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 $$230,000$ per year for the next $40$ years $($based on family history, you think you will live to age $80).$ 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 $8\%$ per year. You will leave the money in this fund until it is completely depleted when you are $80$ years old.

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

$($Click the icon to view Future Value of Ordinary

Annuity of $$1$ table.$)$

Read the requirements.

Requirement $1.$ How much money must you accumulate by retirement to make your plan work? $($Hint$.$ Find the present value of the $$230,000$ withdrawals.$)($Round your final answer to the nearest whole dollar.$)$

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

Requirements

How much money must you accumulate by retirement to make your plan work? $($Hint$.$ Find the present value of the $$230,000$ 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?

A$.$ You need to have the same amount accumulated as you will withdraw because you will not earn further interest on your investment when you reach retirement.

B$.$ You need to have far more accumulated than what you will withdraw because you will withdraw a large portion of the investment every year$-$the balance remains invested where it continues to earn $8\%$ interest.

C$.$ You need to have far less accumulated than what you will withdraw because you only withdraw a portion of the investment every year$-$the balance remains invested where it continues to earn $8\%$ interest.

D$.$ None of the above

Reference

Future Value of $$1$

$\backslash$table$[[$Periods$,1\%,2\%,3\%,4\%,5\%,6\%,7\%,8\%,9\%,10\%,12\%,14\%,15\%$