Financial mathematics
In today's environment of widespread introduction of all kinds of financial instruments - simple and complex, correct and promising unrealistic benefits - not only economists and entrepreneurs, but also educated citizens must have an understanding of financial mathematics. Learning the elements of financial mathematics contributes to competent answers to questions that are natural to most people: "Which financial transaction is more profitable?", "How to dispose of the money?", "What was the price of goods if today it is indicated with a 75% discount?", "What is inflation?", "An income of 0.01% per annum - is it much or little?", "A loan at 2% per day - profitable or not?", etc. Complication of financial activity, which characterizes the current situation, is accompanied by the development of quantitative methods in the field of financial analysis. In order to orient oneself in the great variety of financial algorithms, it is necessary to form basic notions of the basic principles of calculations, which are the basis of most financial calculations, already since school. By now, most models of modern financial computations have been developed in detail, from the simplest and most accessible ones, such as credit calculations, to the more complex ones, such as time-series analysis technology. The variety of questions posed, as well as significant differences in mathematical methods for analyzing financial and economic problems and situations within the educational field of "Financial Mathematics" required the selection of three groups of typical problems.
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These groups differ both by the formal approach (mathematical methods) and by the level of substantial penetration into the situation under consideration (economic theory). The majority of tasks, allowing to acquaint schoolchildren with financial calculations are financial tasks in conditions of certainty. Among them a special place belongs to the tasks of the elementary interest theory, its application to the estimation of the value of financial rent, as well as in the conditions of planning the repayment of loans, accrual of sums and tasks of discounting sums, the simplest calculations in the securities market. Financial mathematics is a rather narrow educational field, but is characterized by a high degree of practicality. We adhere to a broad understanding of financial mathematics as an instrumental basis for subsequent sections of applied mathematics, among which financial management, investment analysis, banking, and risk theory. In other words, the focus of financial mathematics is on the parameters and results of commercial and financial transactions. However, the basics of financial mathematics are needed not only for managers, entrepreneurs, and economists. We are talking about financial and economic culture (functional literacy) of the population, which implies: - the ability to navigate in financial and economic situations; - making optimal decisions swinging their own finances; - working on their own financial stability and security; - the technology of daily financial planning; - the principles of perspective budgeting; - mastering the elements of the technique of comparing the benefits and losses of financial transactions.
Financial mathematics has an important function - to provide an understanding of the essence of entrepreneurship, business. It is important that financial mathematics in its mathematical foundations uses the traditional course of school mathematics, in particular the following questions: -Geometric Progression; -Percentile Function; -Percentages; -Logarithmic Function; -Logarithmic Equations and Inequalities; -Indicative Function; -Indicative Equations and Inequalities; -Systems of Equations. Exactly listed mathematical bases are used for practical financial calculations with regard to inflation, dynamics of exchange rates, interests. Below we will present and methodologically characterize three groups of typical tasks, placing them according to the level of complexity. The first is a descriptive level of typical tasks. Mastering this level is quite accessible for a high-school student, though it is traditionally and systematically carried out at universities. At the descriptive level, the level of familiarity with financial mathematics, all formulas and algorithmic action sequences are given without proof. Calculation technique is simplified, in some cases it is advisable to use ready-made approximate formulas. Deployment of training material is built on generally accessible examples from life and not rich practice of financial relations. A detailed logical and methodical analysis of the educational field of "Financial Mathematics" allowed to isolate from the classical theory of the paramount, the most necessary elements of financial mathematics for the daily life of any person.