Rule of 72

So, a million years ago, I was the first programmer hired in the NYC offices of Montgomery Securities (long since acquired.) to build trading systems or some such.

I was sitting up with the analysts in the cherrywood cube farms late one evening when one day I heard, "Biff, the rule of 72 doesn't really work?" "what do you mean, Chet?" "well, if you get 72 percent return, you don't double your money in one year!"

Then they poked at it with an excel model for like 30 minutes. I eventually had to tell them that you can't precisely model compound interest (an exponential equation) with a linear model. "whoa... Why are you in IT?!?"

Ah, those were the days.

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.

I will see your rule of 72 and raise you the time value of money. http://en.wikipedia.org/wiki/Time_value_of_money

Our engineering economics professor taught this formula - 72/x (where x = interest rate) gives you the time (years) it takes to double your investment. Remember it even after 10 yrs.

If the question you want to answer is, "About how many years will it take for my investment to double?" then the Rule of 72 is exactly as accurate as you would ever need it to be. For practical purposes, the margin of error doesn't go above six months. So if your investment doubles in five years or five years and two days, who cares? Your question was how many years will it take. Can't believe how anal some people are being in the comments here.

I learnt this in programming pearl. There are a lot such tutorials for beginners so to pretend to be pragmatic experienced one, and even with, it is just a first step to be really. Now you know the rule of 72, but it is pure your skill when you can remeber this rule.

I really like Felix's Corollary and the Millionaire's Estimation!

http://en.wikipedia.org/wiki/Rule_of_72#Felix.27s_Corollary_...

It only works when you need to calculate some round numbers or to quickly see if the calculations are logical. When it comes to a real life Rule of 72 is too approximate.