Compound capitalization is one of the ways in which the calculation of an interest can be carried out, being the compound capitalization the one that in its calculation takes into account not only the amount of capital -such as occurs with the capitalización simple or simple interest - but also the amount accumulated as interest until the date of the calculation.

Thus, with compound capitalization, the final capital is made up of the initial capital, the interest resulting from it and the interest resulting from incorporating the interest for each period into the initial capital.

The application of compound capitalization or compound interest is especially beneficial in the calculation of the remunerative interest derived from a deposit or investment, in which case the amount calculated as interest in each period is accumulated to the initial capital generating interest again, a a process that in economics is called capitalization.

## Compound compounding formula

To know the final capital resulting after the application of a compound capitalization, in addition to the initial capital, the rate orinterest rate and the period of time to consider for the calculation.

### Compound interest formula for the first period

To know the resulting capital after the application of a compound capitalization during the first period of time, the following formula is applied:

C1 = C0 × (1 + i)

Where:

- C1 is the final capital resulting after capitalization in the first period.

- C0 is the initial capital.

- i is the interest rate.

- n is the number of time periods.

### Compound interest formula for a certain period

To know the resulting capital after the application of a compound capitalization during a certain period of time, the following formula is applied:

Cn = C0 × (1 + i) n

Where:

- Cn is the final capital resulting after capitalization.

- C0 is the initial capital.

- i is the interest rate.

- n is the number of time periods.

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