The Rule of 72
Tracking your investments the easy way

by Ann Coleman (TMF

Alexandria, VA (March 12, 1999) -- Understanding just how well your investments are doing, both in percentage terms and relative to the market as a whole, is one of the prime tenets of Fooldom.

We will talk about that in a minute, but first, in case you missed it, Caterpillar (NYSE: CAT) warned today that their next quarterly earnings will be as much as 50% below analysts' expectations. Thud. The good news is that the company is still expecting to make their projected yearly earnings numbers. Luckily for the Foolish Four portfolio, J.P. Morgan (NYSE: JPM) is still jumping.

As a Fool, you should know that it's one thing to celebrate a stock that doubles, and quite another to get excited about a stock that doubles after ten years. A stock that doubles over 10 years has grown at an annual rate of 7.2%. Ten years ago 10-year Treasury bonds were paying more than that! More to the point, over the past 10 years, the Standard & Poor's 500 Index has grown at an annualized rate of 19.2%.

Getting excited because a stock doubles, without figuring out how long it took and comparing it to some other investment, is just plain dumb.

I apologize to those of you who have done that. I've done it, too. Then I learned about the rule of 72. The rule of 72 is a short and dirty way to get an approximate compound average growth rate (CAGR) if you know how long it took for a stock to double -- and, incidentally, to figure the number of years it would take for an investment to double if you know the interest rate or CAGR. It's not terribly precise, but it's a good back-of-the-envelope rule that may keep you from celebrating 7% investment returns. And it's a blast for figuring how rich you will be in 20 years.

The rule is simple. If you know the doubling time, divide it into 72 to get the growth rate. If you know the growth (or interest) rate, divide it into 72 to get the number of years it takes for your money to double.

So a stock that doubles after 10 years, returned approximately 7.2% a year. And an investment with a compound growth rate, or interest rate, of 7.2% doubles in 10 years. Neat.

The S&P 500 has grown at a compound rate of 19.2% over the last 10 years -- that means that an investment in the S&P would have doubled every 3.75 years during that period, and an investment in the Foolish Four, with its compound return of 22.6% over the past 10 years, would have doubled every 3.18 years.

This idea of doubling is a very powerful one. Looking at the S&P compared to the Foolish Four in the paragraph above, one might be tempted to conclude that they weren't that different. But consider how it works with a $10,000 investment. In 10 years, the S&P account would have doubled 2.67 (10/3.75) times while the Foolish four would have doubled 3.14 (10/3.18) times. The difference is staggering.

Starting value  $10,000
First Double $20,000
Second Double $40,000
Third Double $80,000
Fourth Double $160,000
Fifth Double $320,000

The S&P account will have doubled twice plus increased another 67%, which would put it somewhere around $67,000, while the Foolish 4 will have doubled 3 times plus 14%, which puts it over $91,000. And the difference keeps growing. After 15 years, the S&P account would have doubled 4 times (provided that it continued to grow at the same average rate), and the Foolish Four would have doubled 4.75 times.

You guessed it, the Foolish Four would then be 75% higher than the S&P. With our $10,000 starting investment, that would put the S&P at $160,000 and the Foolish Four at $160,000 * 1.75 = $280,000.

Let's look at it another way. How many times does $10,000 have to double to hit the one million dollar mark? Well, at the fifth double, you are almost one-third of the way there, right? Doubling again brings you to $640,000. I'll let you figure the rest out.

How long does it take, from any starting amount, if your money doubles every 3.2 years?

You know that saying, "You have to have money to make money"? The Rule of 72 make it very clear that the more you have, the more you can make. It should also make it very clear that you need to get started -- NOW!

Next week: More precise ways to track your investments.

Fool on and prosper!

Call Your Boss a Fool.

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Today's Stock Lists | 1998 Dow Returns

03/12/99 Close
Stock  Change   Last
CAT  -6  3/16  44.69
JPM  +2 13/16  122.00
MMM  +   1/4   80.38
IP   +   9/16  41.88

                   Day   Month    Year   History
        FOOL-4   -2.46%   3.89%   4.95%   6.51%
        DJIA     -0.21%   6.12%   7.72%   7.29%
        S&P 500  -0.24%   4.54%   5.64%   5.89%
        NASDAQ   -1.27%   4.09%   8.61%  10.10%

    Rec'd   #  Security     In At       Now    Change

 12/24/98    9 JP Morgan    105.51    122.00    15.63%
 12/24/98   14 3M            73.57     80.38     9.25%
 12/24/98   24 Caterpillar   43.08     44.69     3.73%
 12/24/98   22 Int'l Paper   43.55     41.88    -3.85%

    Rec'd   #  Security     In At     Value    Change

 12/24/98    9 JP Morgan    949.62   1098.00   $148.38
 12/24/98   14 3M          1030.00   1125.25    $95.25
 12/24/98   24 Caterpillar 1034.00   1072.50    $38.50
 12/24/98   22 Int'l Paper  958.12    921.25   -$36.87

              Dividends Received      $15.04
                             Cash     $28.26
                            TOTAL   $4260.30