The rule of 72 is a handy rule for figuring out the doubling time for something that grows exponentially at a given rate. Consider, for instance, the world’s population. There are currently about 6,750,000,000 humans on the planet (up two times the US over the past 5 years). If the growth rate is 2%/year, this means that the time to double the population is 72/2=36 years. It also means that 36 years ago, there were only half as many people. I am not making this up. When I was born 33 years ago, there were “only” 4 billion people, and when my grandfather was born, there were less than 2 billion.

Fun fact #1: This also means that if we look at the total sum of all humans that were ever alive for the past 50000 years, a large fraction of those are actually still alive.

Fun fact #2: If you gathered all humans, they would emit as much energy as about 500 large nuclear power plants. Nice to know if you want to build your own matrix.

Now you could ask yourself, where does this rule actually come from? Why 72? “Myself”, you’d say, “where does this rule actually come from and why 72?”.

The math is simple. Solve exp(rT)=2, where r is the rate (e.g. 0.02) and T is the doubling time. Then T=ln(2)/r or expressed as a percentage 69.3../p, where p=100r. Using 69.3 gives a more accurate estimate, so why do people use 72? Why indeed?

For the same reason that an hour has 60 minutes and a circle has 360 degrees. 72 has many more divisors than 69, so apparently people who do these kinds of calculations still count on their fingers π

The rule of 72 (instead of ln(2)) is thus an approximation that OVERESTIMATES the doubling time. Particularly for higher percentages (because there are more doubling times for the same time).

So now you can sleep nicely knowing that your money is compounding slightly faster than you though it did. Also you got a nice story to impress your valentine with … or maybe not π

Originally posted 2009-02-09 17:14:39.