Rule of 72
People love money, and they love to see it getting double. Getting a rough estimate of how much time will it take to double an amount of money helps the average man to compare his investments. That is exactly what Rule of 72 does.
It has been used for over 500 years, first published in 1494 by Luca Pacioli. The Rule of 72 can estimate compounding periods using natural logarithms. It helps you quickly gauge an approximate value.
Albert Einstein, the absent-minded genius who gave us the theory of relativity once said, that the compound interest is the eighth wonder of the world.
The Formula for the Rule of 72
The Rule of 72 is a simplified way to estimate the doubling of an investment’s value.
Years to Double = 72 / Interest Rate?
where: Interest Rate = Rate of return on investment
In personal finance if you divide the number 72 with the rate of interest, you get to know the number of years it will take to double your money. Alternatively, it can compute the annual rate of compounded return from an investment given how many years it will take to double the investment.
- E.g: If the rate of interest is 9%, simply divide the number 72 by 9. So, it will take 8 years to double your money, if you invest at 9% rate of interest p.a.
Know the Rate of Interest Needed
Use this Rule of 72 in reverse to know the Rate of Interest needed to double your money and achieve your set goal.
- E.g: If you have 250k today and need 500k in 5 years. Just divide the number 72 by 5 and the answer is 14.41%
This formula is useful for financial estimates and understanding the nature of compound interest. Examples:
- 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.
Understanding Expenses or Inflation
The rule of 72 also helps you understand about Inflation. It helps us calculate an estimate amount of time it will take to make real value of money into half.
- E.g: Let us say the preset inflation is at 6%. Divide 72 by 6 you get 12 years. It means if you have 10k in your kitty, it will be valued as 5k in approximately 12 years’ time.
You can also use the rule of 72 for expenses like inflation or interest:
- If college tuition increases at 5% per year (which is 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!
This simple arithmetic computation is not exact, but it is close enough to the exact results of a logarithmic equation to make it extremely useful. 69.3 gives a more accurate results. This number, 69.3 is nice and all, but not easily divisible. 72 is close by, and has many more factors (2, 3, 4, 6, 12…). Having said that, we could use 70, but again, 72 is nearby and even more divisible; for a mental shortcut, go with the number easiest to divide. So the Rule of 72 it is.
This rule of 72 also shows why a “small” 1% difference in inflation or GDP expansion has a huge effect in forecasting models.
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