The Rule of 70

The Rule of 70 provides a quick and dirty method of calculating how long it will take an asset, economy, etc. growing at a constant growth rate to double in size.

• If my savings grow at a 2% rate each year, it will take approximately 35 years for my savings to double.
• If a country's economy grows at 5% each year, it will take 14 years to double in size (in nominal terms).
• If a town's population is growing at 3.5% per year, it will take 20 years for the population to double
• If a tree grows 15% per year in height, it will take the tree about 5 years to double in height. 

People in finance use this rule all the time. For example, John Bogle of Vanguard in a recent interview with the WSJ:

Over the next decade, Mr. Bogle said stocks are likely to generate an average annual return, including dividends, of around 7%. "Your money will double in 10 years," he said.

70/7 = 10 years. Nice! If he is right, it's time to put my money in the stock market. But where does this rule of thumb come from? In many undergraduate finance classes, the rule is taken as given. Here is how it actually works! (click to enlarge)

This handy rule of thumb gives us a reasonable approximation of the length of time it would take something to double in size with a constant growth rate.

I put together an illustration of the rule of 70 concept in Excel. You can play around with the growth rate and see how the rule of 70 approximation compares to the actual time to double.