Consider the plight of poor Joe. He's planning for his retirement and says:

• I'm now making $40K a year. I'd like to retire in thirty years.
• If I were to retire now I could live on just $30K since the mortgage will be paid, the kids will have left.
• I'll assume 3% per year inflation then $30K NOW means 1.03³⁰ x 30K or about $72,800 thirty years from now.
• I've been reading all that stuff about Safe Withdrawal Rates and I'll assume 4% is "Safe".
• That means, to get my $72,800 thirty years from now, my portfolio should be 72,800/0.04 or about $1,800,000.

>1.8 million? You gotta be kidding, right?
Pay attention. Let Joe finish.

• Suppose my salary increases, say 3% per year ... for thirty years, until I retire.
• Suppose a certain percentage of my salary is invested each year.
• Suppose this investment grows at 8% annually.
• What percentage of my salary should be invested, each year, so this investment grows to $1.8 million?

>Monte Carlo, anybody?
Good idea. We can use the spreadsheet described here.

>I thought that spreadsheet was just for withdrawals?
Yes, but we can put in a negative withdrawal and get a simulation for portfolio evolution with annual investments instead of withdrawals.

If we assume a portfolio devoted 75% to the S&P 500 and 25% devoted to 5-year Treasuries, and we use the inflation and return data from 1928 to 2000, we'd get a result which, on the spreadsheet, would look like this:

>You mean there's just a 74.8% probability that Joe'd make it?
That's a Monte Carlo Probability. It's not reality.
>So what's reality?
Remember, we're talking future here. Of course, I could use my crystal ball
>Fawgedabawdit!
Had we done the Monte Carlo simulation with 25% of Joe's portfolio devoted to each of Large and Small Cap Growth and Value, we'd have got a 88.6% Monte Carlo success rate.
>I assume you're talking about annual rebalancing, to maintain the 4 x 25.
Yes. If we leave out the Small Cap Growth and assume an allocation 25%+25%+50% for Large Cap Growth and Large Cap Value and Small Cap Value we'd get a 91.9% success rate.
>What about 23%+37%+ ...?
Yes ... and what about 40 years to retirement and what about a salary of $80K and what about fixed salary increases of 4% and what about a 6% portfolio growth and what about ...?
>You're trying to tell me something, eh?
Yes. Play with the spreadsheet yourself, but remember: it's a simulation, an estimate of an unknown future, a piece of fiction based upon historical precedent, assuming the future is a replica of ...
>Yeah, I've heard that before. But where is this spreadsheet ... again?
For the spreadsheet, go Here.
If you want to play with the calculators, go to Retirement Calculators. where you must understand that we're talking ballpark here. Everything remains constant, investment returns, salary increases ... everything.
>And inflation and ...
Yes. Everything. However, there's another spreadsheet which is more suited to Saving for Retirement (as opposed to WITHDRAWING after retirement). It's ...
>You said I could just enter a negative withdrawal in the WITHDRAWING spreadsheet.
Yes, that's true, but in the spreadsheet we used above, withdrawals decreased when inflation decreased. That makes sense when withdrawing since your expenses would be less so you could withdraw less. However, when we're Saving for Retirement we don't want our investment amounts to decrease when inflation goes down, so we should ...
>So what does this other spreadsheet do, when inflation goes down?
It assumes there's no salary change, hence no decrease in dollars invested.
>But my salary could go UP, more than inflation, right?
Yes, and the Saving for Retirement spreadsheet allows the user to prescribe a salary increase, over and above the inflation rate. A portion of the spreadsheet looks like this, where your salary increases are 1% MORE than inflation (and we're using actual inflation rate sequences chosen randomly from the data for 1928 to 2000... except we've changed negative inflation to zero inflation):

>That 92.1% looks much better, but 25% of salary invested, that's still ...
High? Yes. I doubt if many people save anywhere near that amount.

>So, what's your conclusion after all this mumbo-jumbo?
If you expect to withdraw just 4%, to live on, after retirement ... don't retire!

>Or count on government assistance?
Yeah. Count on it ... maybe.
However, even with other sources of income I suspect that the Average Joe saves too little for retirement, a conclusion also reached by this study (in PDF format).

See also this article in Business Week

The Saving for Retirement spreadsheet looks like this
Just Right-click here and Save Target or Save Link.