The Rule of 72, 114, and 144

May 14, 2007

Most people are familiar with the Rule of 72, the simple formula that can be used to estimate how long it takes to double your money based a certain expected interest rate. For example, you expect to get an 8% rate of return on your money. At that rate, how long will it take to double your money?

To calculate this, simply divide 72 by 8 to get 9 years.

How accurate is this formula? As the graphic shows below, it’s fairly accurate for estimating:

Rule of 72

This formula is fine for estimating how long it takes to double your money. But what if you want to triple your money?

Enter the Rule of 114

To estimate how long it takes to triple your money, divide 114 by your expected interest rate (or rate of return). Using the 8% return figure from the first example, the formula would look like this:

114 ÷ 8 = 14.25 years

Here’s a look at how accurate this little formula is:

Rule of 114

Not too bad. The higher the expected rate of return, the less accurate the formula. However, this is also true of the Rule of 72.

Now for the Rule of 144

To estimate how long it will take to quadruple your money, you can use the number 144. Simply follow the steps in the above example but substitue 144 for 114. Again, it is a good estimate:

Rule of 144

No, they aren’t perfect but neither is the Rule of 72. However, these formulas will give you a good estimate of how long it takes double, triple or quadruple your money.

Isn’t math fun?

FOLLOW UP: Where does the Rule of 72 come from?

14 responses to The Rule of 72, 114, and 144

  1. Ok rule of 72 I knew but the other two are cool too! If I can just remember 114 ! (144 I can remember…)

  2. Maybe it’s my aging mind, but in my CFP classes, I could have sworn I was taught 115 for tripling. Anyone else out there misled?!!

  3. Stacey,

    115 could be correct. I actually got 114.4 when I figured it out in Excel but rounded it down to 114. I don’t think the 1 point will make that much difference in something that is only supposed to be an estimate in the first place.

  4. Whew! What a relief!!! 😉

  5. In addition to rule of 72, I find calculating ROI useful. Just enter (fv /pv)^(1/years) or 2^.25 (use google search box) will give you interest rate needed to double in 4 years. Ans 19%

  6. quite interesting rules

  7. Addition to post #9 by Joe Reynolds:

    Actually, you’d have to subtract 1 from your formula to get the compound annual growth rate (or CAGR) of your initial capital to have it double in 4 years:

    CAGR = (fv/pv)^(1/number of years)-1 or in the example: 2^0.25-1

    If you don’t do that, you end up with something like 100+ % which could be irritating to some guys…

  8. Exponentially Yours October 21, 2008 at 10:16 am

    With the world full of math idiots, it is reassuring to find a site like this-which endeavors to shine on those lingering in the twilight of enlightenment. It is a sad era. Most do not care about the change they get at the convenience store. Probably just as well since most of them can not predict how much change they should get in the first place. It is fine that there are calculators everywhere (on your phone, in your watch, etc) but you have to be able to use them.

  9. in my math class our teacher is teaching us how to make money and as a homework assignment we had to figure out what the rule of 72 was thanks for all your help.

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