# Selected Chapters from Mathematics for Economists

- Credits: 6
- Ending: Examination
- Range: 2P + 2C
- Semester: summer
- Year: 1
- Faculty of Economic Informatics

## Teachers

## Included in study programs

**Teaching results**

Successful graduates of the course will have knowledge of linear algebra (vector calculus, matrices, determinants and systems of linear equations) and financial mathematics (interest rate, discounting, annuity and redemption) necessary for the study of other economic subjects. After completing the course, students will receive:

Knowledge

- understanding of the basic principles of linear algebra (mastering the connections between vector and matrix calculus and their use in solving systems of linear equations) and their simple applications in economics,

- mastering the method of elementary change of base and understanding the conclusions resulting from it in solving problems in linear algebra,

- understanding the basic principles of interest and discounting and their use in annuity and redemption, financial flows,

- awareness of the need to use quantitative (mathematical) methods in economic applications.

Skills

- solve basic problems from vector and matrix calculus, including simple economic problems,

- solve complex problems from linear algebra using the method of elementary base change,

- solve systems of linear equations (m equations with n unknowns) also using online applications,

- solve the basic tasks of interest rate and discounting and use them in the management of personal finances in the field of investing in common banking products,

- solve problems from financial equivalence and correctly interpret the results of solutions,

- solve the problems of annuity and redemption and use them in the management of personal finances in the area of credit products.

Competences

- actively apply knowledge and skills in financial mathematics in the analysis of investment and credit products of banking and non-banking financial institutions,

- make progress and develop its financial literacy in a targeted manner, depending on the life situations encountered,

- to expand their mathematical knowledge and skills and use them in other subjects of quantitative focus.

**Indicative content**

Vectors, linear combination, linear dependence and independence, rank and equivalence of vectors, linear space and subspace, basis and dimension, elemental change bases, matrices, systems of linear equations, determinants, systems of linear inequalities. Master basic concepts and calculation methods of simple and compound interest and discounting, continuous interest, annuities and redemption. Principles of valuation of financial flows. The use of computer programs in MS Excel calculations.

**Support literature**

1. Sakálová, K. - Simonka, Zs. - Strešňáková, A.: Lineárna algebra pre ekonómov. Bratislava: Letra Edu, 2020.

2. Fecenko, J., Sakálová, K. Matematika 2. Bratislava: ELITA/IURA Edition, 2005.

3. Huťka,V., Peller, F. Finančná matematika v Exceli. Bratislava: IURA Edition, 2010.

4. Šoba, O., Širůček, P. Finanční matematika v praxi. Praha: Grada, 2017.

**Syllabus**

1. The concept of vector. Vector operations. Scalar product. Linear combination, dependence and independence of vectors. Vector system, equivalent modifications of the vector system, rank of the vector system. 2. Linear space and subspace. Dimension and base of linear space. Coordinates of the vector in the base Ln. Elemental change of base and change of vector coordinates after EZB. 3. The concept of matrices, types of matrices, operations with matrices, their economic applications. Types of matrices. Block nuts. The rank of the matrix. Regular and singular matrices. Inverse matrix. Basic decomposition of a matrix into the product of matrices. Matrix equations. 4. Definition of determinant. Determinants of degree n and their calculation. Use of determinants. Systems of linear equations and methods of their solution. 5. Basic concepts of interest rate. Types of interest and their characteristics. Easy interest. Exact and banking method. Interest rate standards. Time charts. 6. The concept of discount. Mathematical and business discount. Discounting at simple interest. Bills of exchange in practice. Equivalent interest and discount rates. Compound interest. Comparison of JÚ and ZÚ. 7. Financial equivalence at compound interest. Nominal and effective interest rates. Interest intensity and continuous interest (informative). Equivalent relationships between compound and continuous interest. 8. Discounting at compound interest. Equivalent interest and discount rates. Financial flows. Analysis of financial flows. Investment decision criteria. 9. Annuities. The concept of financial annuities and types of annuities. Annual rent. Future value of constant half-yearly and pre-mortem annual rents, calculation of basic quantities. 10. Present value of constant half-yearly and pre-mortem annual rents, calculation of basic quantities. Eternal rent. 11. Future value of constant half-term and pre-mortem p-term annuities. Deferred p-term annuity. 12. Present value of constant half-term and pre-mortem p-term annuity. Eternal p-term annuity. Amortization count. Loan classification. Repayment of the loan in a single installment. 13. Gradual repayment loans - installment and annuity debt repayment. Redemption rules. Amortization plan.

**Requirements to complete the course**

The semester work - the written test - 30%,

The final written test (theory and examples) - 70%

**Student workload**

Total study load (in hours):

Participation in lectures – 26

Participation in exercises – 26

Preparing for exercise – 26

Preparation for course credit – 26

Exam Preparation (theory) - 26

Exam Preparation (examples) – 26

Total load - 156

**Language whose command is required to complete the course**

slovak

Date of approval: 10.02.2023

Date of the latest change: 15.05.2022