When I started investing money in assets like fixed deposits, recurring deposits and public provident fund (PPF) I usually ask myself, when my investment would double/triple/quadruple etc.
I pick my pencil and do calculations on paper using formulas of compound interest and I overwhelmed by large calculations. I even used calculators, but computing that period in which your money would double/triple/quadruple with a given rate of interest on a calculator may require significant time and efforts.
I asked the same question with my friends, if I fixed deposit 10,000/- for 8% per annum, In how much time will my amount would be doubled/tripled or quadruple and so on ?. But I realised lot of people do not even know the formula of compound interest and simple interest. And those who knew it, also not able to do it easily. Compound Interest is more complex to calculate, and it requires a pre-requisite knowledge of how compounding formulas work.
Later I found a shortcut called Rule of 72. Using this shortcut, I was able to calculate that period in a blink of an eye, that too, mentally. It is a great mental shortcut to estimate the effect of any growth rate, from quick financial calculations to population estimates.
(i) Rule of 72 i.e. Doubling Period(2X)
Divide 72 by the interest rate. The answer you get is your Doubling Period.
Years to double = 72 / Interest Rate
- If the rate of return is 8%, you can expect your money to double in 9 years (Dividing 72 by 8=72/8=9)
- If the rate of return is 12%, you can expect your money to double in 6 years (Dividing 72 by 12=72/12=6)
- 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.
- If inflation rates go from 2% to 3%, your money will lose half its value in 24 years instead of 36.
- If college fees increases at 5% per year (which is faster than inflation), fees 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!
Now understand, what is the shortcut to calculate the tripling/quadrupling period with a given rate of interest.
- Tripling Period(3X) [Rule of 114]
Divide 114 by the interest rate. The answer you get is your Tripling Period.
Taking the 8% interest rate, you can expect your money to triple in approx. 14 years(Dividing 114 by 8=114/8= approx 14)
- Quadrupling period(4X) [Rule of 144]
Divide 144 by the interest rate. The answer you get is your Quadrupling Period.
Again let 8% is the interest rate, You can expect your money to quadruple in 18 years (Dividing 144 by 8=144/8=18)
Aha ! This is so simple now. With some practice, you would be able to calculate the doubling/Tripling/Quadrupling period of your investment at a given rate of interest without even needing to pick up a calculator, or for that matter, a pen and paper.
There is a very implicit learning is hidden in the rule of 72.
Let’s us consider rate of interest is 8%.
The time period for your investment to double is , 9 years.
Now, notice the time period for your investment to triple is 14 years. In other words, the investment which became 2X in 9 years, took just 5 additional years to become 3X.
Notice, The time period for your investment to quadruple is 18 years. In other words, the investment which became 2X in 9 years, 3X in the next 5 years, reached 4X in just 4 additional years. Continuing further, it would take lesser time for the same investment to grow 5X, 6X and so on. This is the magic of compounding interest.
Thus, here’s is the very important financial lesson:
Always invest for the long term, to reap full benefit of compounding.
The above formulas do NOT give an “exact” doubling/tripling/quadrupling period. They are helpful for calculating the approximate period. Also, they may not be accurate for large rates of interest, like 30% or 40%, they work well for smaller rates of interest. To get more accurate and precise for large ROIs as well as for small ROIs divide by 69.3 (Rule of 69.3).