# Rule of Thumb of the Day

Via Alex Tabarrok, a pair of researchers asked people how big the economy would be if it grew 5% a year for 25 years:

Only around 10–15% of the participants gave estimations between 50% less and 100% more than the true value...furthermore, the majority of the false estimations were systematically below the true value ...which was underestimated by 88.9–92.1% of the participants.

Of course, this is actually a fairly tough calculation even if you're mathematically inclined and understand the whole compound interest thing.  I guessed vaguely that 5% growth would produce a doubling in about 12 years, so the economy would quadruple in 25 years.  Wrong!  Turns out that doubling takes 14 years, so the answer isn't 300%, it's 238%.  But Alex made this worth my time by teaching me a new rule of thumb I hadn't heard of before:

A good way of approximating is to use the rule of 70.  If x is the growth rate then the doubling time is approximately 70/x.  Thus, with a growth rate of 5% we expect a doubling (100% increase) in 14 years and a quadrupling in 28 years so a bit more than a tripling in 25 years (200% increase) is a good guess.

I love good rules of thumb, and this one makes me slightly more knowledgable than I was five minutes ago.  Thanks, blogosphere!