# Fun With Math: The Rule of 72

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Math…pretty awesome stuff and the only thing I actually use from school days.  Why is math so cool.  Well, understanding math can give you a good understanding of money.  The only difference between math and money is adding a symbol in front of a number.  Take for example:

5 x 2=10

If we add the “\$” symbol in front of these number, we’re talking suddenly talking money:

\$5 x 2=\$10

Even the first shirts I made for advertising my site promote the connection of math & money…

Today, we’re looking at a principal called the rule of 72 (not to be confuse with a common topic on my site, Reg72(t)).  The rule of 72 broken down to it’s basic understanding is really about time value of money.  Something magical about the number 72 can be used to simply estimate when money (or a number) would double over time, at a given rate of return.

For example. Say we have \$10,000 that earns 7.2% return for 10 years (see the 72…7.2×10).  That \$10,000 should approximately double in 10 years.

Or, say we have \$10,000 earning 10%.  The principal should double in approximately 7.2 years (10×7.2).

Or, \$10,000 earning 9%, should double in approximately 8 years (9×8).

Noticing the pattern.  There are 2 numbers multiplied together to come up with the number 72.  One number is a return, the other number is time or years.

Now the rule of 72 is simply an estimate.  But you could use it as a bar trick at your next cocktail party to win a free drink when you hear someone talking stock.  “I heard you say you made 8% on XYZ investment.  Bet you a drink I can get real close to when your money would double if it continued to earn 8%?”  Sounds like a pretty lame cocktail party, I know.

What you should notice, the rule of 72 is a simple way of using the a little more complicated time value of money formula:

Future Value= Present Value (1+r)^t

or

FV=PV(1+r)^t

where r is the rate of return, and t is time or number of years

That time value formula may look a little more intimidating to some, and you might have to use a calculator.  But lets compare our rule of 72 examples to the figures we get from using the more exact time value of money (TVM) formula and see how they compare.

Rule of 72:

\$10,000 at 7.2% for 10 years…you have \$20,000

\$10,000 at 10% for 7.2 years…you have \$20,000

\$10,000 at 9% for 8 years…you have \$20,000

Using the Time Value of Money (FV=PV(1+r)^t):

\$10,000 at 7.2% for 10 years…you have \$20,042.31

\$10,000 at 10% for 7.2 years…you have \$19,876.91

\$10,000 at 9% for 8 years…you have \$19,925.62

Financial Calculator inputs would be:

PV= 10,000

I= the respective interest rate or rate of return

N or t= the respective  number of years

Calculate FV

So in comparing the above estimates from the Rule of 72 versus the Time Value of Money figures, we get a really good approximation without even having to use a calculator.  Mind blown yet?  No.

Lets use a practical application of this using my portfolios value.  October 2017, I hit \$1,000,000 for my net worth.  I set a goal to get to \$2million in 7-8 years.  If I want to know the return I need to hit per year in the next 7 years to get to my goal, that means I need to get a 10.2% rate of return per year to roughly get to that \$2million milestone.  Figured out without even having to touch a calculator, and something that I believe is highly achievable.

Now isn’t math cool.  Give it a show for yourself.

Care to read more about money math.  Check out my formula for spending less than you make and investing the difference.

Or, learn the difference between arithmetic and geometric mean and how to calculate geometric mean.

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