## The Rule of 70

What’s the “rule of 70?”

The rule of 70 is an easy method of estimating how quickly a variable will double if you know its annual growth rate. If a variable is growing at a rate of x% per period, you simply take 70 and divide it by x.

The rule of 70 is useful for all sorts of applications. For example, if you’ve saved some money in an investment account that’s growing at 5% per year, you can divide 70 by 5 to get an approximation for how quickly your savings will double. No complicated math required.

But that’s not all! You can calculate how long it will take a country’s GDP to double, how quickly your startup’s users will double given its current growth rate, or when the number of bacteria in a petri dish will double. As you can see, there are many different applications of this rule!

In the video, we’ll walk you through a few scenarios where using the rule 0f 70 lets you easily see the power of compounding without the trouble of actually doing the compounding math. (Bonus: You’ll also learn how to apply the rule of 70 in reverse.)

MRU covers the rule of 70 in its video on "Growth Miracles and Growth Disasters" in the Principles of Macroeconomics course. We also answer your questions on the rule of 70 in our Office Hours video on the topic.

## Teacher Resources

## Transcript

The Rule of 70 is a quick and easy method to tell you how fast something that is growing will double in size over time. It doesn't matter what is growing -- it could be your savings account, the world population, computing power, the number of bacteria in a petri dish, or a country's economy -- the Rule of 70 will allow you to impress your friends and confound your enemies by quickly estimating the doubling time. But what is the Rule of 70?

If a variable is growing at a rate of x% per period, you can calculate how quickly it will double by taking 70 and dividing it by x, the growth rate. For example, suppose you have money in an investment account that has an annual rate of growth of 5% per year. Your money will grow 5% in the first year, and then in the second year, you'll get compound interest. The 5% growth will be on the original amount plus the growth from the first year. Given this compounding growth, how fast will you double your money? Well, if you were to actually calculate this out, the math would look like this. The Rule of 70 is an approximation for this calculation.

In the case of our 5% growth rate, the Rule of 70 says the doubling time is 70 divided by 5, or 14 years. The exact calculation? 13.86 years. So, the Rule of 70 is pretty accurate. The Rule of 70 comes in very handy in all kinds of ways -- for example, when comparing how living standards are changing in various countries. In growth miracles, like Korea, China, and Japan, we've seen annual growth rates of 7 to 10%. At 10% growth, that means living standards are doubling every seven years. China did this for 35 years. So, how much bigger is it 35 years later? If it doubles every 7 years for 35 years, then it doubled 5 times. Doubling five times means you multiply the original size times 2, times 2, times 2, times 2, times 2 -- or, much easier to say, you raise 2 to the 5th power. And that means GDP per capita in China is 32 times bigger than where it started 35 years before. The Rule of 70 lets you see the power of compounding without actually having to do the compounding.

Now, with the Rule of 70, we can quickly compare China's growth rate to most developed countries that typically see only a 2% growth rate, which means only two times bigger in 35 years -- a dramatic difference from being 32 times bigger. The Rule of 70 can also be used in reverse. If you know that house prices doubled between 2000 and 2006, for example, then you know that 70 divided by x equals 6 or that house prices increased at a rate of about 11.6% per year. The Rule of 70 gives us a handy tool to quickly approximate doubling time given that we know the annual growth rate. Check out our practice questions to test your skills on the Rule of 70. Or, if you're curious to learn more about why countries grow at such different speeds, let's start with one of the most extreme examples on the planet: North and South Korea.Click to understand why.

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