r$ is the interest rate per period (0.05), - $n$ is the number of periods (9). 3. **Rearrange to solve for $P$:** $$P = \frac{FV}{\frac{(1 + r)^n - 1}{r} \times (1 + r)}$$ 4. **Calculate intermediate values:** Calculate $(1 + r)^n$: $$ (1 + 0.05)^9 = 1.05^9 \approx 1.551328216 $$ Calculate numerator of fraction: $$ (1.551328216 - 1) = 0.551328216 $$ Calculate fraction: $$ \frac{0.551328216}{0.05} = 11.02656432 $$ Multiply by $(1 + r)$: $$ 11.02656432 \times 1.05 = 11.57789254 $$ 5. **Calculate $P$:** $$ P = \frac{32000}{11.57789254} \approx 2763.89 $$ 6. **Interpretation:** You must deposit approximately 2763.89 at the beginning of each year to have 32000 at the end of 9 years with 5% interest compounded annually. **Final answer:** $$\boxed{2763.89}$$