## Basic concepts

Financial Mathematics is a useful tool in analyzing some investment alternatives or consumer goods financing. It consists of employing mathematical procedures to simplify the financial operation to a cash flow.

## Capital

Capital is the amount invested through some financial transaction. Also known as: Principal, Present Value, Present Value, or Applied Value. Present Value is used in English (indicated by the PV key in the financial calculators).

## Interest

Interest represents the remuneration of capital employed in some productive activity. Interest may be capitalized under two schemes: simple or compound.

**Simple interest**: The interest of each time interval is always calculated on the initial borrowed or invested capital.

**Compound interest**: The interest of each time interval is calculated from the balance at the beginning of the corresponding interval. In other words, the interest of each time interval is incorporated into the initial capital and yields interest as well.

O** swear **It is the remuneration for the money loan. It exists because most people prefer immediate consumption, and are willing to pay a price for it. On the other hand, anyone who is able to wait until he has enough to acquire his desire, and in the meantime is willing to lend this amount to someone less patient, must be rewarded for this abstinence in proportion to his own. **time** and **risk**, which the operation involves.

The time, risk, and amount of money available on the market for loans define what the payoff, better known as **interest rate**.

### When do we use simple interest and compound interest?

Most cash transactions use **compound interest**. These include: medium and long term purchases, credit card purchases, bank loans, the usual financial applications such as Savings Account and fixed income fund applications, etc. We rarely find use for the simple interest regime: this is the case with very short-term operations and the simple duplicate discount process.

## Interest rate

The interest rate indicates how much interest will be paid to the borrowed money for a given period. It is usually expressed as a percentage, followed by the specification of the time period to which it refers:

8% a.a. - (a.a. means the year).

10% a.t. - (a.t. means quarter).

Another way of presenting the interest rate is the unit rate, which is equal to the percentage rate divided by 100, without the% symbol:

0.15 a.m. - (a.m. means month).0.10 a.q. - (a.q. means to the quarter) Next: Simple Interest