What is the Rule of 72?
In the field of investing, it is imperative to realize the magic of compounding. So, wondering what magic has got to do with your money? It is not a magic mantra to make you rich overnight; rather, it is just prudent investment advice.
In the process of compounding, the interest when due is added to the original sum, hence modifying the sum for the next compounding period. Consequently, the interest rate is not only applicable on the principal amount but also on the interest accrued. In simple words, earnings generated from earnings is called compounding.
The formula for the compounded amount:
A = P (1+r) n
Where;
A = Compounded amount
P = Principal amount or the initial investment
r = Fixed annual rate of interest
n = Number of compounding periods
You can double your investments quickly if you get a great rate of return, thanks to the power of compounding. Every time we talk about doubling wealth over time, an important rule, called the "Rule of 72", is employed for calculation.
The Rule of 72 is not just any formula. But It's a time-tested formula used by investors every day to estimate how long will it take for the money to double while they sit back and relax.
So, let's dive deep and see this rule in action and how it can help you double your money.
What is the 'Rule of 72'?
When an investor wants to know the time period related to doubling of the principal amount, the Rule of 72 comes into play. Calculating the compound interest and the time period after which the investment is likely to pay-off, with the traditional method, can prove to be a little complex.
The Rule of 72 is a simple formula that estimates the amount of time it will take for an investment to double in value, earning a fixed annual rate of return. The simple calculation is dividing 72 by the annual interest rate.
How Rule 72 works?
According to the Rule of 72, one has to simply divide the number 72 by the fixed annual rate of interest to get a close approximation of the time it will take an investment to double in value.
The Formula for the Rule of 72:
Doubling Time (Number of years) = 72/Interest Rate
where the interest rate is the fixed Rate of Return on investment.
72 is a number, which is perfectly divisible by the numbers 1, 2, 3, 4, 6, 8, 9, 12, 24, 36 and 72. This provides for a quick and easy division calculation in lieu of a usual compounding problem.
Let us take an example,
An amount of Rs. 1000 with a fixed annual rate of interest of 10%.
According to the compounding formula;
1000 (1+ 0.10) n = 2000
(1.1) n= 2
n = log1.12
n = 7.3 years.
According to the Rule of 72:
An amount of Rs. 1000 will take 7.2 years to grow to Rs. 2000, given that the fixed annual rate of interest is 10%. (Since, 72/ 10 = 7.2)
The sheer speed with which the calculation can be done makes the Rule of 72 a very powerful tool for making investment decisions in an instant.
However, the Rule of 72 tends to slightly overestimate the time period for the amount to double in case of low rates of interest and slightly underestimate the time period for the amount to double in case of high rates of interest.
A table to compare the number of years according to the Rule of 72 and the actual number of years taken by an investment to double at various interest rates is given as follows:
Rate of Interest |
Rule of 72 |
Actual Number of Years |
Quantum of Difference (in years)* |
2% |
36 |
35 |
1.0 |
3% |
24 |
23.45 |
0.6 |
5% |
14.4 |
14.21 |
0.2 |
7% |
10.3 |
10.24 |
0.0 |
9% |
8 |
8.04 |
0.0 |
10% |
7.2 |
7.27 |
0.0 |
12% |
6 |
6.12 |
0.1 |
25% |
2.9 |
3.11 |
0.2 |
50% |
1.4 |
1.71 |
0.3 |
72% |
1 |
1.28 |
0.3 |
100% |
0.7 |
1 |
0.3 |
Important Inferences about Population Increase or Decrease
The population of an area to increases or decreases at a compounded rate. The Rule of 72 can be used to calculate when the population of a region becomes double of its value.
For instance, the population growth rate of a country is 6%. According to the Rule of 72, the country's population would be approximated to double in 12 years.
Important Inferences about Inflation
As the compounding effect increases the value of the money with time, so it can decrease the value of the money with time. The main cause can be attributed to inflation. With the Rule of 72, we can approximate when the value of the money can be halved. A table with inflation rates and respective years it will take for the amount to be halved is given as follows:
Inflation Rate |
Years |
3% |
24 years |
5% |
14.4 years |
8% |
9 years |
12% |
6 years |
Important Inferences about Gross Domestic Product (GDP) of a Country
The GDP of a country increases or decreases at a compounded rate. The Rule of 72 can be effectively put to use to calculate when the GDP of a country becomes twice of its value.
For example, the GDP growth rate of the country is 4%. According to the Rule of 72, the country's GDP would be approximated to double in 18 years.
The Rules of 72, 69.3, and 69
The rules of 69.3 and 69 are also methods to estimate when an investment will get doubled. Rule of 69.3 is considered more accurate than the Rule of 72 but can be much more complicated to calculate. Therefore, investors typically prefer to use the rule of 69 or 72 rather than the rule of 69.3.
Final words
The "Rule of 72" is a practical eye-opener that forces investors to ask shrewd questions before making important money decisions. To conclude, it simplifies the process for an investor to calculate when his investments will be doubled.
To get a better understanding of the above topics with real companies and examples, you can refer to Youtube Video.