### Key Points

- Interest Rate
- Invest
- compound interest

If you have already learned about the importance of organization when planning your personal finances, you have discovered that the excess money you generate over a period of time can be invested. You probably also know a little more about your investment preferences and horizon, so it's time to move on to the next concept you need to consider when analyzing alternatives: the interest rate.

You have probably heard of the interest rate at some point, but do you really understand its meaning? Before we get into the topic, we need to understand what the Time Value of Money is. This principle of the world of finance states that any amount of money today is worth more than the same amount of money tomorrow. This is due to multiple reasons, but we can summarize them in the fact that the present is certain and the future is not.

In many countries that are experiencing inflationary processes, it means that if we want to buy an apple that costs $10 today, it is likely to cost more than $10 within a year. Additionally, there is the "opportunity cost" of postponing the purchase until later, as not only may it be more expensive within a year, but it may also be that the product is not available for sale.

Imagine, for example, that you are a fan of George Lucas and want to buy some limited edition Star Wars figurines. In this case, you will probably ask for a very high interest rate for not having your money at that moment, because they have to reward you for not getting it at that precise moment. What we want to say is that you probably have a greater preference for consumption today and now than postponing that gratification for later. That is why we need an incentive to motivate us to postpone that use of money today.

This incentive is represented by the interest rate and one of its main functions is to reward for that loan of money.

In that postponement there is a risk of not recovering it if the investment is risky, which is why the interest rate also represents the cost of money, that is, the reward you will ask for in exchange for lending it.

#### Simple interest

Simple interest is the interest earned when we invest a certain amount of money for a period of time. Unlike compound interest, which we will see in the next section, the interest earned at the end of the time period is not added to the capital, that is, it is not capitalized.

We can calculate simple interest with this simple formula: Simple Interest = Invested Capital x Interest Rate x Time Period For example, if we want to know what Interest we will earn by investing $1,000 at 7% annual interest for 10 years, we can verify this by doing:

$1,000 x 7% x 10 = $700

However, in the real world, these $700 in interest earned after a certain time are usually reinvested along with the $1,000 capital to generate even more interest.

This is where the concept of compound interest comes into play.

#### Compound Interest

Compound interest assumes, as we saw in the previous paragraphs, that the interest we earn is reinvested along with our capital, that is, it is capitalized.

Following the example above, if we want to know the compound interest when we invest $1,000 at 7% per year after 10 years:

Then, we see that after 10 years and if we reinvest the interest we are earning at the end of each year, the total compound interest we earn is $967.15 vs. the $700 we obtained with simple interest (without investing the interest and only investing the $1,000 capital).

We can arrive at the same result in the table above if we do the following formula:

Compound Interest = Invested Capital x [(1 + Interest Rate) Time Period - 1]

$1,000 x [(1 + 7%) 10 - 1] = $967.15