## What is compound interest?

**Compound interest is a capital gain situation (an interest) in which the profits obtained in each period** are reinvested. In this way, an economic return is created both on the initial investment and on the profit that we have made in each previous period.

The profits obtained in the first period are accumulated with the initial investment, thus generating more profits in each consecutive period. In this way, **thanks to compound interest, a multiplier and exponential effect is obtained on the initial investment**.

For practical reasons, it is simply a matter of not withdrawing the profits that we can obtain with an investment and allowing these profits to generate more economic returns in the years to come.

This strategy, which may seem trivial, **can produce profound changes in the portfolio of any investor**being with great certainty responsible for the fortunes held by the majority of the planet’s millionaires and billionaires.

In fact, among investors, a story is told, the veracity of which is not entirely clear: it is said that when Albert Einstein was still alive, a journalist asked him what was, in his opinion, the most great invention of mankind.

Einstein responded by saying that **mankind’s greatest invention was compound interest,** adding that it was “the most powerful force in the universe. Compound interest is the eighth wonder of the world.

Indeed, when you glimpse the effects of compound interest, its results seem magical.

## A Practical Example of Compound Interest

Let’s see the real effect of compound interest with a practical example. Imagine you invest $10,000 in the stock market. Each year, you get, on average, a 6% profit from the appreciation of your stocks, plus an additional 2% in dividends: **In total, you get an 8% return on investment each year**.

This 8% represents that each year you earn $800, **profits with which you can do 2 things**:

- Take them out and keep them under your mattress
- Reinvest them in the stock market with the rest of the capital.

**With the first scenario**after 30 years you will keep your invested capital ($10,000) and in addition, you will have earned $800 each year for 30 years ($800 x 30 = $24,000), which you will have stored under the mattress. **In total, you will have $34,000**.

**In the second scenario**after 30 years, you will have **a total of $100,626.57**. **You will have multiplied your money by more than 10.**

How is it possible that the difference is so noticeable?

**Due to compound interest**. If you reinvest each year’s return, your profits will not increase linearly, but **exponentially**.

In the case of compound interest, in the second year you would no longer invest $10,000, but $10,800. So your second year’s profit would no longer be $800, but would have increased to $864 as your invested capital increased. In the third year, again, you wouldn’t invest $10,000 either, you would invest $11,664. And so on, getting an ever-increasing increase in your invested money.

### So what is the moral of compound interest applied to stock market investing?

Very simple: **Do not withdraw the profits from the initial investment when your assets appreciate and always reinvest the dividends you earn**.

It may not seem that the difference is big from year to year, but thanks to the “magic” of compound interest, the cumulative difference over the years is abysmal.

## What is the compound interest formula?

Calculating compound interest using its formula is not at all complicated and it may be interesting to know at the mathematical level how it is done. The formula for calculating compound interest is as follows:

### An example of calculating compound interest using its formula

Let’s see how to apply the above formula using a simple compound interest calculation. Suppose we want to invest a total of $20,000 (“P – Principal” in the formula above) for 20 years (“t – Time” in the formula) in an S&P 500 index fund with an average annualized return of 8 % (“r – Interest rate”).

To calculate the total that we will obtain after these 20 years (ie the “A – Total amount”), we only have to solve the equation.

As we can see, the final capital after 20 years and after investing $20,000 with an average annualized interest of 8% would be $93,219.14.

### How do I calculate compound interest for quarterly, quarterly, monthly, weekly or daily periods?

As you can deduce from the formula above, the variable *not* considers saving periods, whether days, months, quarters, years or decades.

More precisely, the variable *not* considers all periods during which interest is “compounded”; that is, when interest is charged.

If you charge interest every day on your investments and want to calculate the daily compound interest after one year, you just need to substitute the variable *not* for 365 (days) and adjust the interest rate (*r*) to what you receive from your investments in the form of daily interest.

If, for example, you receive quarterly interest on your investments and you want to calculate quarterly compound interest after one year, you would substitute the variable *you* for 4 (a year has 4 quarters) and adjust the interest rate to the average returns you receive each quarter.

As we can see, the important thing is that both variables (interest rate and time) are referenced to the same time period, be it days, hours or decades.

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