# Basics of Investing & Portfolio Management

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# The power of compounding interest

### Intro 4

In this section, we will go over what Compounding Interest is, why it is so important and an example to clarify it.
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# The power of compounding interest

In this section, we will learn what compound interest is, why it is so important, and we will see an example that will help you understand it.

## Simple interest

Simple interest is the amount of money you earn every so often (every 3 months, 6 months, 1 year, etc.) for investing in an asset (like putting your money in a savings account). These assets generate a certain benefit in the form of periodic payments (interest).

In the case of simple interest, the amount invested (principal) remains constant for the entire duration of the investment. That is, the interest it generates is withdrawn from the investment. So they do not accumulate to the initial capital, which creates a “fixed” interest that does not grow, or what is known as linear growth of your investment capital.

Therefore, simple interest is generally less attractive than compound interest; because in compounding, the interest accumulates creating more and more interest over time.

### Simple interest example

To understand what compound interest is, we first have to learn what simple interest is. To do this, let’s see an example:

Imagine that you invested \$1,000 in a savings account for 20 years that yielded (generated) 3% annual interest (return) or what is the same, \$30 (3% per \$1,000). In this case, you would earn simple interest if you withdrew that \$30 of interest from the account to buy a cake each year (for example). Let’s take a look at the result of these transactions:

Year 1:

• \$1,000 in account x 3% annual interest = \$30 interest earned
• You withdraw those \$30

Year 2:

• \$1,000 in account x 3% annual interest = \$30 interest earned
• You withdraw that \$30 again

…………………………………………..…………………………………………..………………………………………..……………….

Year 10: \$1,000 in the account x 3% annual interest = \$30 of interest you withdrew

…………………………………………..…………………………………………..………………………………………..……………….

Year 20: You still have \$1,000 in the account x 3% annual interest = \$30 earned interest that you deducted

The total value of your investment is equal to …

Invested capital + sum of all interest payments

\$1,000 + (20 years x \$30) = \$1,600

Because you bought a cake with the portion of interest (\$30) each year instead of reinvesting it, the interest stayed the same (simple interest of \$30 per year) for the 20 years. Due to inflation, your annual \$30 lost purchasing power and you had to buy a cheaper cake every year.

## Compound interest

Compound interest differs from simple interest in that the benefits (interest) generated by the investment are added to the capital of the previous period to generate new interest so that the capital grows exponentially.

Now let’s look at the same example, you invested \$1,000 in an asset that produced an annual interest of 3% for 20 years. However, in this case, you didn’t spend the interest portion on cakes and reinvested it every year. Let’s see what this would look like:

Year 1:

• \$1,000 x 3% = \$30 interest
• You reinvested those \$30
• Now your investment is € 1,030

Year 2:

• \$1,030 x 3% = \$30.90 compound interest
• You reinvested those \$30.90
• Now your investment is \$1,060.90

Year 3:

• \$1,060.90 x 3% = \$31.83 of compound interest
• You reinvested that € 31.83
• Now your investment is € 1,092.73

…………………………………………..…………………………………………..………………………………………..……………….

Year 10:

• \$1,304.77 x 3% = \$39.14 compound interest
• You reinvested that \$31.83
• Now your investment is \$1,343.92

…………………………………………..…………………………………………..………………………………………..……………….

Year 20:

• \$1,753.51 x 3% = \$52.60 compound interest
• At the end of your 20 years, you accumulated a total of \$1,806.11

Total value of your investment = \$1,000 initial + \$806.11 in compound interest (accumulated) = \$1,806.11

If we compare the two cases, we see the difference at the end of the investment:

Simple interest: \$600

Compound interest: \$806.06

### The power of compound interest

Compound interest allows you to accumulate earnings (interest) on previous earnings. This creates a snowball effect that, over time, can help generate much higher profits than with the simple interest. As we can see in the table and graph above, we have extended the investment period of the example to 50 years to accentuate the effect of compounding. We see how, as time passes, the difference between the two cases grows exponentially larger.

### Factors influencing compound interest

Compound interest is a great tool if used with caution, as it is very delicate. It depends on the expected rate of return and the investment period.

#### Expected rate of return

The expected return is the percentage of interest that you expect to receive annually for investing in a certain asset. In other words, it represents the gains that you expect to receive (on average) annually as a percentage of the capital amount.

In our example, we anticipate an annual return of 3%, which is quite conservative. Later we will see what types of investments there are and what level of profitability can be expected from each one.

It is crucial to keep in mind that high return is necessarily accompanied by high risk.

It is very easy to get carried away by the exaggerated and unrealistic figures when speculating with a 15% annual return that would generate an incredible net profit of \$15,533, following our 20-year example; or 20%, which would give us a staggering net profit of \$37,336. Therefore, it is very important not to be impressed by the possibility of winning huge amounts of money and to focus on the risks involved in targeting such high returns. Because risks also increase exponentially.

#### Investment period

The investment period (or holding period) is arguably the most relevant factor in compounding. The longer you hold your investments, the more time you give them to compound over and over, and the exponential growth of your capital eventually kicks in.

Notice: in the table and chart above, the green (compounding) and orange (simple) lines start very close to each other; but they slowly get separated until in the later periods, the green line skyrockets.

There are other factors that influence compounding interest, like the periodicity of compounding, etc. We will see more later on.

In the next sections, we will take a look at the most important and well-recognized investment vehicle in the markets, stocks.

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