BPF_FIMA Financial Mathematics

Faculty of Economics and Administration
Autumn 2012
Extent and Intensity
1/2. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
Ing. Luděk Benada, Ph.D. (lecturer)
Ing. Boris Šturc, CSc. (lecturer)
Ing. Luděk Benada, Ph.D. (seminar tutor)
Ing. Mgr. Juraj Hruška, Ph.D. (seminar tutor)
Mgr. Silvie Zlatošová, Ph.D. (seminar tutor)
Guaranteed by
Ing. Luděk Benada, Ph.D.
Department of Finance – Faculty of Economics and Administration
Contact Person: Iva Havlíčková
Supplier department: Department of Finance – Faculty of Economics and Administration
Timetable
Mon 11:05–12:45 P102
  • Timetable of Seminar Groups:
BPF_FIMA/01: Thu 12:50–14:30 VT203
BPF_FIMA/02: Thu 14:35–16:15 VT203, L. Benada
BPF_FIMA/03: Thu 18:00–19:35 VT206, J. Hruška
BPF_FIMA/04: Thu 11:05–12:45 VT203, L. Benada
BPF_FIMA/05: Thu 16:20–17:55 VT203, L. Benada
BPF_FIMA/06: Thu 9:20–11:00 VT203, L. Benada
BPF_FIMA/07: Mon 14:35–16:15 VT105, S. Zlatošová
Prerequisites (in Czech)
! PFFMFP Financial mathematics for FP
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 170 student(s).
Current registration and enrolment status: enrolled: 0/170, only registered: 0/170, only registered with preference (fields directly associated with the programme): 0/170
fields of study / plans the course is directly associated with
Course objectives
After passing the course is student able to: make clear the fundamentals of financial mathematics and the principles of interest, make use of the interest in fundamental areas of financial mathematics and apply acquired knowledge to the related areas which are not discussed within this course.
Syllabus
  • Thematic plan – lectures:
  • 1. Revision of basic concepts of mathematics (percentage calculation, linear function, exponential function, logarithmic function, calculations with logarithms, sequences and series, means).
  • 2. Single interest. Concept of interest and its calculation, interest period, single interest after-term and before-term, interest number and interest divisor.
  • 3. Discount factor, concept of discount, business (bank) and mathematical discount and their comparison.
  • 4. Compound interest, combination of single and compound interest. Calculation of deposit period, initial capital and interest rates.
  • 5. Nominal and real interest rate. Effective interest rate, interest intensity. Short-term savings after term before-term.
  • 6. Savings long-term before-term, after-term, combination of short-term and long-term savings. Calculation of initial value, calculation of saving period, interest rate.
  • 7. Pensions. Issue of pensions. Pensions immediate after-term, before-term, pensions paid m-times a year.
  • 8. Pensions postponed before-tem, after-term. Perpetual pensions after-term, before-term. Retirement income insurance.
  • 9. Extinguishing debts. Extinguishing debts by unequal repayments, extinguishing debts by equal annuities, determination of number of annuities, determination of debt residue, comparison of extinguishing method with method of decreasing fund, changes in redemption condition - summary method.
  • 10. Methods of interest of checking accounts, bank overdrafts, their usage and interest running.
  • 11. Exchange operations and compound interest. Determination of bond prices, simplified procedure of determination of bond prices, determination of bond prices between coupon dates, estimation of expected rate of return on bonds.
  • 12. Characteristic of assets I. Tangible assets, intangible assets, expected return on assets, risk of changes of return on assets, non-risk assets
  • 13.Characteristic of assets II. Estimation of expected rate of return and risk of asset by historical method and by expert method.
  • Thematic plan - seminars:
  • 1. Introductory tutorial: way of work in tutorials, conditions of evaluation.
  • 2. Revision of elemental concepts (percentage calculation, linear function, exponential function and its use in financial mathematics, logarithmic function and numerical operations with logarithms, sequences and series and its use in financial mathematics)
  • 3. Single interest (calculation of interest, basic equations of single interest, calculation of deposit period, calculation of initial capital for before-term, after-term interest, use of interest number and interest divisor, calculation of business and mathematical discount, use of discount factor in practice)
