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As a follow-on to this question, if you wanted to have a $2.5 million nest egg in 20 years, what would the nest egg value have to be today (assuming no future contributions)?

Assume:

  • 20 years until first withdrawal
  • 4.0% annual inflation
  • 8.0% annual return
  • $2.5 million future balance

Please note: I'm not in school and this isn't a homework question. I'm just trying to learn what formulas are needed for retirement planning.

closed as off-topic by Aganju, Dheer, Pete B., Bob Baerker, Nathan L Nov 21 '18 at 15:05

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  • 4
    I downvoted and would vote to close but I don't have the rep on this site as this is clearly homework with no effort shown. – Ross Millikan Nov 21 '18 at 3:50
  • 6
    I'm voting to close this question as off-topic because this looks like a homework question with no solution effort shown. – Aganju Nov 21 '18 at 6:30
  • @Aganju This is not a homework question. – Seth Nov 28 '18 at 19:08
  • We could reopen this question, but we'd then have to close it as a duplicate of money.stackexchange.com/questions/26368 – Nathan L Nov 29 '18 at 20:38
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The formula for future value with no contribution is just FV = PV(1+r)^n, so reversing that to find present value, you get PV = FV / (1+r)^n.

So in your case:

     2,500,000 
PV = ---------  = 536,360
     (1.08)^20

Note that inflation is irrelevant in your question since you didn't ask about the equivalent of 2.5 million in today's dollars. But if you wanted that, you'd just subtract the rate of inflation from r and make the same calculation.

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    When you adjust for inflation, the number I compute is 536,360*(1.04)^20 or 1,175,230. – Bob Nov 21 '18 at 2:03
  • Just as I was about to comment that 4% felt high, I looked at inflation for 50 years 1967-2017, and sure enough, 4.1% CAGR. Spoiled by the recent low rates, last 20 years or so. – JoeTaxpayer Nov 21 '18 at 2:14

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