Rule of 144

 Four times

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Nifty Tricks with the Rule of 72, 71, 70, 69.3, 114, 144 and My Favorites, 1.5 and 1,080,000

Written by

Rob Berger

Modified date: November 11, 2020

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If you read my article, Can You Solve this Math Problem, than you know I enjoy math. Numbers have always been my friend, and I have a few to share with you today. So let’s get to it.

Rule of 72

Many of you have heard of the Rule of 72, but let’s review just in case. To estimate the time it will take to double your money, divide 72 by the expected growth rate, expressed as a percentage. For example, if you expect to earn 10% per year on a $10,000 investment, it will double to $20,000 in about 7.2 years (72 / 10).

Now here is a neat way to use the Rule of 72 to determine annual growth rate. Let’s assume that in year 1 a company earned $2 per share, and by year 8 it was earning $8 per share. What was the annual EPS growth rate? Using the Rule of 72 makes answering this question easy. First, how many times did the EPS double over the eight year period? It doubled once from $2 to $4 and a second time from $4 to $8. Doubling twice in eight years means that the EPS doubled once every four years. Using the Rule of 72, we know that to double in 4 years the EPS must have grown at an annual compound rate of 18 (72 / 4). So the company’s EPS have grown at an annual rate of 18% over the past 8 years.

By the way, you can do the same thing to determine the growth rate of your salary (if that’s your thing). And you can use the Rule of 72 to determine, at a given inflation rate, how long it will take for your money to buy half of what it can by today (depressing).

The Rules of 71, 70 and 69.3

These rules are for us math geeks. They do the same thing as the Rule of 72, but are considered more accurate depending on the interest rate and compounding period (e.g., continuous, daily, annually). The rule of 71 is the most accurate when dealing with annual compounding. And the rule of 69.3 is more accurate for continuous or daily compounding. The Rule of 70 comes in because who wants to divide an interest rate into a number like 69.3? Ok, some do, but many don’t.

The Rules of 114 and 144

The Rules of 114 and 144 take the Rule of 72 to the next level. Rule of 114 can be used to determine how long it will take an investment to triple, and the Rule of 144 will tell you how long it will take an investment to quadruple. For example, at 10% an investment will triple in about 11 years (114 / 10) and quadruple in about 14.5 years (144 /10).

There is an important implication to the Rules of 72, 114 and 144. Notice that the numbers don’t double? That is, while it takes the interest rate divided into 72 to double, the interest rate divided into 144 doesn’t triple, it quadruples! That’s the power of compounding. And what’s the moral of this story–Save early and save often.