The Rules of 69 and 72

In class on Monday, I gave an informed and eloquent description of the "Rule of 69" for determining the doubling time of an investment, whereupon a few of you took it upon yourselves to inform me that the the rule is, in fact, the "Rule of 72."

Well the happy news is that we are both (all) correct. This page explains why. The short explanation is: The Rule of 69 applies to continuously compounded interest rates, and is valid for all such rates. The Rule of 72 applies to annually compounded rates, and is a good approximation for rates close to 10%. How close is close? Well, how good is good...