Are you interested in knowing about the financial mathematics, What are they and how do they work? Be sure to read this interesting article that is very useful for your professional growth.
Financial mathematics
Globalization has become a holistic phenomenon with multiple edges in every activity carried out by the man of this century. The changes take place successively and with remarkable and at the same time imperceptible rapidity, especially in the financial sphere that serves as a reference for the crystallization of investments and savings mechanisms.
What is financial mathematics?
financial mathematics they can be conceived as a branch of general mathematics, whose object of study is financial phenomena, the interactions of money flows through time.
El financial math concept it is understood as a set of operations that determine the nature of capital and its transformation over time in accordance with a financial law.
Financial operations can be of two types: Simple in which there is a capital at the beginning and another at the end of the operation and include the calculation of interest and discount the other type are complex operations or rents that involve payment streams, such as be the installments of a loan.
Applications of financial mathematics
In the world of operations research, financial mathematics is essential to make the best decision regarding the investment of money in projects or investments, it is through the use of these that the investor acquires confidence in the investment of a project in the future. .
For this reason, a manager responsible for a certain project must handle the basic concepts, such as knowing the importance of the concept of the value of money over time as a key element of financial mathematics, as well as having the ability to determine the interaction between the dynamics of cash flows, either in present or future time. Basically financial mathematics studies the value of money, principal and interest.
How does financial math work?
People and corporations make decisions daily as we pointed out above, but a large number of those decisions are contained with a limitation of an economic nature, especially if the desire consists of investing money in multiple alternatives to be able to select the viable option, consonant with the objectives of the project, this is where financial mathematics comes into action.
The best prediction is the one that generates confidence in the investor or organization and the application of financial mathematics is the best technique or method to guarantee a viable forecast for future investment, guaranteeing the optimization of available resources.
The conception of a predictive investment model, both in the personal or corporate environment, must answer some key questions, such as: Is carrying out the project or investment justified? Is it possible to use the current infrastructure available to achieve the goals proposed in the project prototype? Will the time be adequate to carry out the project? Which of the proposed alternatives will be the best choice for the investment or organization?
Consequently, the answers to these questions are amazing indicators that direct and guide to discard or eliminate investments or projects that do not meet the feasibility conditions if the answers are vague or confused as to the availability of using or not the financial resources. necessary by the investor or organization.
That is why the development of the decision-making process in relation to the approach of solutions or alternatives in relation to the problem that is being faced becomes clearer if the person or project manager resorts to the help of financial mathematics as a tool for reasoning, analysis and evaluation of the process.
Since financial mathematics studies the transformation of money over time, it is extremely important to understand its value.
Money loses its value over time. It is a proven fact, better yet, this situation is visible when there is the phenomenon of inflation or devaluation of money, where the purchasing value is lost. Suppose that inflation at a given time is low or ideally does not exist, in the same way money depreciates and the projection of its future value will be worth much less than in the present.
In this order of ideas, there is for some experts a psychological reason that can explain this situation. It is believed that people have preferences in the use of current current consumption, than in the use of future consumption, with the possibility of making investments in projects that obtain a real and sustainable return.
The definition of the value of money gave rise to interest and created a meaning in which equal sums of money will not have the same value if they are placed in different terms of time, as long as the established interest rate is unequal to zero.
It is important to consider that the economic phenomenon of inflation distorts purchasing power or devalues money. It is opportune to illustrate the action of inflation with a simple example, suppose a person earns $1000 per month, but over the course of a year, their purchasing power is less in the acquisition of goods and services, therefore, it is seen affected by the depreciation of money. In short, his purchasing power is greater today than it will be a year from now.
Let's define interest as the revenue or rent that must be paid for the use of borrowed money. As an illustration we bring the following example:
A person applies to a commercial bank for a personal loan. You must comply with a series of requirements or obligations present in the application, where when returning the borrowed money you must pay an extra money determined by the bank rate in a period established between the user of the loan and the bank entity, that surplus of the payment is the interests.
It can be seen from what was stated in the previous example that interest constitutes the yield that one has when investing money in a productive way.
