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 $$220,000$ 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 $20$ equal annual installments $($from age $20$ to age $40)$ into a fairly risky investment fund that you expect will earn $12\%$ per year. You will leave the money in this fund until it is completely depleted when you are $70$ years old.

$($Click the icon to view Present Value of $$1$ table.$)$

$($Click the icon to view Future Value of $$1$ table.$)$

$($ Click the icon to view Present Value of Ordinary Annuity of $$1$ table.$)$

$($Click the icon to view 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 $$220,000$ withdrawals.$)$

$($Round your final answer to the nearest whole dollar.$)$

To make the plan work, you must accumulate this amount by retirement

Requirement $2.$ How does this amount compare to the total amount you will withdraw from the investment during retirement? How can these numbers be so different?

Over the course of your retirement you will be withdrawing

However, by age $40$ you only need to have invested