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Sunday, 17 March 2013

Why the Rule of 72 is important to know

Those who know me personally know that I enjoy numbers and maths in particular. In my previous blog post i briefly touched on the mental math shortcut Rule of 72.

The Rule of 72 is a great mental math shortcut to estimate the effect of any growth rate, from quick financial calculations to population estimates. Here’s the formula:

Years to double = 72 / Interest Rate
This formula is useful for financial estimates and understanding the nature of compound interest. 
  • At 6% interest, your money takes 72/6 or 12 years to double.
  • To double your money in 10 years, get an interest rate of 72/10 or 7.2%.
  • If your country’s GDP grows at 3% a year, the economy doubles in 72/3 or 24 years.
  • If your growth slips to 2%, it will double in 36 years. If growth increases to 4%, the economy doubles in 18 years. Given the speed at which technology develops, shaving years off your growth time could be very important.

You can also use the rule of 72 for expenses like inflation or interest:
  • If inflation rates go from 2% to 3%, your money will lose half its value in 36 or 24 years. (As you can see 1% makes a BIG difference!)
  • If college/university tuition increases at 5% per year (which is almost faster than inflation), tuition costs will double in 72/5 or about 14.4 years. If you pay 15% interest on your credit cards, the amount you owe will double in only 72/15 or 4.8 years!
The rule of 72 shows why a “small” 1% difference in inflation or GDP expansion has a huge effect in forecasting models.
By the way, the Rule of 72 applies to anything that grows, including population. Can you see why a population growth rate of 3% vs 2% could be a huge problem for planning? Instead of needing to double your capacity in 36 years, you only have 24. Twelve years were shaved off your schedule with one percentage point.

1 comment:

  1. Actually, trying to apply this rule to anything other than counting money is misleading. Population size (or anything dependent on fixed resources such as space , food and time) is subject to something called carrying capacity, and usually grows exponentially (at first) according to a typical S-curve. Population models are therefore best done with a logistic function, or more accurately variations of lotka-volterra differential equations. You seem to do a lot of calculations, what kind of calculator are you using?