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The Rule of 72, 114, and 144
By JLP | 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:
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:
Here’s a look at how accurate this little formula is:
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:
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?
Topics: Financial Math Basics |
May 14th, 2007 at 10:17 pm
Ok rule of 72 I knew but the other two are cool too! If I can just remember 114 ! (144 I can remember…)
May 15th, 2007 at 2:16 am
[...] JLP’s post on the Rules of 72, 114, and 144 got my math juices flowing. Where does the Rule of 72 come from? [...]
May 15th, 2007 at 10:56 pm
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?!!
May 15th, 2007 at 11:03 pm
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.
May 16th, 2007 at 8:08 am
Whew! What a relief!!!
May 16th, 2007 at 4:00 pm
[...] [All Financial Matters: The rule of 72, 114, and 144] [...]
May 19th, 2007 at 4:51 pm
[...] JLP talks about the rule of 72, 114, and 144. MBH tackles the math behind the rule of 72. I like the rule of >, make sure tomorrow’s $ > today’s $. QED. [...]
May 21st, 2007 at 1:11 pm
[...] UPDATE: For an interesting follow-up to this post, see The Rule of 72, 114, and 144 [...]
November 30th, 2007 at 1:18 am
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%
July 4th, 2008 at 1:34 am
quite interesting rules
August 4th, 2008 at 6:43 am
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…