Compound interest, for many it’s the key to successful saving and investing over time.  Sure there are occasional home runs in the investing world, but if you want to ensure success it takes long term investing with annual compounding interest or returns.

So what is the rule of 72?

Here’s the quick answer, the rule of 72 is a simple calculation that determines how long it takes an investment to double.  Here’s how it works:  All you need to do is take the number 72 and divide it by the rate of return or the interest rate you hope to earn. The result is a number that gives you the approximate number of years it will take for your investment to double.

So when does the rule of 72 come handy to use?

The rule of 72 comes in handy when you need a quick and easy way to estimate and compare how long it takes an investment to achieve a return you are seeking.

Here’s an example.  Let’s say I head down to the bank to open a savings account.  This is a terrible idea for me, but illustrates just how much you won’t make in a savings account.  According to bankrate.com the national average is 0.13%, although all of the ads they had below the article were around 2%, so we’ll use that number instead.  So, according the the rule of 72 you take the number 72 and divide it by the rate, 2%.  (72 / 2 = 36).  In this case it would take you 36 years to double your money.

On the other hand if we take a look at what an investment in the stock market may do the results would be very different.  According to Ivestopedia the annual average return of the market based on the S&P was almost 12%, which includes a variety of conditions spanning almost the last 100 years.  Even if we just look at the actual inception of tracking 500 stocks and becoming the S&P 500 Index in 1957, the return was 11.82% through December 2021.  So let’s make it simple and just calculate the return based on 11%.  Using the rule of 72 the time to it would take to double your investment would be 72 / 11 = 6.55 years.  That’s a whole lot better than 36 years, right?

Let’s say for example you had $10,000 to invest and just happened to be willing to invest it for 36 years.  Using the rule of 72 you can quickly calculate at 2% it takes approximately 36 years to double, so you would have $20,000.  Using the same rule but investing in the S&P 500 you may calculate doubling your investment every 6.55 years, so over the same 36 year period it would double 5.5 times (36/6.55=5.5)(rounded).  The total in this example would be $480,000.

What that sounds crazy!  Right? Here’s how it goes:

• $10,000 X 2 = $20,000 (first double)
• $20,000 X 2 = $40,000 (second double)
• $40,000 X 2 = $80,000 (third double)
• $80,000 X 2 = $160,000 (fourth double)
• $160,000 X 2 = $320,000 (fifth double still have a half to go)
• $320,000 X 1.5 = $480,000 (use 1.5 because it’s basically 320k x .5 then adding the 320k back in)

Is this an exact science?  Not quite, but it gives you a pretty quick way to estimate how long it would take your money to double.  Although it give a quick estimate that calculates a 6.55 year of time to double, using that number over a longer period of time to calculate the future value will start to distort the numbers.  It’s great for making a quick comparison though.  In this case, according to a future value calculator on calculator.net the actual total value would be closer to $428,000 after the 36 years.  Still nothing to scoff at.

Where does the rule of 72 come from?

It’s not exact, but it appears to be first recorded in a book by Luca Pacioli.  There are various sites that reference this as the first use.  Luca, a renowned Italian mathematician mentions the rule in his book dating back to 1494.  On wealthsimple.com the following can be found:

The first reference we have of the Rule of 72 comes from Luca Pacioli, a renowned Italian mathematician. He mentions the rule in his 1494 book Summa de arithmetica, geometria, proportioni et proportionalita (“Summary of Arithmetic, Geometry, Proportions, and Proportionality”). Here’s what Pacioli says about it:

In wanting to know of any capital, at a given yearly percentage, in how many years it will double adding the interest to the capital, keep as a rule [the number] 72 in mind, which you will always divide by the interest, and what results, in that many years it will be doubled. Example: When the interest is 6 percent per year, I say that one divides 72 by 6; 12 results, and in 12 years the capital will be doubled.

As you can see, Pacioli presents the rule in a discussion about the timeframes of doubling investments, but he doesn’t derive or explain it. We assume the rule was invented by someone else. Paciolio is just the first to mention it in a published work. Some people credit Albert Einstein for inventing the rule, but there’s no evidence to support this.

It’s been around for a long time.  It works and it’s quick.