[rawatson]

This isn't a hard problem to solve exactly though; anyone with a calculator that can compute logarithms can find the exact time. A bit of algebra and the formula for periodically compounded interest will tell you that an investment will double in time t = ln(2)/ln(1+r)

The value of this rule comes in the fact that it can be computed mentally. I certainly can't tell you what ln(2)/ln(1.06) is, but I can easily compute 72/6 = 12.