Rule of 72 - calculate duplication in an instance

I get 3 % of interest a year so how long will my investment take to double?
Well, obviously 24 years! 72/3 = 24

Okay but I have only 12 years to double it, then which interest rate do I need?
You need 6 % of course! 72/12 = 6

By dividing 72 by the years of investing, you will get a pretty good estimate of the annual rate of return it will take for the initial investment to double. This also works vice versa if you have the annual rate of return and want to figure out the duration.

So let´s do the math right and check:

First case - duration:
lg(2) / lg(1.03) = 23.45 years
accuracy 97.7 %

Second case - rate:
100 * ((2)^1/12 - 1) = 5.95
accuracy 99.2 %

We got pretty close, right!? So, now whenever you hear an annual rate, you can figure out pretty fast how long it will take to double...