You want to be able to withdraw \( \$ 35,000 \) each year for 25 years. Your account earns \( 4 \% \) interest. (a) How much do you need in your account at the beginning? (b) How much total money will you withdraw from the account? \( \$ \) (c) How much of that money is interest? \( \$ \)

To find out how much you need in your account at the beginning, we can use the formula for the present value of an annuity. The formula is given by: \[ PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \] Where: - \( PV \) = present value (the amount you need at the beginning) - \( P \) = annual payment (\$35,000) - \( r \) = annual interest rate (0.04) - \( n \) = number of years (25) **(a)** Plugging in the values: \[ PV = 35000 \times \left( \frac{1 - (1 + 0.04)^{-25}}{0.04} \right) \] Calculating: \[ PV \approx 35000 \times 15.6221 \approx 546,270.50 \] So, you need approximately **$546,270.50** in your account at the beginning. **(b)** Total money withdrawn over 25 years is simply the annual withdrawal multiplied by the number of years: \[ Total\ Withdrawals = P \times n = 35000 \times 25 = 875,000 \] So, the total money withdrawn is **$875,000**. **(c)** To find out how much of that money is interest, we subtract the initial amount from the total withdrawals: \[ Interest = Total\ Withdrawals - PV = 875,000 - 546,270.50 \approx 328,729.50 \] So, the amount of money that is interest is approximately **$328,729.50**.