Compounding Growth: The Rule of 70
Recall the Rule of 70. Remember, this rule is an easy way to calculate the time it takes something to double. If real gross domestic product (GDP) for instance grows at x percent per year, you divide x into 70 to find out how many years it will take for real GDP to double.
Thus, if real GDP grows at 3 percent per year, it will double in 23 years and 4 months, double again in another 23 years and 4 months, and be 8 times what it was 70 years from the start. In contrast, if growth falls to just 2 percent, GDP will double in 35 years and redouble in another 35 years. In that case, it will be 4 times as large in 70 years as it is today — not bad, but only half as large as if the annual growth rate had been 3 percent.
The Rule of 70 is a useful mental calculator. What it really shows is the power of compounding growth. When growth compounds, small changes in the growth rate imply big changes in levels even just a few years out. Of course, that power can work both ways. You don’t want to think about what a college degree might cost in 25 years if tuition prices continue to rise at a 3 percent rate or higher. (Well, maybe you do if you’re a professor.)
Because a small change in annual growth rates has such powerful effects, macroeconomists have tried to understand the process of economic growth for a long time. Why does production grow? What will wage rates and interest rates look like along the growth path? What policies best promote growth?