Question

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 \(215,000 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 10 equal annual installments (from age 30 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 80 years old.

Requirements

1. How much money must you accumulate by retirement to make your plan work? (Hint:Find the present value of the \)215,000 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

Total Accumulated amount by retirement: $2,105,485

Total Amount withdrawn from the fund: $8,600,000

Step-by-step solution

Computation of CB ratios

At present, the age: 30 years

At retirement age: 40 years

Annual withdrawn (annuity) after retirement: $215,000

Withdrawn Period: 40 years

Fund return rate: 10%

So, the required accumulated amount by retirement would be the present value of the future annuity.

$\begin{array}{rcl}\mathrm{Accumulated}\mathrm{amount}\mathrm{by}\mathrm{retirement}& =& \mathrm{Annuity}\times \left[\frac{1-{\displaystyle \frac{1}{{\left(1+\mathrm{r}\right)}^{\mathrm{n}}}}}{\mathrm{r}}\right]\\ & =& \$215,000\times \left[\frac{1-{\displaystyle \frac{1}{{\left(1+0.1\right)}^{40}}}}{0.1}\right]\\ & =& \$2,105,485\end{array}$

Analysis and comparison

During retirement total amount withdrawn would be,

$\begin{array}{rcl}\mathrm{Total}\mathrm{amount}\mathrm{withdrawn}& =& \mathrm{Annuity}\times \mathrm{Time}\mathrm{period}\\ & =& \$215,000\times 40\\ & =& \$8,600,000\end{array}$

The total amount withdrawn is the sum total of the principal amount and interest. The accumulated amount by retirement computed above is the principal amount that has been invested into the fund. So, the comparison of both the amounts is very obvious. The amount withdrawn after retirement is the future value of the accumulated amount by retirement.