Mathematics for Finance (20644)
Degree/study: degree in Business Sciences
Year: 1st
Term: 3rd
Number of ECTS credits: 5 credits
Hours of studi dedication: 125 hours
Teaching language or languages: catalan
Teaching Staff: Oscar Elvira, Miquel Planiol
1. Presentation of the subject
Mathematics for Finance is based on an inequality, i.e. a sum of money does not have the same value today as it will have in the future. This inequality is the root of a mathematical discipline that is very practical in our everyday lives.
In the professional sphere, businesses have financial problems and need professionals who solve these problems with the knowledge that this subject provides.
In the private sphere, in personal finances, various financial operations have to be undertaken throughout a person's life, such as investing money that has been saved, or arranging debts in order to buy a car or a property, which are related to this subject.
The objective is to learn, and as much as possible, to enjoy learning, how to adapt mathematical theory to real life.
After an introduction to the key concepts, we will take the two basic operations of updating and capitalisation as the starting point. The various financial regimes and interest rates will be reviewed. One of the key points is the calculation of the AER and finally the valuation of returns, in both constitution and amortisation operations.
2. Competences to be attained
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General competences |
Specific competences |
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Instrumental 1. Basic general knowledge of financial mathematics. 2. Basic knowledge of the profession related with the financial sector (banks, savings banks, investment services companies, etc.) or in financial departments of any company. Interpersonal 1. Analysis skills. 2. Ability to decide between investment alternatives. Systemic 1. Solving everyday problems. 2. The ability to generate new ideas to finance a project or invest money. 3. Calculation of a return. |
1. Calculation of a final capital. 2. Calculation of an initial value and a future capital. 3. Calculation of the initial and final value of a model income. 4. Calculation of the initial and final value of a deferred, advance and permanent income. 5. Calculation of an AER on a 6-month deposit and a 10-year pension plan. 6. Calculation of the final value of a capital constitution operation. 7. Calculations of loan payments using the French and American amortization systems.
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3. Contents
Subject 1. Basic grounding
(Miner, chapter 1)
1.1. Financial capital.
1.2. Financial operation.
Subject 2. Financial laws. Capitalisation and updating
(Miner, chapters 2 and 3)
2.1. Financial laws and financial systems.
2.2. The most commonly used financial systems.
2.2.1. Simple updating and capitalisation.
2.2.2. Simple commercial / simple rational updating.
2.2.3. Compound updating and capitalisation.
Subject 3 . Financial operations and interest rates
(Miner, chapters 2 and 3)
3.1. Interest rates.
3.1.1. Nominal interest rates and effective interest rates.
3.1.2. Equivalences between interest rates.
3.1.3. The annual equivalent rate (AER).
3.2. Financial operations.
3.2.1. Definition and components.
3.2.2. Classification of financial operations.
3.2.3. Long-term operations. Operating procedure and examples.
3.2.4. Short-term operations. Operating procedure and examples.
Subject 4. Current net worth and internal rate of return
(Miner, chapters 9 and 10)
4.1. Current net worth.
4.2. Internal rate of return.
4.3. IRR and AER.
Subject 5. Study and valuation of discrete financial returns
(Miner, chapters 4, 6 and 7)
5.1. Definition and classification of financial returns.
5.2. Ordering of discrete returns.
5.3. Constant and immediate income.
5.4. Constant and deferred income.
5.5. Constant and early returns.
5.6. Split or mixed returns.
5.7. Prepayable and postpayable returns
5.8. Variable returns: in a geometric progression.
5.9. Variable returns: in an arithmetic progession.
Subject 6. Amortization operations (loans)
(Miner, chapter 8)
6.1. Definition.
6.2. General approach.
6.3. Specific cases.
6.3.1. The American method.
6.3.2. The French method.
6.4. The loan repayment table.
6.5. Extensions.
6.5.1. Exclusion period.
6.5.2. Variable interest rates.
Subject 7. Constitution operations
(Miner, chapters 5, 6 and 7)
7.1. Definition and components.
7.2. The constitution table.
4. Assessment
Students engage in continuous learning. Theory is constantly combined with practice, and the students will engage in constant self-evaluation while the subject is being taught, as it is based on exercises and practical cases that require the student to have assimilated the concepts discussed in class in order to resolve them.
The final mark consists of three components:
- Corrections of practical exercises, which must be done individually or in a group and handed in at seminars, will account for 10% of the final mark.
- A partial examination will account for 30% of the final mark.
- The final examination will account for 60%.
Students failing the examination can resit at the September sitting. In this case, the mark will be calculated based on 90% of the resit examination mark and 10% of the practical classes. The mark from practical classes is therefore retained, and the partial examination mark is not taken into account.
5. Bibliography and teaching resources
5.1. Basic bibliography
MINER, J. Curso de Matemàtica Financiera. Madrid: McGraw Hill, 2003.
BRUN, X.; ELVIRA, O.; PUIG, X. Matemàtica financiera y estadística bàsica. Barcelona: Profit, 2008.
5.2. Complementary bibliography
THEORY
BONILLA, M.; IVARS, A. Matemática de las operaciones financieras (teoría y práctica). Madrid: AC, 1994.
DELGADO, C.; PALOMERO, J. Matemática financiera. 6a. ed. Logronyo: Distribuciones Texto S.A., 1995.
GIL PELÁEZ, L. Matemática de las operaciones financieras. Madrid: AC, 1987.
MENEU, V.; JORDÁ, M. P.; BARREIRA, M. T. Operaciones financieras en el mercado español. Barcelona: Ariel, 1994.
RODRÍGUEZ, A. Matemáticas de la financiación. Barcelona: Ediciones S, 1994.
SANOU, L.; VILLAZÓN, C. Matemática financiera. Barcelona: Foro Científico, 1993.
TERCEÑO, A. i d'altres. Matemática financiera. Madrid: Pirámide, 1997.
VILLAZÓN, C.; SANOU, L. Matemática financiera. Barcelona: Foro Científico, 1993.
PRACTICAL
ALEGRE, P.; BADÍA, C.; BORRELL, M.; SANCHO, T. Ejercicios resueltos de matemática de las operaciones financieras. Madrid: AC, 1989.
CABELLO, J. M.; GÓMEZ, T.; RUIZ, F.; RODRÍGUEZ, R.; TORRICO, A. Matemáticas financieras aplicadas (127 problemas resueltos). Madrid: AC, 1999.
GIL PELÁEZ, L.; BAQUERO, M. J.; GIL, M. A.; MAESTRO, M. L. Matemática de las operaciones financieras. Problemas resueltos. Madrid: AC, 1989.
5.3. Teaching resources
6. Metodology
The methodology used is highly practical, with internalisation of the theoretical concepts explained by means of exercises and practical cases.
The organisation of the classes is structured around theory classes with all the students in the group, and seminars with a third of the group in each.
The new concepts to be covered will be set out in the theory classes, and work will be done initially by means of exercises.
The seminars include exercises and cases to establish the concepts worked on in the theory classes, and correction of the practical exercises that the students have solved and handed in.
There are also lectures for students providing more in-depth consideration of the topics covered.
Distribution of hours of work by students:
- Theory classes: 22 hours 30 min
- Seminars: 12 hours
- Partial examination: 1 hour 30 min
- Final examination: 2 hours
- Preparation of practical classes: 20 hours
- Reading and exercises: 45 hours
- Study for the final examination: 22 hours
TOTAL: 125 hours
7. Planning of activities