The Rule of 72

When teaching about interest, it’s always useful to make an aside and familiarize students with the rule of 72.  The rule allows for a rough approximation of doubling time once a rate of growth is known.  One merely takes 72 and divides it by the rate; the result is a rough estimate of doubling time. Thus something that grows at 4% should take about 18 years to double in size. Something that grows at 6% will take 12 years, etc.

It is usually used when talking about compound interest. I’ve even heard it used when discussing inflation. The power of growth working on growth is impressive, when you start to talk about larger numbers. Conversely, small numbers make you wonder why you should bother, as seen in this XKCD cartoon.

However even smaller numbers, left on their own over long periods of time, can result in truly astronomical sums.  Here’s a story from Lapham's Quarterly (HT to Arts & Letters Daily) on that very topic that can be used to wind up class when you have time.

And the government thinks it has troubles with the debt now….