One of the fundamental financial concepts that investors must understand is the interest rate. It is essential to understand how much you can earn or lose on investment over time.

The interest rate can be defined as the ratio between the amounts paid or received at the end of a pre-agreed period.

In other words, the profitability of any operation, whether in the form of dividends or cash, can be classified as interest.

In this Guide, we will detail how the interest rate works, how it is calculated, what simple and compound interest are, and explain the relationship between the interest rate and investments.

## What is an Interest Rate?

First, you need to understand the interest. A simple way to translate it is to say that interest is the time value of money, or as if it were rent paid to borrow money (or received to lend money). Therefore, interest will always be associated with these two factors:

- 1) The amount involved in the transaction;
- 2) Time.

In this way, banks and other financial institutions mediate between those who have the money (saver or investor) and those who need that money (borrower or debtor). In this exchange between one and the other, interest arises.

It works like this: the person who saves or invests his money in a financial institution will lend that money to a borrower/debtor. This debtor will then pay the amount received plus interest to the financial institution. Finally, the bank retains a portion of the amount paid as remuneration and returns to those who save/invest the amount previously borrowed but with interest in the future, as agreed.

In short, the borrower will return to the bank an amount greater than what was borrowed, and the investor will receive an amount greater than what was invested.

And that’s when the interest rate appears, which is calculated in percentage.

## How the interest rate is calculated

The interest rate is the “rent” price of money for a certain period. It is the percentage calculated by dividing the interest that was contracted by the borrowed/saved capital.

An example:

You lend $10,000 (capital) to a friend, and you agree that the interest paid on loan will be $900 per year. In this way, the borrower of this money will pay an interest rate of 9% pa (per year). The calculation is done like this:

· Interest/capital. That is, 900/10,000 = 9/100 per year = 9 per year

If the agreement was that the friend would repay the loan at the end of one year, you would receive $10,000 (borrowed capital) + $900 (interest) = $10,900.

But this account can change a little depending on how long the money will be borrowed and the type of interest used.

There are basically two types of interest rates: simple interest and compound interest.

## What is a Simple Interest Rate?

The simple interest rate is always applied or charged on the initial capital, which is the amount borrowed or invested.

There is no incidence of interest on interest accrued in previous periods. That is, the initial value will always be the basis for interest to be incurred in the coming periods.

A practical example:

On that same loan of USD 10,000, with a simple interest rate of 9% pa, with a duration of two years, the total interest will be USD 900 in the first year and USD 900 in the second year.

At the end of the period, the borrower will return the principal amount and simple interest for each year. Thus, the amount returned will be: USD 10,000 + USD 900 + USD 900 = USD 11,800.

Note that, in this case, the interest was always calculated on top of the initial amount, that is, always on the $ 10,000.

## What is compound interest?

Compound interest is interest on interest. Unlike simple interest, compound interest does not take into account only the initial amount but the initial amount and also the interest incurred over the periods.

Thus, for each contract period (whether daily, monthly or annual), there is a “new capital” for which the interest rate is calculated.

This “new capital” is, in fact, the sum of the initial capital and also the interest charged in the previous period.

Let’s exemplify the following:

In the USD 10,000 loan, with a compound interest rate of 9% pa, with a duration of 2 years, the total interest will be USD 900 in the first year. So far, the calculation is the same as simple interest.

But from the second year onwards, the interest paid in the first year is added to the initial capital (USD 10,000 + USD 900 = USD 10,900), and the interest calculation base becomes USD 10,900. The result is that, in the second year, the same 9% pa adds up to $981 – 9% of $10,900.

At the end of two years, the amount to be returned is $11,881.

The difference may seem small, only $81 in this example, but the potential for interest on interest is to grow over time, forming a snowball effect.

At the end of 10 years, for example, while a loan of USD 10,000 with simple interest of 9% pa would result in a payment of USD 19,000, a loan of the same USD 10,000 but with compound interest of 9%, pa would result in USD 23,673.64.

## Are Interest Rate and Federal Funds Rate the same thing?

In the US, the best-known interest rate is the Federal Funds Rate. This is because it is the basic interest rate of the US economy. This means that the Federal Funds Rate ends up influencing all other interest rates, such as loans, financing, and financial investments.

