You want to be able to withdraw \( \$ 30,000 \) each year for 30 years. Your account earns \( 10 \% \) interest. a) How much do you need in your account at the beginning? b) How much total money will you pull out of the account? c) How much of that money is interest? \( \$ \)

To determine how much you need in your account at the beginning to withdraw $30,000 each year for 30 years with an annual interest of 10%, we can use the present value annuity formula. a) The present value \( P \) of an annuity can be calculated using the formula: \[ P = \frac{R \times (1 - (1 + r)^{-n})}{r} \] Where: - \( R \) = annual withdrawal amount ($30,000), - \( r \) = annual interest rate (10% or 0.10), - \( n \) = total number of withdrawals (30). Plugging in the values: \[ P = \frac{30000 \times (1 - (1 + 0.10)^{-30})}{0.10} \approx \frac{30000 \times 9.645}{0.10} \approx 289,350 \] So, you would need approximately **$289,350** in your account at the beginning. b) To find out how much total money you will pull out of the account over the 30 years, simply multiply the annual withdrawal by the number of years: \[ Total\ Withdrawn = 30,000 \times 30 = 900,000 \] So, you will pull out a total of **$900,000**. c) To find out how much of that money is interest, subtract the initial amount from the total withdrawn: \[ Interest = Total\ Withdrawn - Initial\ Amount = 900,000 - 289,350 = 610,650 \] Thus, the amount that is interest is **$610,650**.