Question

If your retirement account shows $800,000 on the day of retirement and you plan to live to be 90 (you are 33 now), how much can you withdraw each month if your annual investment rate of return is 7% with a annual inflation rate of 2.5%.

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Answer 1

This problem is that of a growing annuity. The rate for the annuity calculation needs to be adjusted to take into account the inflation that is to expected in every year. Due to inflation the expenses will increase every year by a constant 2.5%. However we want to factor in that inflation to our calculations so that we get to withdraw a constant amount every month.

The adjusted rate for the growing annuity can be given by the formula:

$r = (1+i)/(1+g) -1$

where

r = adjusted rate of return for a growth annuity

i = expected return

g = growth rate

In this question, the retirement age is assumed to be at 33 years, hence this amount is available at the age of 33 and has to last till the age of 90. Therefore number of years that this corpus has to be used for is 90-33 = 57 years.

Since the withdrawals are monthly, the number of periods and rate to be used in the solution will also be monthly.

The amount in the retirement account will be the Present Value, PV.

The monthly withdrawals can be given by the formula:

$PMT = r * PV/[1-(1+r)^{-n}]$

where

r = adjusted required return for a growing annuity

PV = Present Value

n = Number of periods

B9 X Fc =PMT(B8,B3,B1) A 1 Present Value 2 Number of years 3 Number of months 4. Annual required rate 5 Annual inflation rate 6 Monthly required rate 7 Monthly inflation rate 8 Adjusted return 9 Monthly withdrawal amount B 800000 =90-33 =B2*12 = 7% 0.025 =B4/12 =B5/12 =((1+B6)/(1+B7)) - 1 =PMT(B8,B3,B1)

B9 - X V fc =PMT(B 57 A 1 Present Value $8,00,000.00 2 Number of years 3 Number of months 684 4 Annual required rate 7% 5 Annual inflation rate 2.50% 6 Monthly required rate 0.58% 7 Monthly inflation rate 0.21% 8 Adjusted return 0.37% 9 Monthly withdrawal amount | $ -3,245.98