You want to be able to withdraw \( \$ 35,000 \) from your account each year for 25 years after you retire. You expect to retire in 20 years. If your account earns \( 10 \% \) interest, how much will you need to deposit each year until retirement to achieve your retirement goals? \( \$ \) Round your answer to the nearest cent.

Let the amount needed at retirement be \( A \). Since you wish to withdraw \(\$35,\!000\) per year for 25 years at an annual interest rate of \(10\%\), the present value of this annuity at retirement is given by \[ A = 35000 \times \frac{1 - (1.10)^{-25}}{0.10}. \] **Step 1.** Compute \(A\): \[ (1.10)^{-25} = \frac{1}{(1.10)^{25}}. \] A typical calculation yields \((1.10)^{25} \approx 10.8333\), so \[ (1.10)^{-25} \approx \frac{1}{10.8333} \approx 0.0923. \] Thus, \[ A \approx 35000 \times \frac{1 - 0.0923}{0.10} = 35000 \times \frac{0.9077}{0.10} \approx 35000 \times 9.077 = 317695. \] So, you need approximately \(\$317,\!695\) at retirement. **Step 2.** Find the annual deposit \(X\) required. You plan to make annual deposits at the end of each year for 20 years, and the future value of an annuity (with interest rate \(10\%\)) is \[ \text{Future Value} = X \times \frac{(1.10)^{20} - 1}{0.10}. \] We set this equal to \(A\): \[ X \times \frac{(1.10)^{20} - 1}{0.10} = 317695. \] **Step 3.** Solve for \(X\): \[ X = \frac{317695 \times 0.10}{(1.10)^{20} - 1}. \] A calculation gives \((1.10)^{20} \approx 6.7275\), so \[ (1.10)^{20} - 1 \approx 6.7275 - 1 = 5.7275. \] Thus, \[ X \approx \frac{31769.5}{5.7275} \approx 5549.24. \] **Final Answer:** You need to deposit approximately \(\$5549.24\) each year for 20 years to achieve your retirement goal.