  • 4. Compound interest (basic concepts, derivation of relation for compound interest, calculation of final and initial capital, calculation of deposit period and interest rate, combination of single and compound interest – calculations)
  • 5. In-term test I
  • 6. Nominal and real interest rate (nominal interest rate, real interest rate, effective interest rate, interest intensity, exercises for short-term savings, calculation of saving amount)
  • 7. Savings, combination of short-term and long-term savings (calculation of saving amount, saved amount, calculation of saving period and final capital, calculations of long-term before-term and after-term savings)
  • 8. Pensions (calculations of annual pensions immediate before-period, after-period, calculations of pensions immediate before-term and after-term paid m-times a year, pensions postponed and pensions with declining pension payment, pensions perpetual and their calculations)
  • 9. Extinguishing debts (extinguishing debts by unequal repayments, creation of extinguishing plan, extinguishing debts by equal annuities and determination of number of annuities, calculation of annuities paid m-times a year and interest running of debt m-times a year)
  • 10. In-term test II
  • 11. Checking accounts (used methods for interest calculation, depreciated method, regressive method, successive method)
  • 12. Bank overdrafts (interest of banks overdraft, practical calculations of costs)
  • 13. Characteristics of assets (calculations of rate of profit and risk of changes in this rate, calculation of bond price, duration)
  • Students will individually solve tasks where they use theoretical fundamentals of financial mathematics from lectures and their self-study.
Literature
    required literature
  • ČERVINEK, Petr and František ČÁMSKY. Finanční matematika - Distanční studijní opora. 2009, 91 pp. info
  • RADOVÁ, Jarmila, Petr DVOŘÁK and Jiří MÁLEK. Finanční matematika pro každého. 7. aktualiz. vyd. Praha: Grada, 2009, 293 s. ISBN 9788024732916. info
    recommended literature
  • CHÝNA, Vladislav and Jiří MÁLEK. Finanční matematika v příkladech. Edited by Jarmila Radová. 2. vyd. Praha: Professional Publishing, 2005, 160 s. ISBN 8086419975. info
  • CIPRA, Tomáš. Finanční a pojistné vzorce. 1. vyd. Praha: Grada, 2006, 374 s. ISBN 802471633X. info
Teaching methods
lectures, during the seminars - solving of problems related to interest, savings, annuities and credits
Assessment methods
The course has a form of lectures and seminars (1/2 per week).
Exam: written
1. The in-term test I and in-term test II will be written in the seminars, in the weeks given by the time schedule (if a student is unable to take one of these in-term tests (no more than one test) – a lecturer will consider student apology and can enable the student to take a substitute test of the whole course at the beginning of the examination period. The evaluation of the substitute test will be the same as evaluation of the scheduled in-term tests.)
2. The final evaluation of results of work in the seminars (the prerequisite for taking part in the exam is both passing scheduled in-term tests and a minimum 70 % attendance in the seminars, the prerequisite for passing the test is 60 % success rate and more.)
3. The exam and final evaluation (the exam has two parts – running, which consists of the in-term test I, in-term test II and the final test).
Each test consists of three problems of different difficulty.

The final grade is comprised of:
Evaluation of In-term test I (25 %) + evaluation of In-term test II (25 %) + Final test (50 %)
Student knowledge will be assessed using the following grading scheme:
A= 92 – 100 %
B= 84 – 91 %
C= 76 – 83 %
D= 68 – 75 %
E= 60 – 67 %
F= less than 60 %

Important information! If student commits a prohibited act, such as usage of various forbidden tools, cribbing, taking out any part of the exam or any other cheating, teacher is allowed to interrupt an exam and to grade a student with F, FF or FFF according to the seriousness of the offence. Mentioned procedure relates to all the activities that are included to the final evaluation of the course (seminar work, essays, tests etc.).
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
General note: Nezapisují si studenti, kteří absolvovali předmět PFFMFP.
Credit evaluation note: k=1,33.
The course is also listed under the following terms Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2012, recent)
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