Question

You will retire in 30 years. At the beginning of each month until you retire, you will invest X earning interest at 9% convertible monthly. Starting at year 30, you will withdraw $4,000 at the beginning of each month for the next 15 years. Also, starting at year 30, your fund will only earn interest at 6% convertible monthly. Find X such that your account will be empty after the last withdrawal.

Answer 1

Until you retire in 30 years you will invest "X" at the beginning of each month.

Starting at retirement, you will withdraw $4,000 at the beginning of each month for the next 15 years.

First, Calculating the Present value at retirement of withdrawal using Present value of annuity Due formula:-

Where, C= Periodic Withdrawal = $4000

r = Periodic Interest rate = 6%/12 = 0.5%

n= no of periods = 15 years*12 = 180

Present Value = $476,384.13

Now, this Present value will be used to calculate X by taking it as Future value at retirement of monthly deposits of X.

Calculating X using Future value of annuity Due formula:-

Where, C= Periodic Deposits = X

r = Periodic Interest rate = 9%/12 = 0.75%

n= no of periods = 30 years*12 = 360

X = $258.28

So, Value of X such that your account will be empty after the last withdrawal is $258.28

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