Magic rule of 70

During one lecture, my current boss Tomas Sedlacek has asked me to do a quick calculation:"How fast would it take to reduce the Czech budget deficit from current 33% of GDP to almost zero?" 

It's not a very simple task (when you don't have a calculator and you have around one minute for the answer) but it is not difficult either. 

There is the Magic Rule of 70, which I have discovered when reading one of the most sold economics book: Economics by N.Gregory Mankiw (here is his blog I tr

y to follow).

The rule basically says that if you grow by x% a year it would take you 70/x years to double your GDP (assuming zero inflation).

Therefore, it would take you ten years (70/7 as x=7) to double your GDP when growing 7%

 a year (real GDP growth).

That means that you would get from 1/3 of debt/GDP ratio to 1/6 debt/GDP ratio.

It would take you another 10 years to get to 1/12 debt/GDP ratio and another 10 years to get to reasonable 1/24,  i.e. 4.17%  debt/GDP ratio.

The conclusion is striking. It would take 30 years of 7% real growth (impossible) to reduce the debt/GDP ratio to 4% (of course assuming that the debt would remain nominally constant).

The original Rule of 70:

I really like Mankiw's examples, Maynard is the winner, and Milton is the loser. I believe that even Mankiw's

 cat is called Maynard (or Keynes?)