# Calculation base

The calculation basis is the number of days used to update, discount or annualize among other calculation factors in finance.

In other words, the calculation basis is the convention of days that is used according to the place or the finance subsector in question.

## Calculation base formula

The calculation basis is just one more factor of calculation in financial formulas. These are composed of the following concepts:

• Final capital (Cf): It is the capital that is produced at the end of the maturity of the financial operation as a result of the interest rate and the calculation basis to which it has been subjected.
• Initial capital (Ci): It is the capital that is used at the beginning of the operation. This capital will always be greater than the final capital.
• Interest rate (i): It is the percentage that is applied to the capital in the form of remuneration. The calculation base is needed to know the form of the payment due dates and the operation itself.
• Maturity (t): It is the time that the financial operation lasts in a certain way. Within the maturity we find the calculation basis.

If we bring together all the calculation factors in a formula we can find two types at a general level. The first would be simple capitalization and the second compound capitalization:

In both cases we see that 't' is essential for the financial formula to have mathematical sense at an economic level.

## Calculation base types

There are different types of calculation basis, so we are going to focus on the three main ones:

• In the first, if we say that 't' is equal to 30/360, we are affirming that the entire year has 360 days in total, and that its twelve months each have 30 days.
• In the second, if we find the expression "t" is equal to 30/365, in this case, although the months remain constant, the year that happens to have a total of 5 more days is not.
• In the third and last, if we take into account the reality of that moment, we would say that 't' is equal to the number of days in that month divided by the number of days in the target year.

To better understand the types of calculation basis, several examples are presented below.

## Calculation basis examples

Given a simple capitalization financial operation, there is an initial capital of € 1,000, an interest rate of 5% and a maturity of 8 years. Calculate the final capital according to each type of calculation basis:

In the first place, if t = 30/360, it would be: Cf = € 1,000 * (1+ (0.05 * (2,880 / 360)). Or what is the same calculated 't': Cf = € 1,000 * ( 1+ (0.05 *).

Secondly, if t = 30/365, it would be: Cf = € 1,000 * (1+ (0.05 * (2,920 / 365)). Then the factor 't' is calculated: Cf = € 1,000 * (1+ ( 0.05 *).

Third and last, if for example we chain leap years (unlikely in reality but we use it as a practical calculation example in this example), then we would have t = X / 366, so it would be: Cf = € 1,000 * (1 + (0.05 * (2.928 / 366)). Or what is the same again, calculated the factor 't': Cf = € 1,000 * (1+ (0.05 *).

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