You are planning for a very early retirement. You would like to retire at age $40$ and have enough money saved to be able to withdraw $$200,000$ per year for the next $30$ years $($based on family history, you think you will live to age $70).$ You plan to save by making $15$ equal annual installments $($from age $25$ to age $40)$ into a fairly risky investment fund that you expect will earn $10\%$ per year. You will leave the money in this fund until it is completely depleted when you are $70$ years old.

Read the requirements.

View the Present Value of $$1$ table.

View the Future Value of $$1$ table.

View the Present Value of Ordinary Annuity of $$1$ table.

View the Future Value of Ordinary Annuity of $$1$ table.

Requirement $1.$ How much money must you accumulate by retirement to make your plan work? $($Hint$.$ Find the present value of the $$200,000$ withdrawals.$)($Round your final answer to the nearest whole dollar.$)$

Money to be accumulated by the time of retirement $=$

Requirements

How much money must you accumulate by retirement to make your plan work? $($Hint: Find the present value of the $$200,000$ withdrawals.$)$

How does this amount compare to the total amount you will withdraw from the investment during retirement? How can these numbers be so different?