# Compound interest

Compound interest in monetary assets is called that which is added to the initial capital and on which new interests are generated.

The interest generated is added period by period to the initial capital and to the interests already generated previously. In this way, value is created not only on the initial capital, but the previously generated interest is now also responsible for generating new interest. In other words, the interest earned accumulates to generate more interest.

On the contrary, simple interest does not accumulate the interest generated. Interest can be paid or collected, on a loan that we pay or on a deposit that we collect. The condition that differentiates compound interest from simple interest is that while in a compound interest situation the accrued interest is added and producing new profitability together with the initial capital, in a simple interest model only the interest on the initial capital is calculated borrowed or deposited.

It is often said, incorrectly, that when a loan or deposit is greater than one year, the compound interest system is established, being simple interest in the case of short operations, less than one year. However, this is not always the case, since it will depend on the agreed conditions and the reinvestment of the returns and not so much on the temporality.

## Advantage of compound interest on investments

Compound interest has a multiplier effect on investments, since previous interests generate new interests, which are added. This makes compound interest a great ally for long-term investment. Humorously, Albert Einstein went so far as to say that compound interest is the most powerful force in the universe.

Let's imagine an operation in which we invest 10,000 euros and each year they give us a 5% return on the capital invested. Since compound interest reinvests previously earned interest, unlike simple interest, the future benefit is exponentially greater with compound interest.

If we continue with the sequence and draw it on a graph, the difference between compound interest and simple interest is represented as follows. It can be seen that while investment with simple interest increases linearly, investment with compound interest increases exponentially:

## Formula for calculating compound interest

The formula is as follows:

Cn = C0 (1 + i) n

C0 being the initial capital borrowed, i the interest rate, n the period of time considered and Cn the final resulting capital.

## Compound interest calculation example

A practical example to determine compound interest with an initial capital of € 1,000 and an interest rate of 5% in a period of 5 years:

Period | Amount at the beginning of the period | Interest for the period | Amount owed at the end of the period |
---|---|---|---|

1 | 1.000 € | (1.000 *5%)= 50 € | 1.000 + 50 €= 1.050 € |

2 | 1.050 € | (1.050 *5%)= 52,50 € | 1.050 + 52,50 € 1.102,50 € |

3 | 1.102,50 € | 55,13 € | 1.157,63 € |

4 | 1.157,63 € | 57,88 € | 1.215,51 € |

5 | 1.215,51 € | 60,78 € | 1.276,28 € |

As we can see, the resulting annual interest is not € 50 (except for the initial period), but the interest generated and accrued in subsequent periods is incorporated, obtaining at the end of the operation a profit or payment of € 276.28, and not € 250 which would be in a simple interest situation.