Question

You estimate you need to supplement your social security payments with monthly withdrawals of $1,210.00 per month from a private investment account during the first 21 years of your retirement. Assuming you can earn annual returns of 5.5% in your investment account during your retirement years, how much money do you need to have accumulated in your investment account by the day you retire in order to fund the aforementioned monthly withdrawals?

Answer 1

In the question, we have been given the monthly withdrawal amount and we have to find the total amount to be in the account at the beginning of retirement.

The following formula can be used:

$P_{o}=\frac{d* [1-(1+\frac{r}{k})^{-k*n}]}{\frac{r}{k}}$

Where,

P_o = Accumulated investment by the day of retirement

d= regular withdrawal amount

r = rate of interest

k= No. of months

n= No. of years

$P_{o}=\frac{1,210* [1-(1+\frac{0.055}{12})^{-12*21}]}{\frac{0.055}{12}}$

$P_{o}=\frac{1,210* [1-(1.0046)^{-252}]}{0.0046}$

$P_{o}=\frac{1,210 *[1-0.3146]}{0.0046}$

P = 1,210 * 0.6854 0.0046

$P_{o}=\frac{829.334}{0.0046}$

You will need to have accumulated $180,290 in your investment account by the day you retire in order to withdraw $1,210 per month for the first 21 years of your retirement.