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Use This Math Trick to Be Smart With Your Money

January 12, 2016 | Elizabeth Knowles

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How fast can you double your money?

Financial literacy is a problem for Americans. According to the National Financial Educators Council (NFEC), more than half of millennials say that debt is their “biggest financial concern” and only 14 percent of baby boomers have a written retirement strategy.

This quick trick won’t solve all of your financial problems, but it is a fast and easy way to think about interest rates.

The rule states that if you take any interest rate, you can approximate the number of years it will take your money to double by dividing 72 by the interest rate. Basically, if you have an interest rate of 1 percent, it will take about 72 years for your money to double, whereas if you have an interest rate of 4 percent, it will only take about 18 years.

Sounds too easy? Here’s where the formula comes from.

Let’s pretend we’re investing a single dollar at interest rate R (in decimal form).

After a year, our total (T) will be T=1*(1+R).

After two years, we have T= 1*(1+R)*(1+R) = 1*(1+R)2.

After N years, we have T=1*(1+R)N.

What we want to know is how many years (N) it will take us for our total to double so we have: 2=1*(1+R)N.

SEE ALSO: The Mystery of the Missing Dollar

We can take the natural logarithm of both sides. If your math skills are a little rusty, we’re using the logarithm to bring N down from the exponent:

ln2=ln(1+R)N

ln2=N*ln(1+R)

0.693=N*ln (1+R)

Luckily for us, ln (1+R) is very close to R. So, we can say:

0.693=N*R

N=0.693/R

But that’s still not the formula we’re looking for. We can multiply the right-hand side by 100 so we can talk about the interest rate as a percent rather than decimal giving us:

N= 69.3/R

Now if I told you that I had a nice and simple trick where you could use the rule of 69.3 and divide 69.3 by any interest rate to find the number of years it would take your money to double, you would probably look at me like I’m crazy. 69.3 is not a nice and easy number.

70 isn’t bad — it has a few factors, but 72 is even better. It is divisible by 2, 3, 4, 6, 8, 9, 12, 18, 24, and 36. So, since we’re approximating anyways, we call it the rule of 72.

Want to triple your money? Use the rule of 114!

Based on information provided by Better Explained.

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