Interest has two aspects, as a cost of capital: It is the interest paid for the use of borrowed money or as a return or rate of return when the reference is the interest obtained from the investment. If you are interested in knowing more about interest, we offer you this link Financial interest rates
Interest is generally measured by the increase between the original amount invested or borrowed (P) and the final amount or value accumulated or paid. From the above it follows that if we make a loan or an investment of a capital of $P, after a while we would have an accumulated amount of $F, then the interest paid or obtained can be represented by the following expression:
I = F – P
Let's see a simple example: Let's suppose that the sum of $1.200.000 is deposited in a commercial bank in a period of 8 months. What will be the interest earned by the saver?
I = FP= 1.400.000-1.200.000= $200.000
This variation of money in $200.000 over 8 months is called the time value of money and its measure represents the interest earned.
We will explain each of the terms used in financial mathematics, for your better understanding.
Interest rate
The interest rate measures the value of interest as a percentage for a given period of time. It is the value that is fixed in the unit of time for every hundred monetary units ($100) that are invested or taken as a loan.
for example, it is said: 30% annually, 15% semi-annually, 10% quarterly, 3% monthly. That is, if the rate is 30% per year, it means that for every $100 that is invested or lent, an interest of $30 per year is generated. If the rate is 15% per semester, of course for every $100, $15 will be paid every six months, if the rate is 10% per quarter, $10 will be received or paid for every three months and finally if the rate is 3% monthly, then $3 monthly will be received or paid.
The interest rate may depend on a large number of economic variables that may occur in a State, such as: the money supply, the policies adopted by the government in relation to economic matters, inflation and others.
Then, the interest rate constitutes a great indicator when presenting how a State distributes its finances over time, stimulating investment initiatives in a transparent and viable way among investors. The interest rate is expressed as the ratio of the money received from interest (I) and the amount invested or borrowed.
Using this equation:
i=I/P.
The interest rate is always presented in percentage form, like this: 3% per month, 10%, semi-annually, 30% per year, but when it is used in any mathematical equation it is necessary to convert it to a decimal number, for example: 0,03, 0,10 .0,30 and XNUMX.
The unit of time generally assumed is the year, however, they are also expressed in units of time smaller than the year; in case the unit of time is not indicated, it is always assumed that it is an annual rate.
We will explain this by means of an example:
A commercial bank lends a person the sum of $2.000.000 and after one month he pays back $2.050.000. Calculate the value of the interest and the interest rate paid.
I= FP = 2.050.000 – 2.000.000 = $50.000
I= I/P = $50.000/2.000.000 = 0,025 or 25% per month
Capital is the mass of money that is invested and constitutes one of the important elements for understanding the financial world.
Interest rates
Below we will describe the interest rates.
Simple interest
It consists of a method in which it is always calculated based on the initial value, that is, the capital in which it becomes is taken into account, in this way in each period of time, the Interest is equal to the initial value multiplied by the interest rate. Interest. This is the simple interest equation.
M= C (1+it)
In the above equation, we refer to the amount as future value, by referring to the amount of money that an investment will reach at some future date, since it is the amount of money that an investment will reach at a future date by generating interest at some rate simple.
We graph what is expressed with an example:
You have a principal of $100, and you want to know what the amount will be in 6 months, assuming that the applicable interest rate is 5% per month. Under this formula, the mathematical expression brings the following result:
M= C (1+ It)
100+(1+6*0,05) = 130
$100 for six months with all the agreed conditions, will mean that the final amount will be $130.
Compound interest
Money and time are two factors that are present in the people-business relationship. In the event of excess cash, these can be saved in a given time, so that the interest increases the amount of the initial capital.
In the case of compound interest, it is used in the long and short term, the main characteristic being that the interest generated over a period of time becomes part of the capital, so that interest accumulates more interest. Its formula is as follows:
M = C+(1*i) t
Let's see what is expressed through an example
You have a principal of $100, and you want to know what the amount will be in 6 months, assuming that the applicable interest rate is 5% per month. Under this formula, the mathematical expression brings the following result:
100 + (1*0,05)6 = 134
The difference of $4, corresponds to the fact that the interest of month 1, was principal of month 2 and so on.
Next, we offer you the following audiovisual material on financial mathematics.