In a simplified way, the Federal Funds Rate indicates what the government pays in interest to financial institutions that buy government bonds from the National Treasury.

But the the Federal Funds Rate, in fact, is the main monetary policy instrument used by the Central Bank to control the country’s inflation. When the Central Bank wants to reduce inflation, it increases the Federal Funds Rate because, in this way, it will increase the “cost” of money. As a result, it becomes more expensive to borrow, finance, and consume. The reduction in consumption forces a reduction in inflation.

## Federal Funds Rate relationship with inflation, and exchange rate

With the ups and downs of the Federal Funds Rate, the investor needs to understand the relationship between the country’s basic interest rate and other indicators. This will be essential to define, month by month, where to invest your money.

- Federal Funds Rate
**and inflation**: when the limit of the inflation target runs the risk of being exceeded, the Central Bank uses interest rates as a strategy to try to contain this rise. As the higher Federal Funds Rate represents an inhibition to consumption, the upward pressure on prices in the country is reduced. But, on the other hand, when inflation is under control, and the government wants to encourage the economy, it can reduce the Federal Funds Rate. Lower interest rates stimulate credit and consumption, which in turn stimulates the economy. Thus, the Federal Funds Rate is a way for the government to manage inflation in the country. With the high Federal Funds Rate, there is less credit in the market, less money circulating, and the demand for products and services is lower. - Federal Funds Rate
**and exchange rate:**when the Federal Funds Rate is high, many foreign investors and speculators invest money in the US to take advantage of high interest rates. In this way, much more dollar circulates in the US economy, which can make the real gain strength. Thus, when the interest rate rises, the real tends to appreciate against the dollar, reducing the cost of imports.

## Why does the interest rate influence investments?

Interest rates affect everyone’s daily life, as they have an influence on several areas of the economy, among their investments.

Some types of investment, particularly those of fixed income, function, to some extent, as a loan of money between the investor and financial institutions or companies. When the investor lends money to a bank to finance its operations, he will do so by investing in a CDB (Bank Deposit Certificate). When it chooses to lend so that the bank, in turn, finances the agribusiness or the real estate sector.

If the investor prefers to lend his money to a company, he can do so by investing in debentures.

At the end of each operation, within the agreed period, the investor will receive the initial capital invested plus the combined interest after the deduction of Income Tax, which is levied only on income and never on the total amount invested.

In these operations, the investor will be able to choose between a predetermined fixed rate, also called a fixed rate, or opt for a rate that will be linked to some indicator of the economy, such as the Federal Funds Rate.

## What is the best investment when interest rates are high?

The answer to that question will always be: it depends. There is no magic formula or a 100% right answer because this will depend on a number of factors, such as investment time horizon, liquidity needs, investor profile, and financial objectives, among others.

But it is certain that, when the interest rate is high, investments in fixed income gain attractiveness. This is because they are investments, theoretically, with less risk than investments in variable income.

When choosing an investment and an interest rate from among those available, one must take into account that inflation generates a loss in purchasing power, which decreases the value of money over time. Thus, for an investment to have a real return, it must earn above inflation. If the inflation rate grows, the chances of investments not meeting this objective are higher.

Then comes another concept: the real interest rate.

## What is the real interest rate?

Now that you understand simple interest, compound interest, the Federal Funds Rate, and inflation, it’s time to understand the real interest rate.

The real interest rate is nothing more than nominal interest after discounting inflation. That is, it is the real profitability of a given value. Thus, we have:

- Nominal interest rate: It is the one disclosed by financial institutions when making an investment or assuming a debt without considering the effects of inflation.
- Real interest rate: These are the nominal interest already with inflation discounted.

That is when a bank announces that the return on a certain investment is 8% per year. This value is nominal. If the inflation in the period is 6%, for example, it is necessary to calculate the discount of inflation on earnings to obtain the real interest that the investor will have with that investment.

The actual rate is calculated using a formula. The nominal rate and inflation are considered variables. The formula is as follows:

In the investment world, obtaining real gains – above inflation – is a good way to make your money grow over time.

Finally, we can also understand that the nominal rate is equal to the real rate plus inflation.

**Nominal** rate = real rate + inflation.

**Sources:**

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