Rule of 72

A quick and easy way to determine the doubling of value for a given sum based on an interest rate is the Rule of 72. This simple formula has three factors. The first is the interest rate; the second is the amount of time in years to double the value and of course the number 72. Simply stated, the Rule of 72 is as follows:

72 divided by the interest rate (as a whole number) equals the number of years to double the value of the investment.

As a straight forward example, assume you want to know how long it will take to double your investment if the interest rate you will receive is 5%. Well, let’s use the formula and find out:

72/5 = 14.4 years

In effect, it will take 14.4 years to double the money at a 5% rate of return on the investment.

The reason the Rule of 72 is so useful, is that it works in reverse too. If you want to know a given interest rate and only have the amount of time in years to double the investment, you can determine the rate of return using this formula.

An example is that you will double your money in 9 years. Immediately, you realize that the interest rate has to be higher than the 5% used above because the doubling effect is much less than 14.4 years. What is the interest rate to achieve this? Well, let’s plug the formula:

72 divided by the doubling time period equals the interest rate of return

Therefore: 72/9 years = 8% rate of return

Effectively, 8% rates of return for an investment will double the investment in 9 years.

Now this seems too easy doesn’t it? This is because there are issues with this formula and as a businessman, you should be aware of the drawbacks to this formula. To fully understand the Rule of 72, you need to understand some history about this term and how it should be properly used in business.

History About the Rule of 72

In Mesopotamia, interest was used due to the nature of the agricultural based society. Fronted proceeds or use of land required some form of interest payment to the lender. Greek and Roman documents identify rates of 10 percent down to 8 and 1/3. Another old reference about interest is about 1400 years old and found in the Quran. Several writings denounce the use of interest when lending money. Based on this information, interest rates commonly impoverished the debtor thus creating many problems for families and society. As time continued, interest becomes a standard of reward for the associated risk involved. It is not until the 1400’s that some form of formal writing of formulas is drafted and still exist today.

The most likely individual to develop the formula is Luca Pacioli, a Friar and an Italian mathematician. He is considered the father of accounting. He was instrumental in the development of bookkeeping and the dual entry accounting concepts used widely today. Sometime around 1494 he wrote:

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.

The problem is that many people today believe that Albert Einstein invented the Rule of 72. However, the rule is considered a ‘Rule of Thumb’ which means it is not accurate. Almost all scientists and mathematicians talk in specifics and Einstein was no different. I’m sure he fully understood the principles of compounding interest which is the underlying equation of this rule. The problem is that the Rule of 72 is only an estimate and its accuracy decreases at an increasing rate once the interest rate involved exceeds 15% or goes below 4%. In general, the formula has a limited range of 4 to 15%. Otherwise, the outcome is increasingly inaccurate as the following illustrates using 7% and 18% as the rates of return:

At 7% rate of return, the rule states that to double your money, it will take 72/7 or (123.5 months) 10.285 years. In reality it will take 123 months or 10.245 years to double your money. The Rule of 72 is .39% inaccurate at 7% which is mid-range for use of the Rule.
At 18% rate of return, the rule states that to double your money, it will take 72/18 or (48 months) 4 years. In reality it will take 50.25 months or 4.188 years. The Rule of 72 is 4.69% inaccurate at 18%.

The most accurate point for the Rule of 72 is at 8% where the rule is .07% inaccurate.

It is because of these highly inaccurate outcomes related to this Rule that I do not believe Einstein invented the Rule or even so much as used the Rule in any form. To my knowledge there is no written documentation nor verbal recording of his use of this Rule.

Proper Use of the Rule of 72

“They’re really not rules, but more like guidelines …” as quoted from one of the movies in the series of Pirates of the Caribbean when referring to the Pirate’s Code. Well, that is about as best as I can compare the Rule of 72 to its accuracy. It is more of guideline and calling it a ‘Rule’ is really a misstatement.

As a business entrepreneur, you should understand that using this ‘Rule’ as a function of your day to day operations is not a good idea. It is simply inaccurate and therefore unreliable. Use a good business calculator to calculate the correct answer to the interest question. Furthermore, this rule assumes compounding at an annual rate. Many loans today are using more frequent compounding and often many institutions are using daily compounding to entice deposits to their banks.

This ‘Rule’ is really only acceptable when sitting around the dinner table and discussing how long to double your money at reasonable interest rates. Furthermore, nobody will hold you to the final calculation or state that you are way off in the final number.

Conclusion – Rule of 72

Overall, I don’t think it wise to use this rule as a tool in your day to day business dealings. The more accurate you as a business entrepreneur are in your communication with others, the greater the likelihood others will look to you as an authority. With authority comes greater respect. This isn’t to say you shouldn’t use the Rule of 72. When you are without a calculator and you are involved in simple table talk, then using the Rule of 72 is justifiable, but qualify your calculation by stating: ‘If you use the Rule of 72, then the approximate amount of interest earned or time to double the investment is X (rate or years)’. This way, nobody can hold you to your word because they too should understand the Rule. Surprisingly, you will discover many don’t understand the rule or have ever heard of the rule; even bankers. Act on Knowledge.

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