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?