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Rule of 72

People who belong to the equity market or any financial market know about the Rule of 72 very well. This is one of the basic principles that everybody uses. This one is nothing more than a simple illustration of how quickly money will double at a given interest rate. It works by dividing 72 by our annual compound interest rate and seeing how many years it will take for our investment to double. But this one is only applicable to compound interest rates or any compounding calculation. Any index that compounds, like inflation, population, credit card interest, loan interest, and so on, can be used with this formula. Basically, the formula is;

            Number of years to double = 72/ annual interest rate

        For instance, if I consider someone who can earn an annual interest rate of 8%, their money will double in 72 x 8% = 9 years. Similarly, we can also use this one in the case of GDP growth. If Indian GDP grows at a rate of 7.8% annually like this year, we can expect it to double in 72/7.8% = 9.2 years. It shows that by the year 2031, we can expect a (2*3.5T) 7-trillion dollar economy.

        Also, in some cases, let's say someone has 100 rupees in his pocket and needs 200 rupees in 3 years. Now the question is, at what rate does he have to earn so that his money will be $200 after 3 years? We can also use the Rule of 72 here to get the result.

    We have, 

            Number of years to double = 72/ annual interest rate 

            Or, annual interest rate = 72/ Number of years to double. 

            Here we have, Number of years = 3 years 

            So, Annual required interest rate= 72/3 = 24%

    We have found that if he grows his money at a rate of 24% annually, his money will double in 3 years. 

    Now the question is, is this one 100% correct? All the calculations are for the future, so we cannot predict that this one will happen for sure. So, 99 out of 100 use this one. But we know that for every statistical calculation, there is an error. Let's derivate this one.

    Let's consider the beginning arbitrary value of Rs 1. My goal is to find out how long it will take for my $1 to double at an interest rate of "r%."

            After a year I will get= Rs1(1+r) 

            After 2 years I will get= Rs1(1+r) (1+r) 

            After 3 years I will get= Rs1(1+r) (1+r) (1+r) 

    So for "n" number of years I will get= Rs1(1+r)^n 

    We have to find out how many years(n) our Rs1 will be Rs2. 

    That’s 

            Rs1(1+r)^n=Rs2 

            Or (1+r)^n=2 

            Or ln ((1+r)^n)=ln 2                                 *taking log

            Or n x ln (1+r)= 0.693 

            Or n x r = 0.693 

            Or n= 0.693/r 

        If we turn r into an integer, which is generally used in % form to calculate easily. So we get n = 69.3/r.

        We can conclude that 69.3 is more accurate than 72. But worldwide, everyone used 72 to get this calculation easily. In financial planning, knowing this basic concept is very important. It helps me a lot to know the expected figure to calculate some future estimates for the companies. I think in most cases, it doesn’t require going too deep to calculate at 69. I generally used this one to predict the future profit of the company. Assume company A has experienced annual profit growth of 15% over the last 8-10 years. So, using Rule 72, we get that it will double its profit in 4.8 years. If company A makes a profit of 1,000 crores this year, After 4.8 years, its profit will be 2000cr. After the next 4.8 years, its profit will be Rs 4000 cr. So I got the approx. Earnings of 4,000 rs are expected after 8-10 years. Then the various parameters I will next consider are P/E, cash flow, the present value of future cash flow, how much I can pay for that, and so on. But maybe my thought process is not 100% correct to evaluate future profit. In the year 2022, I used this one like this. As the time passed, I also tried to improve myself. Maybe in the next 10–15 years, I'll use this in a different way in different contexts. The prospect or use may be different, but the basic concept will be the same. Happy Investing.

-Shaishab

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