72 "Rules" - The Rule of 72

The Rule of 72 is a handy, easy-to-use tool within the DividendFarmer’s toolbox.  It’s perfect for quickly ball-parking the time required for your investment to grow to your desired level.  For instance, you may ask yourself, “Self, if I have a $10,000 dividend portfolio with a 4% yield, how long will it take for my money to double?”

If you're familiar with the Rule of 72, you’ll know that at 4%, your money will double in about 18 years.  But what if your portfolio is paying 6%?  Then your money will double in roughly 12 years.  What if your portfolio is paying a meager 2%?  Then 36 years is the general length of time needed to double your money, left to its own devices.

So how does this Rule of 72 work?  How can you quickly determine the length of time needed for your money to double based only upon the dividend yield of your stock?  Investopedia explains the Rule of 72 in mathematical terms.  If you understand logarithmic functions, the explanation hits the spot.

However, if you’re like this Dividend Farmer, you may want a less technical explanation which starts with the principle of compound interest.  If you invest $1 today at 7%, compounded annually over several years, you will have a progression that looks something like the table below.

Start	Year 1 (end)	Year 2 (end)	Year 3 (end)	Year 4 (end)	Year 5 (end)	Year 6 (end)	Year 7 (end)	Year 8 (end)
$1.00	$1.07	$1.14	$1.22	$1.31	$1.40	$1.50	$1.60	$1.71

At the end of year 8, your investment will have grown by $.71 or 71%.  This doesn’t sound like much, but it’s only a dollar and you didn’t add anything to it.  You simply waited and watched it grow much like traditional farmers do with their crops.

Using the principle of compounding and applying the aforementioned logarithmic function, an ingenious little formula was developed, called the Rule of 72, allowing you to closely approximate the length of time needed to double your money for a given interest rate. 

Behold the magic formula:    72 / interest rate (or yield) = years to double.

Using an earlier example of 6% and applying the Rule of 72 results in the following:  72 / 6 = 12 years to double.  It’s that easy.

The best part is that you can work the formula back and forth using basic algebra to find out what interest rate is required for your money to double in a given number of years.  For instance, if I want my money to double in 10 years, what interest rate do I need to earn on my investment?

If 72 / x = 10 years then 72 / 10 equals 7.2.  This conversion actually requires a little cross multiplication, then division to put x in the right place, but it works!  I need to earn 7.2%, compounded annually, for my money to double in 10 years.

It’s not uncommon for me to contemplate the length of time it might take a dividend stock I’m investigating to double in value based upon its dividend yield.  I use the Rule of 72 when I do.  And when I had a longer time horizon, I used the formula to determine how much money I might have after a 40 year work period assuming a specific interest rate compounded annually.  By-the-way, this exercise is great for fresh college grads or industrious high schoolers as well.

For instance, after 40 years of compound interest at 4% starting with $10,000, I quickly estimated I would earn in the neighborhood of $50,000.  My napkin math went something like this.  At 4%, my money doubles in 18 years becoming $20,000.  In another 18 years (36 total) it will double again to $40,000 and I’ll still have 4 years left of the original 40.  Those 4 years represent almost 25% of a third 18 year period-to-double in which case I should see close to 25% of the $40,000 added to it during those 4 years.  Consequently, I expected to see the figure grow to approximately $50,000.  Using Excel and the Future Value (FV) formula, which we’ll talk about in another post, I can work the same problem to discover my actual earnings will be $48,010.21.  Not bad for ballpark, eh?

Some caveats are in order at this point. 

First, the Rule of 72 works well until you begin talking about very large interest rates e.g., north of 50%.  However, investment returns of that scale are infrequent and probably warrant a healthy dose of caution if ever presented to you.  Better yet, run away.   

Second, the Rule of 72 works best when investments are compounded on an annual basis.  For dividend paying stocks that distribute quarterly or monthly, the approximation given by the Rule of 72 may be slightly farther off the mark, but not so far as to be of no value.

Third, the Rule of 72 doesn’t account for additional payments you make to your investment portfolio during the compounding period.  To calculate the size of your nest egg at retirement, including compound interest and infusions of money into your investment basket for example, you’ll need to use the Future Value formula in Excel I mentioned earlier.

Fourth, and very importantly, the Rule of 72 is applicable when discussing compound growth rates – thus the heavy use of the words “compound” or “compounding” in this post.  Some financial advisors may try to bamboozle you with the Rule of 72 and average rates of return which can be VERY different from the compound growth rate used as the foundation for the Rule of 72.  The compound growth rate and average rate of return are different beasts and will be discussed in another post.

There you have it.  The Rule of 72.  It took longer for me to explain than it will for you to use once you get the hang of it, but it’s a simple, invaluable tool in the Dividend Farmer’s kit.  That’s why The Rule of 72 “Rules”.

The thoughts and opinions expressed here are those of the author, who is not a financial professional.  Opinions expressed here should not be considered investment advice.  They are presented for discussion and entertainment purposes only.  For specific investment advice or assistance, please contact a registered investment advisor, licensed broker, or other financial professional.