Compound Interest: Formula and Examples

Compound interest

Albert Einstein calificó al interés compuesto como "the most powerful force in the galaxy". As you will see below, this small exaggeration was not far from the truth. Understanding compound interest is essential, since it is one of the basic pillars of financial mathematics, and it is also essential to know how to make decisions in our personal finances. In this article we will explain how compound interest works, its formula, the difference with simple interest and some examples of its power in the world of stock investment.

Compound interest formula

The compound interest calculation formula is as follows:

Compound interest formula

As you can see, the compound interest formula has an exponential component, which causes it to increase to a greater extent over time. Later we will see its exponential character graphically.

Difference between simple interest and compound interest

While the total amount in compound interest increases exponentially, in simple interest it always increases by the same amount. The simple interest formula is as follows:

Fórmula del interés simple

Below you can see through examples the difference between simple interest and compound interest for a capital invested at different interest rates.

Examples of the power of compound interest

The best way to see the power of compounding is through examples. In the following graphs we can see the difference between the profitability of € 10.000 invested over 50 years through simple interest and compound interest with different annual returns.

Profitability of € 10.000 invested over 50 years through simple interest

Profitability of € 10.000 invested over 50 years through simple interest

Profitability of € 10.000 invested over 50 years through compound interest

Profitability of € 10.000 invested over 50 years through compound interest

As you can see, the difference between the different total returns increases in a much more pronounced way in the case of compound interest. In the following table you can better appreciate the difference in the results:

Difference between simple interest and compound interest

Difference between simple interest and compound interest

Compound interest on stock investment

Why is understanding compound interest so important in our personal finances? The reason is that it will help us understand that we must look for investments that grow continuously over time in a similar way to what happens with compound interest. If we invest in fixed income assets, the normal thing is that they offer them a constant simple return, so it is not usually interesting in the long term with few exceptions. This can be seen more clearly in the article in which we see the Stock market profitability in historical figures.

What we should look for are companies with long-term competitive advantages, such as Coca-Cola, Inditex, Disney, McDonalds or Google, that have profits that increase exponentially. Of course, we should not pay an excessive price for the shares of companies, but one that guarantees an interesting profitability in the long term together with a good safety margin.