Course detail

Financial Mathematics

FP-fmaPAcad. year: 2026/2027

The Financial Mathematics course focuses on teaching the fundamental mathematical methods and techniques used in finance. The course covers a wide range of topics, including simple and compound interest, short-term securities valuation, time value of money analysis, portfolio theory, and investment decision-making. Students will learn to calculate the value of annuities and rents, the principles of debt amortization, and the basic rules for valuing bonds and stocks. The course also includes the analysis of derivative instruments and foreign exchange market operations. Upon completing the course, students will be able to apply mathematical tools to real financial problems and make effective investment and financial decisions.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

Natálie Rontóová, Ph.D.

Department

Institute of Informatics (ÚI)

Entry knowledge

Basic knowledge in the scope of mathematics and statistics courses.

Rules for evaluation and completion of the course

Requirements for awarding a graded credit:
Completion of control tests and achieving at least 50% of the points or completion of a comprehensive written assignment and achieving at least 50% of the points. The final classification will be according to the ECTS grading scale.

Individual study plan
For ISP, the conditions are identical, except for any mandatory participation in classes. Deadlines for course completion are arranged individually according to the conditions approved in the ISP.

Attendance at seminars is monitored.

Aims

The aim of the course is to provide students with fundamental knowledge of mathematical methods and their applications in the field of finance. Upon completing the course, students will learn to use mathematical tools for analyzing specific financial problems.

Study aids

See the literature.

Prerequisites and corequisites

Not applicable.

Basic literature

CIPRA, Tomáš. Praktický průvodce finanční a pojistnou matematikou. Vyd. III. / v Ekopressu II. Praha: Ekopress, 2015. ISBN 978-80-87865-18-7. (CS)

Recommended reading

PEREN, Franz W. Financial math for business and economics: compendium of essential formulas. Berlin: Springer, 2023. ISBN 978-3-662-67645-5. (EN)
RADOVÁ, Jarmila. Finanční matematika pro každého: 8. rozšířené vydání. Grada, 2013. ISBN 9788024748313. (CS)
ŠOBA, Oldřich. Finanční matematika v praxi: 2., aktualizované a rozšířené vydání. Grada, 2017. ISBN 9788027102501. (CS)
SHARPE, William F., GORDON J. ALEXANDER a JEFFERY V. BAILEY. Investments. 6. vyd. Upper Saddle River: Prentice Hall, 1999.  ISBN 0-13-010130-3. (EN)

Classification of course in study plans

  • Programme BAK-MIn Bachelor's 1 year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

13 hours, optionally

Teacher / Lecturer

Natálie Rontóová, Ph.D.

Syllabus

  1. Introduction to financial mathematics. Simple interest.
  2. Compound interest.
  3. Time value of money.
  4. Annuities and rents. Debt amortization.
  5. Bonds. Stocks.
  6. Derivative instruments. Portfolio theory.
  7. Foreign exchange market operations. Summary of covered material.

Exercise

26 hours, compulsory

Teacher / Lecturer

Natálie Rontóová, Ph.D.

Syllabus

  1. Fundamentals of discipline-focused mathematical methods. Introduction to financial mathematics.
  2. Simple interest and discounting: interest and discount calculations; basic applications to short-term transactions.
  3. Compound interest (part I): compound interest, mixed interest, continuous compounding.
  4. Compound interest (part II): interest with random interest rate, real interest rate.
  5. Time value of money: value equation, present value, rate of return, payback period.
  6. Investment decision criteria. Summary of covered topics.
  7. Annuities and rents: calculations of regular payment values, annuity schemes, applications to mortgages.
  8. Debt amortization: creating amortization schedules, calculating installments and interest costs.
  9. Bonds: bond valuation, yield.
  10. Investments in the stock market.
  11. Derivative transactions: forwards, futures, swaps, options. Portfolio theory: risk, construction, basic financial analysis models.
  12. Summary of covered topics.
  13. Foreign exchange market operations.  Applications of financial mathematics in practice.

 

Professional knowledge:

The student knows the basic principles of financial mathematics, including simple and compound interest, the time value of money, annuity and rent calculations, debt amortization, bond valuation, derivative transactions, and portfolio theory. They also understand foreign exchange market operations and the practical application of financial mathematics in an economic context.

Professional competence:

The student is able to select and apply appropriate mathematical methods to solve problems in financial mathematics. They can interpret the results of calculations in both economic and investment contexts.

Professional skills:

The student can perform calculations related to financial products and decisions, using a calculator or software tools, and presents the results clearly and accurately.

Self-study

35 hours, optionally

Teacher / Lecturer

Natálie Rontóová, Ph.D.

Individual preparation for an ending of the course

30 hours, optionally

Teacher / Lecturer

Natálie Rontóová, Ph.D.