Question

You are planning for 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 instalments (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 70 years old.

Requirements

1. How much money must you accumulate by retirement to make your plan work? (Hint: Find the present value of the \)220,000 withdrawals.)

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?

Short answer

1. Amount of money to get accumulated: $2,476,760.
2. There is a vast difference between the amount invested and the amount withdrawn during retirement because of the time value of money and interest factor.

Step-by-step solution

Definition of Time Value of Money

The concept states that the value of money now in hand is worth more than the value of the same amount of money in a future period is known as the time value of money.

Value to get accumulate

$\begin{array}{rcl}\mathit{A}\mathit{c}\mathit{c}\mathit{u}\mathit{m}\mathit{u}\mathit{l}\mathit{a}\mathit{a}\mathit{t}\mathit{e}\mathit{d}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}& \mathbf{=}& \mathit{W}\mathit{i}\mathit{t}\mathit{h}\mathit{d}\mathit{r}\mathit{a}\mathit{w}\mathit{a}\mathit{l}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{y}\mathit{e}\mathit{a}\mathit{t}\\ & & \mathbf{\times }\mathit{P}\mathit{r}\mathit{e}\mathit{s}\mathit{v}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{}\mathit{a}\mathit{n}\mathit{n}\mathit{u}\mathit{i}\mathit{t}\mathit{y}\mathbf{}\mathit{f}\mathit{a}\mathit{c}\mathit{t}\mathit{o}\mathit{r}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathbf{8}\mathbf{\%}\mathbf{}\mathit{f}\mathit{o}\mathit{r}\mathbf{}\mathbf{30}\mathbf{}\mathit{Y}\mathit{e}\mathit{a}\mathit{r}\mathit{s}\\ & \mathbf{=}& \mathbf{\$}\mathbf{220}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{11}\mathbf{.}\mathbf{258}\\ & \mathbf{=}& \mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{476}\mathbf{,}\mathbf{760}\end{array}$

 Comparison between the amounts

Actual amount invested	<	Withdrawn during retirement
$2,476,760	<	$6,600,000

The amount invested in the retirement plan is less than the withdrawal made during the year because of the time value of the money and the interest factor. The amount invested today will increase by 8% per year, and the accumulation of interest and investment will lead to the difference between the amount invested and the amount withdrawn during retirement.