Compound Interest: Definition and Importance

Compound interest is the kind where the initial capital grows during the operation. In other words, with each period, the earned interest is added to the initial capital, generating new interest. This is why it’s also known as "interest on interest."

Here, let’s quote Albert Einstein: “Compound interest is the most powerful force in the universe.” This teaches us an important lesson: understanding compound interest and learning how to use it in your favor can be a powerful force for your financial health. In this post, we will explain in detail the difference between simple and compound interest and show you how to calculate it.

Definition and Example of Simple Interest

Simple interest always applies to the same capital. This is typically measured over a year. For example, if you leave $100 for a year, you will earn $1, and you will have $101. At the end of the second year, you will have $102. That’s simple interest: each year, the interest applies to the same initial capital.

This type of interest means the initial capital remains the same throughout the operation. In other words, the interest is the same for each period. The interest rate is applied to the invested or initial capital. In summary, simple interest is calculated on the initial capital, and the same amount repeats for the next year.

What is Compound Interest?

In simple terms, compound interest generates a cumulative effect of gains. That is, the amount of your initial capital increases over time, and new interest is added to that gain, creating a multiplying effect year after year.

We call it a multiplying effect because as interest grows, you earn interest on interest, leading to the capitalization of money.

One thing to consider is that for this to work, you must be able to leave your money untouched and let it grow over time. In the end, you are paid interest on your initial capital and all the accumulated interest from previous years.

Sustaining it over time, such as for retirement, is a great option. Just keep in mind that this is money you won’t touch for several years. The long-term increase is substantial.

This makes compound interest very attractive in products that generate returns but can be detrimental in loans, as the debt increases exponentially.

Difference Between Compound and Simple Interest

There is a fundamental difference: with simple interest, the capital remains constant, while with compound interest, the capital changes at the end of each period. Let’s look at an example of an initial investment of $100 with 10% interest to see the final result if simple or compound interest is applied. Check the following table:

Advantages of Compound Interest

• The main advantage of compound interest is that all the generated interest continually adds up, resulting in a faster increase of your capital. So, year after year, your capital grows.
• You can reinvest your earnings every year, and each year, they grow a little more, leaving a higher return each time.
• Time is crucial—the longer you leave it, the more earnings you will get.

In short, the only disadvantage is that discipline is needed. To apply compound interest, you need to have a long-term amount, money you won’t need in the near future.

Manage a monthly budget

But How Does Compound Interest Work?

Let’s see its operation in a long-term investment example using this interest:

• Imagine you have $100 in an account with an annual interest of 10%. After one year, $10 is added to that account.
• By the end of the first year, the total amount is $110.
• By the end of the second year, the generated interest is $11, which is the result of applying 10% to $110, bringing your total to $121.
• By the end of the third year, $12.1 is added, resulting in a total of $133.1, and so on…

How is Compound Interest Calculated?

To know exactly how much your initial investment will earn, just use this formula by inputting the data as accurately as possible.

• Final Capital = C0 x (1+Ti) ^t
• (^t = Raised to the time period)
• C0 = Initial capital
• Ti = Annual interest rate
• t = Duration of the investment

Example of Compound Interest Calculation

Remember those $100 from earlier? Let’s see it grow using the compound interest formula:

• To calculate the increase for the first year, apply the following:
  • Final capital = 100 X (1 + 0.10/1) ^ 1 = 110
• For the second year, the formula adapts with some modifications:
  • 110 x (1+ 0.10/1) ^ 1 = 121
• For the third year, repeat the formula, adjusting the final amount of the second year:
  • 121 x (1+ 0.10/1) ^ 1 = 133.1

As you can see, your initial capital is modified as compound interest makes your money grow each year. Now you understand why time is valuable, and the sooner you start, the better.

The Importance of Compound Interest

The importance of compound interest lies in the fact that when you invest long-term, your money can earn significant returns, considering the interest rate and time.

It creates a reinvestment effect over time. We mean that the interest adds to the money you already had, and those earnings get reinvested, making your wealth grow more and more.

Why Should You Calculate Your Compound Interest?

Because it allows you to know the exact amount of your future earnings, which can be motivating to save more and become more disciplined with your spending. For example, you can learn how to identify and reduce your small, everyday expenses by checking out our tips here.

By applying compound interest, you’re taking the first step towards building a financial plan and achieving a more stable and financially free future.

If calculations aren’t your strong suit, don’t worry! We’ve got you covered with a free online compound interest calculator. You can find it here, so there’s no excuse not to get started!

Compound Interest: Warren Buffet’s Investor Secret

Once, Warren Buffet was asked what the secret to winning in investing was. The well-known investor and CEO of Berkshire Hathaway responded: the key is compound interest.

Do you need any more reasons? Remember that Warren Buffet is one of the richest and most influential people in the business world. So, start earning interest on your interest by applying Warren Buffet’s trick.

He added, praising his secret with the following quote: "The best thing to do is invest in the world’s most representative stock index and simply wait for compound interest to work its magic."

Finance Guide: Compound Interest as Your First Step

Organizing your personal finances and applying compound interest requires consistency and discipline because it demands the creation of healthy financial habits, which takes time—step by step.

To help you get started, we’re sharing a guide with four simple steps:

1. Identify where your personal finances stand;
2. Set personal financial goals for the short, medium, and long term;
3. Manage your debts;
4. Periodically monitor the goals guiding your personal finances;
5. Seek out more ways to grow your savings.

Invest to Grow Your Capital

If you want to know more about how to invest, check out our blog for more information. We recommend reading our post, Is It Better to Save or Invest Money? Find Out Now!.

In addition to letting the "magic" of compound interest do its work, there are other ways you can more quickly reach financial freedom. For example:

By investing in the U.S. stock market. Now you may be wondering:

Can I invest in the stock market if I’m in Latin America?

Hapi Inversiones is a certified Fintech from Silicon Valley, backed by top-tier institutions (learn more here), aiming to facilitate secure and easy access to the U.S. stock market for Latin Americans. Now, you can invest with confidence in a quick and straightforward way. Simply create your account here!

It's worth mentioning that Hapi is one of the few most reliable brokers for the LATAM sector, with no commission fees and no minimum deposit requirements. What do you think? Shall we start growing that money by investing in ETFs? (That’ll be the topic of our next article, so don’t miss it!)