The Rule of 70

This graph’s smooth curve shows how an investment, economy, population, or any other quantity will grow at a constant rate of interest or growth—that is, at a constant percentage. In this case the percentage is 2.8 percent, compounded annually.

In the graph, in year 0 the value is 1. Soon, though, the value is twice as high, rising to 2. It doubles again to 4, doubles again to 8, and again to 16. An economy or investment growing at 2.8 percent per year will double every 25 years. Thus, it will double 4 times in a century: 2, 4, 8, 16.

There is a very useful tool for quickly calculating the doubling time for a given growth rate: the Rule of 70. If you know the percentage growth rate and want to know how long it will take an initial value to double, simply divide 70 by the rate. In this case, 70 divided by 2.8 = 25. The value doubles every 25 years and therefor increases 16-fold in 100 years.

By the Rule of 70 we can calculate that a growth rate of 7 percent will cause an initial value to double in just 10 years. China’s economy has been growing by more than 7 percent since the early 1990s. If a value—the size of China’s economy, for example—doubles every 10 years, it will go through 10 doublings in a century: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. If China’s economy maintained a 7 percent growth rate for a century it would become more than 1,000 times larger. It is important to recall such facts the next time the Dow or some other economic indicator falls on the news that Chinese growth has “slowed” to 7 percent or less.