What is the importance of compound interest? Why many financial analyst refers to it the secret sauce to increase wealth over time? Several financial ‘gurus’ has described it as their secret to become wealthy. Even Albert Einstein said: “Compound interest is the eighth wonder of the world. **He who understands it, earns it; he who doesn’t, pays it”**

We will explain in the article what it is, and provide some practical examples to better understand the concept. Let’s start!

#### Table of Contents

## What is compound interest?

Essentially, it means earning interest not only on your initial investment, but also on the interest that your investment earns over time.

In other words, compound interest is a type of interest that is calculated on both the principal amount and the accumulated interest. This means that the interest earned in one period is added to the principal amount for the next period, resulting in a larger principal amount for the subsequent period. This process is known as compounding.

This compounding effect can lead to exponential growth in your wealth, making it a valuable tool for anyone looking to save for the future.

### Importance of compound Interest : an example

Consider the following example to better understand how compound interest works:

Let’s say you invest $1,000 in a savings account that earns 5% interest per year. After the first year, you would earn $50 in interest, bringing your total balance to $1,050.

In the second year, you would earn interest not only on your initial investment of $1,000, but also on the $50 of interest you earned in the first year.

This would bring your total balance to $1,102.50, making you earn an additional $52.50 in interest.

Therefore, the power of compounding lies in the fact that the interest earned in one period is added to the principal amount for the next period, resulting in exponential growth. **It is earning interest on the interest! **

Of course, the amount of interest you earn will depend on a number of factors, including the interest rate, the length of time you leave your money invested, and the frequency with which interest is compounded.

## Compound Interest vs Simple Interest

Simple interest is a type of interest that is calculated only on the principal amount. This means that the interest earned in one period is not added to the principal amount for the next period.

Let’s analyze an example to better understand the difference between compound interest and simple interest. Imagine an individual invests $1000 at an interest rate of 5% per annum. If the interest is simple, the individual will earn $50 in interest at the end of the first year. The principal amount for the second year will still be $1000, and the interest earned will be $50. This process continues for subsequent years, resulting in a constant interest earned.

In contrast, if the interest is compounded annually as we already saw in the first example, the individual will earn $50 in interest at the end of the first year. The principal amount for the second year will be $1050, and the interest earned will be $52.50. This process continues for subsequent years, resulting in a larger principal amount and higher interest earned.

Overall, compound interest is a more powerful tool for growing money over time due to its compounding effect.

Here an graphic demonstrating the huge impact and importance of compound interest in the long term. More precisely it show the total return of dividends reinvested vs just withdrawing it:

### How to calculate interest compounded?

#### Compound Interest Formula

The compound interest formula is used to calculate the amount of interest earned on a principal amount over a certain period of time. The formula takes into account the principal amount, the interest rate, and the compounding period. The formula is as follows:

```
A = P(1 + r/n)^(nt)
```

Where:

- A = final amount
- P = principal amount
- r = annual interest rate
- n = number of times interest is compounded per year
- t = number of years

### Compound Interest calculation examples

Let’s consider some practical examples to better understand how the formula works.

#### Example 1:

Suppose you invest $1,000 in a savings account that pays 5% interest per year, compounded annually. How much money will you have after 5 years?

Using the compound interest formula, we have:

```
A = $1,000(1 + 0.05/1)^(1*5) = $1,276.28
```

Therefore, after 5 years, you will have $1,276.28 in your savings account.

#### Example 2:

Suppose you borrow $10,000 at an annual interest rate of 8%, compounded monthly. If you make monthly payments of $200, how long will it take to pay off the loan?

Using the compound interest formula, we can find the number of periods (months) it will take to pay off the loan:

```
10,000 = 200((1 + 0.08/12)^(12t) - 1)/(0.08/12)
```

Solving for t, we get:

```
t = 62.29 months
```

Therefore, it will take approximately 62 months (or 5 years and 2 months) to pay off the loan.

As shown above, it is possible to calculate the future value of an investment or the amount of interest paid on a loan by using the compound interest formula. It takes into account the principal amount, the interest rate, and the compounding period.

Finally, you can use this **simple calculator** from the US government site to calculate your own examples.

## FAQs

### How does compound interest differ from simple interest?

Compound interest is interest that is calculated on both the principal amount and the accumulated interest of a deposit or loan. Simple interest, on the other hand, is calculated only on the principal amount. This means that with compound interest, the interest earned each period is added to the principal amount, and interest is then calculated on the new total. With simple interest, the interest earned each period is constant and does not change.

### What is a real-life example of compound interest?

One real-life example of compound interest is a mortgage. When you take out a mortgage, you are essentially borrowing money to buy a house. The interest on the mortgage is compounded over the life of the loan, which means you end up paying more in interest than you would with a simple interest loan.

### myFrenchMoney tip : The 72 rule

You can use the 72 Rule which is a simple way to calculate compound interest. If you divide 72 by your rate of return, you find out how long it will take your money will double in value. For example, if you have $100 that was earning a 4% return, it will double to $200 in 18 years (72 / 4 = 18)

## Key take aways

- Compound interest is about earning ‘interest on interest’;
- The importance of compound interest is its ability to multiply your money exponentially over time;
- Interest can be compounded on any given frequency schedule, such as continuous, daily, or annually.

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Bon chance!

**Disclaimer**

Please remember that we are neither financial nor tax advisors. We are just sharing our best understanding based in our own experience. This blog is for educational purposes only. Do not make investment decisions solely based on what you read in this blog. What works for us, may not for you. Do your own research and look for professional service if required. Read our full disclaimer in the ‘about’ page.