If there is one thing in the world that can make you richer (or poorer) this is **compound interest** . Those who earn it will never have to worry about having enough money. Whoever pays him will never get out of his debts.

But let’s go in order.

### What is compound interest?

According to the latest Savings Report, **20 million Italian savers do not know the meaning of the compound interest.**

We are talking about the ability to **generate interest on interest** , a mechanism also known by the term ” **compound capitalization** “.

But an example can clarify ideas even more.

The easiest way to understand the capitalization of interests is to think **of rice grains on a chessboard** .

Legend has it that in 600 AD, an Indian emperor, enchanted by chess, decided to reward a farmer who had invented the game.

” *Choose what you want,* ” said the emperor to the young peasant.

The peasant’s response shocked the king.

“

I am a simple man with few wishes. I would like to receive a grain of rice for the first square of the board, two for the second, four for the third, eight for the fourth and so on …“

### A 10% return …

Assuming a 10% return, and imagining investing € 1000 in a fund, here’s what we get:

- First Year: 1000 € + 100 € Yield = 1100 €
- Second Year: 1100 € + 110 € Yield = 1210 €
- Third Year: 1210 € + 121 € Yield = 1331 €
- Fourth Year: € 1331 + € 133.10 Yield = € 1464.10
- Fifth Year: € 1464.10 + € 146.41 Yield = € 1610.51
- Sixth Year: € 1610.51 + € 161.05 Yield = € 1771.56
- Seventh Year: € 1771.56 + € 177.15 Yield = € 1963.56
- Eighth Year: € 1963.56 + € 196.35 Yield = € 2159.91
- Ninth Year: € 2159.91 + € 215.99 Yield = € 2375.90
- Tenth Year: € 2375.90 + € 237.59 Yield = € 2616.49

In ten years we have almost tripled the initial investment, and over the years, the compound interest grows more and more, as you can also see from the annual return, which is no longer on the starting capital, but on the capital plus the various interest generated.

It is therefore a **long-term investment** : the maturity must be 30 years or more, and consequently we must not be influenced by how our investment is going in the short term.

### The Rule of 72

In finance there are three rules that can help us estimate the time in which an investment can double.

The three rules are the **rule of 72** (which I’ll talk about in this article), the rule of 70 and the rule of 69.3.

Basically the number referred to in the rule must be divided by the interest rate on the period (it is worth adding for the years) to obtain an approximation of the number of years required to double the amount invested.

An example will better clarify the rule.

Imagine an investment of € 200 and a compound interest rate of 9% per year. According to the 72 rule, 72/9 = 8 years will be needed to double the capital.

## Compound Interest Calculation

How is compound interest calculated? There are sites such as the one available on the **dossier.net** site that allows you to automatically calculate the compound interest using various calculators.

## Compound Interest Formula

The calculation formula is: (1) IV = CP (1 + Y) ^ X where **IV is the value of the investment after X years** , while **CP is** the initial capital.

Y is expressed as a percentage and the symbol ^ + the symbol of exponentiation.

Moreover, not everyone knows that there are actually three types of compound interest: the discontinuous compound interest year, the discontinuous convertible IC and the continuous or mathematical IC.

Finally, as I have already written in this article, the longer the investment and the more the multiplier of the compound interest grows, but in the event that you are the debtor, this plays against you.

Banking anatocism, or the production of interest on interest by banks a few years ago and now prohibited by law, was based precisely on this system.

### he magic formula of compound interest

As you have seen before, the **magic of compound interest** is based on **exponential** rather than linear **growth** (like that of simple interest).

To better understand this concept, suppose you receive **a 3-week job offer** . The company offers you to choose between two different wage conditions:

**Every day you get paid 100 euros more than the previous day**. So, 100 euros on the first day, 200 on the second, 300 on the third and so on for 21 days.**On the first day you get paid 1 cent and on the following days you double the pay of the previous day**. So, 1 cent on the first day, 2 cents on the second, 4 cents on the third and so on for 21 days.

### Compound interest in investments: how important is the time horizon?

None of us would like to be in the same situation as the Indian emperor, crushed by the burden of compound interest.

So, thinking about an investment is the first step in taking advantage of the benefits of capitalizing on interest.

As we have seen, compound interest is based on an exponential function and **the time horizon** plays a key role in the result of the investment.

**Warren Buffet is living proof that time is an investor’s best ally.**

As can be seen from the image below, Warren Buffett’s growth in net wealth is reminiscent of the exponential function of compound interest.

The Omaha Oracle started investing at the age of 14, but **only in recent years has it seen its assets grow dramatically.**

Today at 88 years of age, Warren Buffett is the third richest man in the world with a fortune of 87 billion dollars.

### Compound interest and how to earn it

We have seen the devastating force of the compounded interest in growing a heritage over time. But how is it possible to earn it?

**Investing in financial markets** is undoubtedly the natural habitat where you can build your wealth by taking advantage of the benefits of capitalization of interest. And mutual funds can be considered one of the most interesting products to take this opportunity.

But money doesn’t fall from the sky.

Investing takes time and patience and the results require long time horizons.

For example, taking the past 70 years as a reference, the growth of an investment in global stocks has been 7% per year.

As can be seen from the table below, the effect of capitalization is seen over time. For example, the difference between investing $ 10,000 at 5% versus 7% over a 10-year horizon is just over € 3,000.

After 20 years this difference is around 12,000 euros and after 30 years it’s almost 33,000 euros.