Question

You want to make one single deposit today (year 0), so that when you retire in 39 years from now, you can make annual withdrawals for the subsequent 21 years. Your first withdrawal will be at time 40 and your last withdrawal will be at time 60. You want your first withdrawal (in year 40) to be $57,000 and then increase this payment by 4% every year after the prior one to compensate for inflation. If your interest rate is 8% APR, how much money did you deposit today?

Answer 1

- You will retire in 39 years from now and will make annual withdrawals of $57,000 for 21 years after retirement being first withdrawal start from year 40.

Firstly Calculating the Present Value at year 39 of Annual growing annuity using PV of growing annuity formula:-

Where, C= First Payments = $57,000

r = Periodic Interest rate = 8%

g = growth rate of annuity = 4%

n= no of periods = 21 years

Present Value = $779,916.22

So, Present value at time 39 years is $779,916.22

Now, Calculating the Present Value today from Year 39:-

Where, PV39 = Present value at time 39 years = $779,916.22

r = Periodic Interest rate = 8%

n= no of periods = 39 years

PV0 = $38,772.29

So, the money you should deposit today is $38,772.29

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