“Compound interest is the 8th wonder of the world. He who understands it, earns it; he who doesn’t, pays it.”
These were the words of the smartest person believed to have lived on Earth, Albert Einstein. If a person is disciplined and patient, their money can grow several fold over the years due to the power of compounding. If not, then, at least you’ll still have the capital that you started with (mixed with some regrets).
Returns increasing at increasing rate
It’s due to the snowball effect that the returns from compounding are so remarkable. Once the interest is earned on your capital, interest is again paid out on the new capital (which is capital plus interest). This means that you earn interest not only on the initial capital but also on the interest amount.
Start early
The benefits of starting early are numerous and cannot be overlooked. Consider this: Sachin starts investing his money at the age of 19, putting aside Rs. 2,000 from his monthly earnings for his portfolio. Whereas Virat starts setting aside Rs. 2,000 only when he is 25 years of age. Who do you think will be the quicker to reach Rs. 5,00,000? Further, the gap betweeen them increases since by the time Sachin is 25, he has already amassed Rs. 1,96,222.62. He will now also earn interest on the corpus he has amassed.
Another example demonstrating the power of compounding is highlighted in the table below:
| Case 1: Virat invests every year and earns simple interest | Case 2: Sachin invests every year and earns compound interest | ||||
|---|---|---|---|---|---|
| Year | Principal Amount (Rs.) | Interest Earned @ 12% p.a. | Year | Principal Amount (Rs.) | Interest Earned @ 12% p.a. |
| 1 | 100000 | 12000 | 1 | 100000 | 12000 |
| 2 | 100000 | 12000 | 2 | 112000 | 13,440 |
| 3 | 100000 | 12000 | 3 | 1,25,440 | 15,052.8 |
| 4 | 100000 | 12000 | 4 | 1,40,492.8 | 16,859.1 |
| 5 | 100000 | 12000 | 5 | 1,57,351.9 | 18,882.2 |
| 6 | 100000 | 12000 | 6 | 1,76,234.2 | 21,148.1 |
| 7 | 100000 | 12000 | 7 | 1,97,382.3 | 23,685.9 |
| 8 | 100000 | 12000 | 8 | 2,21,068.1 | 26,528.2 |
| 9 | 100000 | 12000 | 9 | 2,47,596.3 | 29,711.6 |
| 10 | 100000 | 12000 | 10 | 2,77,307.9 | 33,276.9 |
As you can see from the table above, Virat ends up with a total of Rs. 1,00,000 + (12,000 X 12), which is equal to Rs. 2,44,000; whereas Sachin ends up with a sum of Rs. 2,77,307.90 + 33,276.95, which is equal to Rs. 3,10,584.80. Now you can decide whether you want to be like Sachin or Virat? Our advice: be like Sachin!
Calculating compound interest
Calculating compound interest and the final amount that is amassed using compound interest is a bit complicated.
The formula for calculating the final amount after earning compound interest looks like this:
A=P[(1+r)^t]
where A=Final amount after earning compound interest; P=Initial principal invested; r=Rate in percentage earned as interest; t=Time period for which compounding takes place
As an example, let’s assume Rs. 100 is the principal, rate of interest is 10% and the time period is 3 years. The amount earned after 3 years looks like this:
A=100[(1+0.10)^3]
The final result therefore is Rs. 133.10.
Rule of 72
The Rule of 72 helps an investor determine the time period within which his/ her return shall be doubled. In order to find out the number of years taken to double the invested amount, 72 can be divided by the rate of interest earned over a period, say a year. The result is the number of time periods, here years, that it shall take to double the invested amount.
As an example, if one expects to earn 10 percent interest compounded annually, then the amount invested can be expected to double in 72/10 or 7.2 years approximately. Do note that the calculations made using this rule are approximate and cannot be used to substitute exact mathematical calculations. However, this rule does give the investor a rough estimate as to how much time and patience is necessary to double the funds, at a specified rate of compound interest.
Conversely, this rule can also be used to determine the interest rate earned on an investment, given the time period in which it has doubled. Just divide 72 by the time period in which the sum has doubled and bingo! Consider this example, say a sum of Rs. 1000 has doubled over a period of 4 years. Using the rule of 72, we can determine that the interest rate earned would be roughly 72/4 or 18 percent. Neat, right?
Rule of 114
Similar to the rule of 72, the rule of 114 helps us determine the time period within which a sum can be tripled. By dividing 114 by the rate of interest, we can determine the time within which an investment can be tripled.
Rule of 144
This rule helps us determine the time period within which a sum can become 4 times or quadruple. As an example, in case rate of interest earned is 10 percent, we can say that it shall become 4 times in roughly 14.4 years. Do note that this rule leads to approximate figures and is an aid towards easy mental calculations and should not be taken as a yardstick.
Click on the arrow button to the right to glance over this article again and revise the calculations. Thanks for reading!
