You began an investment, but you are unaware of when your investment will double. The dilemma is understandable; it’s most certainly the thing with all the investors! The Rule of 72 can help in this case.
The scientific logic behind 72 is known, and 72 is how you’ll figure out at what rate or by what time your “Investments Will Double.” So, what’s in the Rule of 72?
The discovery of The Rule of 72
Albert Einstein once said, “There is no force more powerful than the compound interest,” And we all assume that he might also be the one behind inventing, The Rule of 72. But there is no evidence that he discovered it.
The Rule of 72 was on the paper even before Einstein, around 400 years ago. The aftermath is found in the book Summa de arithmetica geometria, proporzioni et proporzionalita written by Luca Pacioli, an Italian Friar in 1494.
Shifting the focus from Albert Einstein to Luca Pacioli, let’s figure out The Rule of 72!
What is The Rule of 72?
It’s so simple to understand! Any investment that is previously made, should have a fixed rate of compound return to be considered for applying The Rule of 72 and with no other considerations.
It gives a fair idea of “The time or the interest rate it takes to double your investment.” So it is essential to have one of the factors, such as either interest rate or the time (years), to calculate the time or interest rate on the investment.
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How is it estimated?
To calculate, one must simply divide the number 72 by either the interest rate or the time to find the respective values you are looking for.
Case 1: Figuring out the Time it takes to double
To set the grounds, let’s consider an example: you have invested Rs 10,00,000 lakhs and received an interest rate of 6%. And you are wondering, when will my investment double to Rs 20,00,000?
To determine the years it would take to double, divide the 72 by the rate of return. In our context, it is 72/6, which gives 12. So it takes 12 years to double your investment to Rs 20,00,000.
Case 2: Figuring out the Rate of Interest it takes to double
Let’s assume you want your Rs 10,00,000 to double in 6 years. Then what do you think the interest rate should be on your investment?
In this case, divide 72 by the years you expect your money to get doubled. That is 72 / 6, which results in 12. So you need to get an interest rate of 12% on your investment to fold it in 6 years.
Generally, the higher the interest rate on your investment, the less time it takes to double it.
Where can The Rule of 72 be used?
1. GDP Doubling Estimation
In general, GDP is the value of the goods and services in the market produced by a country within its border in the stipulated time, where the real GDP was 7% in FY 2022 – 2023 and is anticipated to be 6.5% in FY 2024 as per NDTV.
Now, when will the country’s GDP grow by double? Say it’s increased by 2% a year, then it takes 72/2, i.e., 32 years. Meaning you can see the GDP doubling in 32 years.
Estimating it can give you a clear idea of how a 1% difference in GDP can significantly impact the future.
2. Population Growth Estimation
In the same context, what difference does it make if the growth is by 2% or 1%? Then it can impact the future planning of the growth projection in the country.
First, 1% can take about 72 years, and 2% can take about 36 years. So if the growth rate is 2%, you can cut down 36 years to double the population.
3. Inflation Risk Estimation
Let’s assume the inflation is raised by 4% against 2% this year. Then the 4% will constitute for it to take 18 years to lose your money’s value by half over 36 years in the case of 2%. This means your money will lose value in less time if it’s 4% compared to 2%.
Hence giving you ideas as to where you can invest your money to tackle the inflation risk.
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The logic behind The Rule of 72
If the question is why are we multiplying by 72, and what logic does it even have? Then let’s understand it with a penny of Rs 1. Assuming that you are receiving an interest rate of 12%, So after a year, you have;
1*(1+0.12) = 1.12
By the end of a year, you have Rs 1.12
Similarly, in two years, it would be;
1*(1+0.12)^2 = 1.25
By the end of 2 years, it would be Rs 1.25
Albert Einstein was right in this case that “Compound Interest is more potent than any other force”. By keeping the money invested from the earnings, it made more money!
So, it is reliable to put the calculation done above in general as;
1*(1+R)^N
That’s precisely how your money is growing with an interest of R and time of N years.
Without forgetting our agenda, let’s see how to double the money by Rs 2.
1*(1+R)^N = 2
On applying natural log on both sides,
It’s now;
N ln (1+R) = 0.693
While considering the smallest value of R of about 0.25, ln(1+R) is still equal to R.
With that;
N = 0.693 /R
To cut out on the decimals, it becomes;
N = (0.693 / R) * 100
Leaving us with;
N = 69.3 / R
Well, why is it not 72 / R?
Almost coming there, 69.3 is a fraction and will be hard to divide. In that case, 70 can be used, but that number mainly doesn’t divide every number, and the closest is 72.
That’s how we have:
N = 72 / R
But the crux is, with a small value of R, it all makes sense, but not when we hit the higher side of the value concerning accuracy.
The use of a Logarithmic Formula for accuracy
Though the value is rounded off to the whole number 72, it might not be accurate. To be accurate, it’s good to abide by the logarithmic formula that we used above while deriving.
That is,
N = ln(2) / ln (1+R).
Using that, you can expect the most accurate value possible for any interest rate.
A quick fact: 72 is taken, so you can mentally calculate it quickly!
Takeaway from The Rule of 72!
The Rule of 72 gives an overall picture in forecasting models to predict and do better financial planning. In a gist, to understand how much time or the rate of return it takes to achieve the desired outcome. The outcome in the context is “By when you can double your money.” For better accuracy using The Rule of 69.3 or 70 can be implemented compared to 72.
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FAQs on the Rule of 72
1. What is The Rule of 72?
The Rule of 72 is the calculation used to determine the time or the interest rate it takes to double your investment.
2. How is the Rule of 72 calculated?
It is calculated by dividing the 72 by the rate of interest or the time, whichever is applicable, and what you are looking for.
3. For an accurate estimate, what formula to use?
The Rule of 72 is for a quick calculation in mind. For example, one can use N = ln(2) / ln(1+R) for accuracy.
4. Where did The Rule of 72 come from?
It’s assumed that Albert Einstein came up with this, but it was found 400 years ago by Luca Pacioli in 1494.
