Financial Mathematics 2600-LFBRdz1MF
The course is divided into four parts. The first part is dedicated to the calculation of money changes over time, the so called TVM (Time Value Money) calculations. The problems of compound and simple interest are discussed as well as the mathematical and trade discount. Students will learn the rules for calculating the financial instruments such as promissory notes, treasury bills, term deposits, bills of exchange, loans, credits, etc. Students dealt with issues related to calculations of the time (both actual day-count method and 360 day-count method) and to customize interest rates for specified periods of time. The concept of the effective rate and the formula for the calculation of this rate depending on the number of compounding periods per year is introduced in the case of compound interest. The problems of inflation are discussed also. The basic tool in the discussion is the Fisher’s equation defining the relationship of nominal rate, rate of inflation and real interest rate. The formula for the calculation of the annual rate of inflation based on inflation rates in the subperiods is provided.
The second part of the course is devoted to the general issues associated with the problem of changes of the value of principal at the time. The universal model of capital change over time is built on the basis of the general rules of the determination of the value of money. The model is used to introduce the concept of equivalent equities and to perform calculations that confirm this equivalence. Students learn to use the derived formulas for comparing capital in different periods and predict their future value.
The third part concerns the project appraisal and investment performance. Dynamic methods of evaluating investment projects: the net present value (NPV), internal rate of return (IRR), profitability index (PI) and discounted payback period (the DPP) are discussed. Students learn to understand the importance of the given factors, calculate all of them and use the computed values to compare various investment projects based on established criteria that include restrictions on cost of capital or reinvestment rate.
The fourth part applies to annuities and repayments of debts. Students will learn the general calculation formulas and rules for their application. They solve problems for the valuation of cash flows (including infinity many cash flows) the missing instalment and the application of the balloon loan balance formula. The formula for calculation of the equated monthly instalment is provided. Students learn to construct a loan repayment plan according to various scenarios (fixed capital instalment or equated monthly instalment). They work on the actual examples from the Polish financial market.
Student should spend 70 to 100 hours of work, including the 30 hours to participate in the classes and the other, from 40 to 70 hours, to practice their skills of the use of appropriate formulas, perform calculations, and to search and recalculate of the actual financial instruments available on the real market.
Type of course
Prerequisites (description)
Learning outcomes
The general effects. After the completion of the course the student:
• has a basic understanding of concepts and categories related to economics, finance, accounting and insurance (K_W03);
• has the basic knowledge of quantitative analysis and statistical tools (K_W08)
• is able to correctly analyze the validity of action taken with finance and to request from them (K_U06).
The detailed effects. After the completion of the course the student:
• identifies and describes the characteristics of the underlying financial instruments, calculates their pricing and performs comparison;
• carries out the calculations concerning the basic financial instruments (loans, promissory notes, bank deposits, bill of exchange, etc.), develops loan repayment plans (either fixed capital installment or equated monthly installment);
• explains problems of impairment of value of capital, equity equivalent and applies the universal model of change of capital in time to update the capital to a specified time;
• analyzes the financial investments in terms of their cost effectiveness, applies dynamic methods of evaluating investment projects, calculates the basic indicators (NPV, IRR, PI, DPP) and compares various financial investments on the basis of the value of the indicators;
• calculates the valuation of annuities and finds the missing instalment.
• Students use EXCELA's financial functions related to financial mathematics.
Assessment criteria
Passing rules: pass consists of two tests (90% of possible points) and a term paper (10% of points). Each test must be completed with half the points, i.e. 22.5%. The pass mark is 60% of the points available.
60-68% - 3
69-74% - 3+
75-85% - 4
86-90% - 4+
91-100% - 5
Bibliography
1. Podgórska M., Klimkowska J., Matematyka Finansowa. PWN, 2013
2. Szałański M., Matematyka finansowa. Toruńska Szkoła Zarządzania, 2001
3. Piasecki K., Ronka-Chmielowiec W., Matematyka finansowa. Wydawnictwo C. H. Beck. 2011
Dodatkowo:
1. Sobczyk M., Matematyka finansowa, Placet, 2011
2. Kellison S., The theory of an interest. Irwin,1992
3. Jajuga K., Jajuga T. Inwestycje. PWN 2007
4. Szałański M., Matematyka finansowa wspomagana komputerowo, Wydawnictwo Naukowe Wydziału Zarządzania, 2003
5. S. J. Garret, An Introduction to the Mathematics of Finance. A Deterministic Approach. Elsevier, 2013.
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: