What is the composed interest?

Compound interest is one of the most powerful and fascinating concepts in the world of finance. Unlike simple interest, which is only calculated on the original principal, compound interest is calculated on both the initial principal and the interest accrued in previous periods. This means that interest “compounds” or accumulates, allowing an investment to grow at an accelerated rate. In this article, we will explore in detail what compound interest is, how it works, its advantages, and how it compares to simple interest.

What is the composed interest?

Compound interest is calculated on the initial capital and on the interest that has accumulated in previous periods. This means that, as time passes, the total amount of the investment or debt grows exponentially. The formula to calculate compound interest is:

A=P(1+r/n)nt

Where:

• $A$ is the total accumulated amount (principal plus interest).
• $P$ is the initial capital (principal).
• r is the annual interest rate (in decimal form).
• n is the number of times interest is compounded per year.
• t is the number of years.

Thanks to this formula we can calculate compound interest very easily. For example, if you invest €1.000 at an interest rate of 5% per year, compounded annually for 3 years, the calculation would be:

A=1000(1+0.05/1)1⋅3 

A =1157.625

This means that at the end of 3 years, you will have €1157,63, which means you have earned €157,63 in interest.

Advantages of compound interest

Compound interest has several significant advantages that make it a powerful tool for capital growth:

• Exponential growth: As interest accumulates, the principal grows at an accelerated rate. This is especially beneficial in the long term, as growth becomes increasingly pronounced.
• Reinvestment effect- If the interest generated is reinvested, even more interest can be generated in the future. This is common in savings accounts, investment funds and pension plans.
• Long term benefits: The longer you leave your money invested, the more significant the effect of compound interest will be. For this reason, it is advisable to start investing as soon as possible.
• Inflation- Compound interest can help combat the erosion of purchasing power caused by inflation by allowing capital to grow at a faster rate than the increase in prices.

Compound Interest vs Simple Interest

Simple interest is calculated only on the initial principal, which means there is no “interest on interest.” The formula to calculate simple interest is:

I = P(r⋅t)

Where:

• I It is the total interest.
• P It is the initial capital.
• r is the interest rate.
• t It's the time.

Comparison of examples

Let's imagine that we invest €1.000 at an interest rate of 5% for 3 years, both in simple interest and compound interest.

• Simple interest: I = 1000(0,05⋅3) = 150. At the end of 3 years, the total will be: 1000 + 150 = €1150
• Compound interest: A=1000(1+0,05/1)1⋅3 = 1157,63 €

As we can see, compound interest generates a total of €1157,63, while simple interest only produces €1150. The difference may seem small in the short term, but it becomes much more significant as the investment period or amount extends.

A tool for savings

Compound interest is a fundamental concept in the world of finance that can have a significant impact on the growth of your investments and especially on your savings options. Through the accumulation of interest on interest, compound interest allows capital to grow at an accelerated rate, especially over the long term. Understanding how it works and its advantages is crucial for anyone interested in maximizing their savings and investment.

While compound interest can be a powerful ally for investors and savers, it can also be a challenge for those in debt, as interest can add up quickly. Therefore, it is vital to be aware of how interest is applied to your investments and debts to make informed decisions that benefit your financial situation.

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