## The Concept of Compounding

Compound interest is “the greatest mathematical discovery of all time”. It’s the eighth wonder of the world. This statement is also acknowledged by Albert Einstein.

Why Compound Interest is so important in the world of finance? The simple answer is that the wonder of compounding can transform your money into a powerful income-generating machine. Compounding is the process of generating income on an asset’s reinvested income. Its efficient working requires two fundamental things: first is the reinvestment of income into the original capital and the second is time. The more time you give your investments, the more you can speed up the income potential of your initial investment. As a matter of fact, a sum of \$100,000 compounded for 30 years at the rate of 10% will turn into \$1.7 million.

### Importance of Time Period In Compounding

The end result of compound interest can be significantly different from an investment with a less compounding period than an investment with a more compounding period. Just remember that the more you give time to your investment, the more compounding effect you will receive. The possibility of generating more money by investing it with the same initial principal amount for a more extended period is far more than investing it for a shorter period. That is to say, \$100,000 invested for 15 years will generate more money than investing the same amount for five years.

## Importance of Rate of Return In Compounding

When calculating compound interest, the rate of return also makes a significant difference just like the compounding period makes. It is interesting to know that if you can get a higher return rate on your investments, you will receive more compounding effects. The potential of generating more money by investing it with the same initial principal amount for a higher rate of return is far more than investing it for a lower rate of return even though your time period is the same. That is to say, \$100,000 invested for ten years at the rate of 10% will generate more money than investing the same amount at 7% for ten years.

The following example demonstrates the difference that the number of compounding periods can make for a \$10,000 loan with an annual 10% interest rate over ten years.

If you invest \$10,000 today at 10%, you will have \$11,000 in one year (\$10,000 x 1.10). Now let’s say that rather than withdraw the \$1000 gained from interest, you keep it in there for another year. If you continue to earn the same rate of 10%, your investment will grow to \$12,100.00 ($11,000 x 1.10) by the end of the second year. Because you reinvested that \$1000, it works together with the original investment, earning you \$1100, which is \$100 more than the previous year. This little bit extra may seem like peanuts now, but let’s not forget that you didn’t have to lift a finger to earn that \$100. More importantly, this \$100 also has the capacity to earn interest. After the next year, your investment will be worth \$13,310 (\$12,100 x 1.10). This time you earned \$1,210, which is \$210 more interest than the first year. This increase in the amount made each year is compounded in action: interest earning interest on interest and so on. This will continue as long as you keep reinvesting and earning interest.

## Starting Early

Consider two individuals, we’ll name them Alex and John. Both Alex and John are of the same age. When Alex was 25, he invested \$100,000 at an interest rate of 7%. For simplicity, let’s assume the interest rate was compounded annually. By the time Alex reaches 50, he will have \$542,743 (\$100,000 x [1.07^25]) in his bank account.

Alex’s friend, John, did not start investing until he reached age 35. At that time, he invested \$100,000 at the same interest rate of 7% compounded annually. By the time John reaches age 50, he will have \$275,903 (\$100,000 x [1.07^15]) in his bank account. What happened? Both Alex and John are 50 years old, but Alex has \$266,840 (\$542,743- \$275,903) more in his savings account than John, even though he invested the same amount of money!

By giving his investment more time to grow, Alex earned a total of \$442,743 in interest, and John earned only \$175,903.

## Using Rule of 72 with Compounding Effect

If you want to know quickly in how many years your investment can be doubled in value then the rule of 72 is the method to use. In other words, the Rule of 72 is a formula that estimates the amount of time it takes for an investment to double in value, earning a fixed annual rate of return.

The Rule of 72 only gives a shortcut to find the fair estimation of the doubling time for an investment. Remember, this method only works with compounding interest. Simple interest does not work very well with this method.

## Formula:

Number of years for the investment to double = 72 divided by Annual rate of return.

**Example:** Suppose you have \$100,000 in your pocket to invest in a Corporate Bond that gives 9% compound interest annually, and you want to know after how many years your investment of \$100,000 will turn double. So, rather than doing a detailed calculation to see the number of years, you can simply use the rule of 72. All you have to do is divide 9% with 72 and get nine years. It means it will take nine years to double up your investment if you invest \$100,000 in a corporate bond that gives 9% compound interest annually.

You should be careful regarding the nature of the rate of return here. Suppose a corporate bond gives 9% simple interest annually instead of compound interest, then this formula will not help you know the number of years to double up your investment.

## Conclusion:

The Rule of 72 is a simple, effective, and short tool that investors can use to estimate how long a specific compound interest investment will take to double their money.