In the field of investing, it is imperative to realize the power of compounding. 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.
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
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 payoff, with the traditional method, can prove to be a little complex. The Rule of 72 provides a simple method to find out a very close approximation of how much time will an investment take to double, provided that there is a fixed annual rate of interest operating on the initial investment.
How to Use the Rule of 72?
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/fixed annual rate of interest
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 lieuof a usual compounding problem.
Let us take the example of 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 = log_{1.1}2
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 taking 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 too, increases or decreases at a compounded rate. The Rule of 72 can be used to calculate that when will the population of a region become double of its value.
For example; 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 that when will the GDP of a country become 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.
To conclude, Rule of 72 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.