Course guide of Introduction to Financial Operations (2261114)

They are not required.

• Basic concepts: financial capital and financial operation.
• Classic financial theorems.
• Short-term operations.
• Annuity Theory.
• Constitution and amortization of a loan: dynamics and effective interest rate.

The objective of this program is to provide the student with an overview of the basic concepts of Financial Mathematics.

More specifically, the student:

• will understand the simple financial theorem and will applicate it to short-term operations.
• will understand the compound and continuous financial theorems.
• will know how to identify and value an annuity.
• will understand the concepts of loan and obligation and calculate the magnitudes related to them.

Unit 1. Basic concepts.

1. Financial Capital.
2. Financial Theorem. Properties.
3. Financial Operation.
4. Mathematical reserve or financial balance.
5. Commercial characteristics, effective interest rate and APR.
6. How interest rates are formed. The EURIBOR.

Unit 2. Simple interest.

1. Simple capitalization with due interest rate.
2. Simple discount with due interest rate or Rational Discount.
3. Simple discount with prepaid interest rate or Commercial Discount.
4. Change in units of measure: equivalent rates.
5. Substitution of capital: common maturity and average maturity.
6. Annex I: Simple capitalization with prepaid interest rate.
7. Annex II: Comparison of the different theorems.

Unit 3. Short-term operations.

1. Discount of bills of exchange.
2. Settlement of current savings accounts.
3. Settlement of current credit accounts.
4. Market operations:
   1. Spot purchase-sale.
   2. Forward purchase-sale.
   3. Operations with repurchase agreement (REPO).

Unit 4. Compound and continuous theorems.

1. Compound capitalization with due interest rate.
2. Compound discount with due interest rate.
3. Change in units of measure: equivalent rates.
4. Effective and nominal interest rate.
5. Continuous capitalization and discount.
6. Application of compound and continuous theorems.
7. Annex I: Compound capitalization and discount with prepaid interest rate.
8. Annex II: Comparison between the different theorems.

Unit 5. Valuation of annuities.

1. What is an annuity? Types of annuities.
2. Value of an annuity: present and future values.
3. Constant progressions: ordinary and perpetuity.
4. Geometric progressions: ordinary and perpetuity.
5. Arithmetic progressions: ordinary and perpetuity.
6. Fractional progressions.
7. Examples. Constitution of a capital through an annuity.

Unit 6. Loans.

1. What is a loan?
2. Evolution of a loan.
3. Amortization systems.

   1. Periodic payment of interest.

   2. French system.

   3. Constant repayment amortization.

4. Floating interest rate loans.
5. Grace period and cancellation in a loan.
6. Commercial characteristics: Effective interest rate and TAE.
7. Amortized Cost.
8. Annex I: Amortization with Geometric or Arithmetic payments.
9. Annex II: Sinking Fund and German System.

The theory program is complemented by the practical program.

CAPINSKI, M., & ZASTAWNIAK, T. (2003). Mathematics for finance: an introduction to financial engineering (1st ed. 2003). Springer London. https://doi.org/10.1007/b97511

FRÍAS-ACEITUNO, J.V. (2025). Introduction to Financial Operations. Editorial: Técnica Avicam.

FRÍAS-ACEITUNO, J.V. (2025). Introducción Operaciones Financieras. Editorial: Técnica Avicam.

LOVELOCK. D., MENDEL, M. & WRIGHT, A.L. (2007). An Introduction of he Mathematics of Money. Saving and Investing (1st ed. 2000). Springer New York. ISBN: 978-0387-34432-4.

PETTERS, A. O., & DONG, X. (2016). An Introduction to Mathematical Finance with Applications: Understanding and Building Financial Intuition (1st ed. 2016). Springer New York. https://doi.org/10.1007/978-1-4939-3783-7

POLLARD, A. H. (1977). An introduction to the mathematics of finance (Second edition). Pergamon Press.

ALEGRE ESCOLANO, P. y otros. (1989): Ejercicios resueltos de matemática de las operaciones financieras. Ediciones AC.

ALEGRE ESCOLANO, P. y otros. (1997): Curso interactivo de matemática financiera. Editorial McGrawHill.

BONILLA, M.; IVARS, A.; MOYA, I. (2006): Matemática de las Operaciones Financieras: teoría y práctica. Editorial Thomson.

DE PABLO, A. (1994): Unidades didácticas de matemáticas de las operaciones financieras. UNED.

GARCÍA BOZA, J. (2002): Problemas resueltos de matemática de las operaciones financieras, Ed. Pirámide, Madrid.

