Question

You are planning for your retirement in 32 years. At that time you want to have enough saved to be able to afford to spend $250,000 per year (starting at time 33) for 22 years (if you live longer than 22 years your kids will have to support you).

How much will you need to have saved by time 32 if the expected interest rate from time 32 to 54 is 14 percent per year?

Answer 1

Periodic withdrawal each yaer for 22 years during retirement = $250,000

calculating the Present Value of these cash flows at the age of 32:-

$Present Value= C*\frac{[1-(1+r)^{-n}]}{r}$

Where, C= Periodic Withdrawal = $250,000

r = Periodic Interest rate = 14%

n= no of periods = 22

$Present Value= 250,000*\frac{[1-(1+0.14)^{-22}]}{0.14}$

$Present Value= 250,000*\frac{[1-0.05598778299]}{0.14}$

Present Value = $1685,736.10

So, you need to save $1685,736.10 by the time of age 32.

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