Rule of 72

The Rule of 72 is a way of quickly computing how long money will take to double given any compound interest rate. You take 72 and divide it by the interest rate and the number you get is how long it takes to double.

You probably have seen this about stock market returns someone probably wrote something like: "The stock Market Returns are 9% so by the Rule of 72 it will take 8 yrs to double."

What they are saying if we were to write it out all mathy would be given any amount of money X with a certain amount of interest 9% will take how many years to be 2 times as big?
(X * 1+ .09)^years = 2X

Year 1	1.09
Year 2	1.1881
Year 3	1.2950
Year 4	1.4116
Year 5	1.5386
Year 6	1.6770
Year 7	1.8280
Year 8	1.9925

You might have spotted a big flaw in this if I get a 72% interest rate it will double in 1 year! How did those math geniuses sneak 28% off of 100%?!?

The Rule of 72 like most easy to understand rules is a rule of thumb, it works better with most of the common returns but around 20% it starts losing accuracy and you will need to stick to the real numbers.  Also please note if your planning on achieving 20% returns consistently think again.

The way to use the rule of 72 is for forecasting what your financial situation will be in the future, assuming that you've got some assets that are earning for you.

If your 40 and you have 300,000 dollars saved up and you've placed it in stocks and you get a 9% return than by the time your 48 you've hit 600,000 dollars! (Of course no one gets exactly 9% returns each year the market is choppier than that)

Compound interest of course is most fun when you think about long times. Lets think about the case of an inheritance. If your kid makes 5,000 dollars in a year at age 20 you can get them started on a ROTH IRA. Assuming a 7% compounding interest in a low cost index fund of the S&P 500 by the time the kid starts thinking about retiring at the age of 50 how much money would they have?

Using the rule of 72 we have 72/7 =  10.2857 so lets say 10 years.

20	5,000
30	10,000
40	20,000
50	40,000

That 5,000 dollars grew in a tax advantaged account where they will not be paying an inheritance tax latter down the road, now don't you wish your parents had been reading this when you were 20?



*When researching google returned this cool calculator  http://www.moneychimp.com/features/rule72.htm