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<<WARNING!!! Long post and nasty algebra to follow!>>

I have only joined The Motley Fool in the past few months, but I already feel Foolish. Primarily, I've learned that I need to start saving NOW for when I retire (I'm only 28). While I've been reading the amusing, enlightening, and enriching stories on TMF, a question has come to my mind: "How much do I need to retire?"

You see, I don't expect that I'll need money after I die, so I don't mind ending up with zero. If I live too long, however, I'll end up broke. Broke and old does not sound very fun. Also, I'm married, and my wife will probably live longer than me. Then there's that whole "leaving stuff to your kids" thing.

Wouldn't it be nice to balance my investment returns against my distributions so I'll never run out of money? That way, I know I'll never be broke. Then again, I kind of want to retire as early as possible to enjoy it as much as possible, so I want to know what a reasonable target balance might be.

Ideally, the amount I take out each year to pay my expenses should match the return I make on my investments. However, each year I'll have to take out more than the year before to cover inflation. To handle that, my returns have to exceed the amount I'll take out. Basically, I want my principle at the end of the year to equal the principle at the beginning of the year, times the rate of inflation (i.e. if inflation is 5%, P(end) = P(begin)*1.05).

If I take my yearly distribution out of my principle at the beginning of the year, and leave the result to grow at some rate (in percent), then the amount of earnings I'll have at the end of the year can be expressed thus:

Earnings = Rate * (Principle(begin) - Distribution) or
E = R * (P(begin) - D)

Now the amount of principle at the end of the year is the amount of principle at the beginning of the year, less the distribution, plus the earnings:

P(end) = P(begin) - D + E
...substitute in for E...
P(end) = (P(begin) - D) + R * (P(begin) - D) or
P(end) = (1 + R) * (P(begin) - D)

Now from our discussion of Inflation we know that P(end) = P(begin) * (1 + I). We substitiute into the above equation:

P(begin) * (1 + I) = (1 + R) * (P(begin) - D)

...from this point we'll just talk about the Principle at the beginning of the year...

P - D = P * (1 + I) / (1 + R)
P - P * (1 + I) / (1 + R) = D
P * [1 - (1 + I) / (1 + R)] = D
P * [(1 + R) - (1 + I)] / (1 + R) = D
P * [R - I] / (1 + R) = D
P = D * (1 + R) / (R - I)

If I wanted to retire this year, and I have \$60,000 in household expenses, I expect inflation to average 5%, and I expect to earn 10% on average (near the historical average return for stocks), I can retire if I have \$1,320,000 (\$60,000 * (1 + .10) / (.10 - .05)). On the other hand, if I expect to earn 22.9% on average (Fool 4 CAGR from 1971-1996), I only need to have \$411,955 (\$60,000 * (1 + .229) / (.229 - .05)).

If you don't like those nasty fractions, use this formula: P = D * (100 + R) / (R - I), and you don't have to divide your percentages by 100 (\$411,955 = \$60,000 * (100 + 22.9) / (22.9 - 5)).

Alternatively, if I have \$800,000 (5% interest, and 10% returns), my next-to-last formula tells me I can withdraw \$36,363 each year (\$800,000 * (.10 - .05) / (1 + .10) = \$36,363 or \$800,000 * (10 - 5) / (100 + 10) = \$36,363, whichever).

Really, I should have been able to figure this out months ago, but my algebra is rusty.

PLEASE NOTE!!! One problem with this mechanism is that "average returns" in the stock market never occur; some years are better than average, some years are worse. See http://www.fool.com/DDow/1998/DDow980401.htm, for a discussion of the problems to which this fallacy can lead.

Robert uses the "Rule of Twenty" to avoid this problem, but his example uses the S&P 500 (12% CAGR since 1961) and 4% interest. The formula above would have predicted needing a little below \$600,000 for retirement. Obviously, you'll want to give yourself a "cushion" over and above this minimum to handle bad timing.
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There were a few posts that actually took the FF returns on a per year basis and tested a few different percentages. It seems that a 5% (Rule of Twenty) draw, adjusted every year for inflation, allowed the stash to last forever, even through market downturns.

Another variation is to keep 3-5 years worth of expenses in money-market/bond funds. In the years following a market downturn, you spend the cash. In the years following an upturn, you replenish the cash with your gains.

Zev
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<<<It seems that a 5% (Rule of Twenty) draw, adjusted every year for inflation, allowed the stash to last forever, even through market downturns.>>
I suggest that you take a very serious look at the following Site in order to study this question in much greater detail. The devil is in the detailed assumptions. http://www.geocities.com/WallStreet/8257/safewith.html
Best of study and calculating. Dick
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Greetings, Suvarov454, and welcome. You wrote (in part):

<<I have only joined The Motley Fool in the past few months, but I already feel Foolish. Primarily, I've learned that I need to start saving NOW for when I retire (I'm only 28). While I've been reading the amusing, enlightening, and enriching stories on TMF, a question has come to my mind: "How much do I need to retire?"

You see, I don't expect that I'll need money after I die, so I don't mind ending up with zero. If I live too long, however, I'll end up broke. Broke and old does not sound very fun. Also, I'm married, and my wife will probably live longer than me. Then there's that whole "leaving stuff to your kids" thing.

Wouldn't it be nice to balance my investment returns against my distributions so I'll never run out of money? That way, I know I'll never be broke. Then again, I kind of want to retire as early as possible to enjoy it as much as possible, so I want to know what a reasonable target balance might be.>>

Aye, and therein lies the rub, don't it? Just how does one take the distributions to satisfy all these needs? Others have mentioned their thoughts and referred you to some excellent links that may be of use. I've done some analyses myself, which you can read about in the 23 or so posts on this board that start at http://boards.fool.com/registered/Message.asp?id=1040013000079000&sort=postdate . I'll be doing some more "what ifs" later this year after I retire. I wish I could give you a magic answer, but I truly believe one doesn't exist. Reality doesn't seem to correlate well with theories that use "averages." I also think that generalized approaches like Robert's Rule of Twenty provide a very rough guide, but they certainly don't provide a guaranteed solution. Life just ain't that simple, and much depends on the "when" of retirement, a person's ability to sleep at night, and one's desire to maintain purchasing power for income and/or principal.

As you struggle with this issue, keep in mind that much must, of necessity, be assumed for any long range forecast. Change one or more of the assumptions, and you radically change the results. I'll be playing with a bunch of scenarios starting in March. If I don't get distracted too much by the good life (or discouraged by the results of those analyses), I may even publish the outcomes. Personally, I think I, too, will arrive at pretty much the same conclusions: Taking 4% to 6% of the portfolio will allow for an inflation-adjusted income; however, it might not allow for the preservation of inflation-adjusted principal. We'll see.

Regardsâ€¦.Pixy

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Check out the Retire Early Study on Safe Withdrawal Rates. They used 128 years of stock and fixed income data to calculate safe withdrawals for pay out periods from 10 to 50 years. It includes a large Excel spreadsheet you can download to run your own scenarios. The URL is: