# The Rule of 72

When comparing the rate of return on investments, it is helpful to have a consistent standard.  By far the most common standard is to simply compare the annualized rate of return.  If investment A return 3% and investment B returns 5%, the risk of the two choices being equal, the obvious choice is investment B.

That is good as far as it goes, but what does it really mean in terms of long-term growth?  In other words, how meaningful is that 2% difference?

The Rule of 72 allows you to measure investment returns in term of time instead of percentage points.  If you use doubling time (how long will it take for money to double) as a standard of measure, you can see how long your investments will take to bear fruit.

## The Rule of 72 in action

To determine how long it will take for an investment to double at a given rate of return, simply divide 72 into that rate.

You were hoping for something a little more involved?

Sorry to disappoint, but it really is that easy.

To return to our previous theoretical investments, we have already decided that, risk being equal, we would like to invest in the option that pays a 5% return.  We know that the return is 2% better, but now we can see how much better it is in terms of time.  Starting with the 3% investment, 72÷3=24 years to double.  The other option, a 5% return, looks like this: 72÷5=14.4 years to double.

So in terms of the amount of time it take for your investment money to double, there is almost a 10 year difference between a 3% return and a 5% return!

Here, for your amusement, is a table:

Rate of ReturnDoubling time
172 years
236 years
324 years
418 years
514.4 years
612 years
710.3 years
89 years
98 years
107.2 years
116.5 years
126 years

## Assumptions

It should be noted that there are some assumptions to the Rule of 72:

• all returns are reinvested (You don’t get your money until it has finished doubling!  Early withdrawals really mess up the math.)
• the returns are reinvested annually (If your dividends are paid quarterly or monthly, you can reduce your doubling time!)
• interest rates and purchase price of new shares remain constant (Obviously, this is never the case in practice.)
• no taxes or fees are taken into account (Taxes can be deferred or eliminated in an RRSP or TFSA respectively, but you will probably still have to pay some fees.)

It should also be noted that the Rule of 72 doesn’t hold up if you push it too far.  If you assume a 72% rate of return, the Rule of 72 predicts that you will be able to double your money in one year.  Common sense tells you that for that to work, you would need a rate of return of 100%.  The “Guideline of 72” doesn’t roll off the tongue as well as the “Rule of 72”, so the name probably won’t change.  Then again, if you’re getting an annual rate of return of 72%, what are you doing reading this post in the first place?

## Bonus Material

As an extra-special bonus for having read all the way to the bottom of this post, I’m willing to share a few more little gems with you, for no extra charge:

• to calculate the rate of return you need to double your money in a given amount of time, divide 72 by the number of years you want your money to double in.  Example: If you want your money to double in 6 years, then 72÷6=12.  In other words, to double your money in 6 years, you need a rate of return of 12%.  (Helpful hint: Read the above table from right to left for some more examples of these mathematical gymnastics in action.)
• To calculate the time it takes to triple money at a given rate of return, you can use the Rule of 114.  To see how long it takes to quadruple your money, you can use the Rule of 144.  Both of these rules work in exactly the same way as the Rule of 72.

Now you can figure out how long it will take you to become filthy rich!