Compound interest: understand with a simple explanation

See what compound interest is and how to calculate it

Have you ever wondered why, in many financial contracts, the final amount you pay or receive seems to increase so quickly? The answer lies in compound interest, which is the most common in investments and debts.

But what exactly is compound interest and why does it cause so much confusion? It works in a simple way, by charging a percentage on the initial amount, but also on the interest that has already been added. Is that clearer? Below, we’ll explain with examples to make it easier to understand.

What is compound interest?

Compound interest is a form of calculation that is applied to the initial amount of a loan or investment, but not only that: it is also applied to the interest accumulated over time.

In other words, compound interest makes the amount grow faster because you pay or receive interest on what has already been added. This creates a multiplication effect, where each period the amount gets bigger and bigger.

What is the difference between simple and compound interest?

To fully understand what compound interest is, it’s important to know the difference between it and simple interest, which is also used in some situations.

In simple interest, the percentage is applied only to the initial amount, without taking into account the accumulated interest. For example, if you have a loan of R$1,000 at a rate of 10% per year, you will pay R$100 in interest each year, without this amount changing.

Compound interest, on the other hand, is a different story. If you take the same amount of R$1,000 and the same rate of 10%, in the first year you will pay R$100 in interest, but in the second year, the 10% will be applied to R$1,100 (the initial amount + the interest from the first year).

So you’ll pay R$110 in the second year. The snowball effect means that compound interest grows much faster than simple interest.

How does compound interest work?

Compound interest works in such a way that, with each new period (year, month, etc.), the interest accumulates. This means that the amount you earn or pay increases progressively, at an accelerated rate.

The main characteristic of compound interest is precisely this: interest is calculated on the total amount, not just on the initial amount.

Let’s look at this in practical terms. If you invest R$1,000 in a fund that offers a compound interest rate of 10% per year, in the first year you earn R$100 in interest. In the second year, you earn 10% on R$1,100 (R$1,000 + R$100 in interest), i.e. R$110 in interest.

What happens? Your earnings increase from year to year, because the amount on which the interest accrues grows. Over time, the effect becomes more evident and the final amount can be much higher than the initial amount.

How do I calculate compound interest?

To calculate compound interest, you need a simple but powerful formula. The compound interest formula is:

M = P (1 + i)^n

Where:

• M is the final value (amount), i.e. the value you will have at the end of the period.
• P is the initial amount (principal), i.e. the amount you invested or borrowed.
• i is the interest rate per period (like 10% per year, for example, or 0.10).
• n is the number of periods (if monthly, yearly, etc.).

For example, if you invested R$1,000 at a compound interest rate of 10% per year for 3 years, you would calculate it like this:

• M = 1.000 (1 + 0,10)^3
• M = 1.000 (1,10)^3
• M = 1.000 * 1,331
• M = R$ 1,331

In other words, after 3 years, your investment of R$1,000 would have grown to R$1,331, considering compound interest of 10% per year.

Why is it important to understand compound interest?

Understanding how compound interest works is fundamental to making smart financial choices.

If you know how to use it to your advantage, you can make your money grow quickly in investments. On the other hand, if you’re in debt and compound interest is working against you, you could end up paying a lot more than you thought.

For example, a mortgage or credit card with compound interest can make your debt grow rapidly if you don’t pay it off on time.

That’s why, whenever possible, try to negotiate high-interest debts or, better still, prevent compound interest from working against you.

Finally, compound interest is a powerful tool that can be both an ally and a villain, depending on how you handle it. If you know how to invest intelligently, your earnings can grow rapidly.

But if you’re not careful with your debts, the “interest on interest” effect can make you pay much more than the initial amount. Now that you have a better understanding of compound interest, it’s time to apply the tips in your daily life.

Written by

Juliana Raquel