GARCÍA BOZA, JUAN (2011). Matemáticas Financieras. Editorial: Pirámide.

GIL PELAEZ, L. (1987): Matemática de las operaciones financieras. Editorial AC.

GIL PELAEZ, L. (1987): Matemática de las operaciones financieras: problemas resueltos. Editorial AC.

GONZÁLEZ CATALÁ, V. (1992): Análisis de las Operaciones Financieras, Bancarias y Bursátiles. Ciencias Sociales, Madrid.

GONZÁLEZ CATALÁ, V. (1999): Operaciones Financieras, Bancarias y Bursátiles. Curso práctico. Ciencias Sociales, Madrid.

MENEU, V.M.; JORDÁ, M.P.; BARREIRA, M.T. (1994): Operaciones Financieras en el Mercado Español. Editorial Ariel Economía.

RODRIGUEZ RODRÍGUEZ, A. (1984): Matemática de la financiación. Romagraf. S.A.

TOVAR JIMENÉZ, JOSÉ (2ªedición): Operaciones Financieras (Teoría y Problemas Resueltos). Editorial CEF.

• European Central Bank
• Tesoro público
• Banco de España
• Financial Times
• Invertia. El Español

• MD01. Face-to-face teaching in the classroom 
• MD02. Individual work by the student; retrieval, consultation and processing of information; problem solving and practical case studies; and completion of assignments and presentations 
• MD03. Individual and/or group tutoring and evaluation  

The preferred system will be the continuous assessment system. However, a single final assessment could be applied when students cannot comply with the continuous evaluation method for working reasons, health status, disability, mobility programs or any other justified cause. The student may request the single final assessment in accordance with the Student Assessment and Grading Regulations (art. 8).

The continuous assessment system is based on:

• A mid-term exam, corresponding to the first four units, that will suppose a 40% of the final grade for the subject (4 points). This exam will consist of two parts: theory and theoretical-practical, each of them will have a maximum score of 10 points. Theory will be weighted at 30% (1.2 points), and theoretical-practical part, at 70% (2.8 points).

To pass this exam, students must obtain at least a minimum of 4 points out of 10 points in each of above parts (0.48 points in theory and 1.12 points for the theoretical-practical part). Otherwise, the grade will be "Not Passed", and the student will have to redo an exam of this part of the subject (Units 1 to 4) in the Ordinary Call on the date set by the Center. Likewise, students may also choose to redo the mid-term exam (Units 1 to 4), renouncing the grade obtained in the previous mid-term exam, on the day set in the Centre's exam calendar for the Ordinary Call of this subject. In this case, the mark obtained in the new exam will replace the mark obtained previously.

The theoretical part will consist of multiple-choice questions with only one correct answer. Wrong answers will be marked negatively (the student will be informed of the penalty), questions not answered neither add nor subtract. The theoretical-practical part will consist of solving several exercises.

• A final exam to be taken on the official date set by the Center (Ordinary Call), which will consist of two parts, one corresponding to units 1 to 4 and the other, for units 5 and 6.

The part corresponding to the first four units, which will only be taken by those students who have not passed the mid-term exam or who have renounced to their grade, will have the same structure, weight and requirements for passing it as the mid-term exam. The part corresponding to units 5 and 6 will account for 60% of the final grade for the subject (6 points) and will also consist of two parts: theoretical and theoretical-practical. Each of them will have a maximum score of 10 points and will be weighted at 30% for the theory (1.8 points) and 70% for the theoretical-practical part (4.2 points). The theoretical part will consist of multiple-choice questions with only one correct answer. Wrong answers will be marked negatively (the student will be informed of the penalty), questions not answered neither add nor subtract. The theoretical-practical part will consist of solving exercises.

To pass the part corresponding to subjects 5 and 6, the student will have to obtain a minimum of 4 points out of 10 points in each of the above parts (0.72 points in the theory and 1.68 points for the theoretical-practical part).

On the day established by the Centre for the Ordinary Call, firstly, all students will be examined on the contents corresponding to subjects 5 and 6. Subsequently, those students who have not passed the mid-term exam or have opted to renounce the mark obtained in the mid-term exam, will be examined on the contents corresponding to the first four units.

In summary, students will have to meet the following requirements to pass the subject:

1. Pass the exam corresponding to units 1 to 4.
2. Pass the exam corresponding to units 5 and 6.
3. The sum of the marks obtained in the first (Units 1 - 4) and second part (Units 5 and 6) must be equal to or higher than 5 points out of 10.

In those cases in which the student does not obtain a minimum mark of 4 out of 10 points in each of the parts (theory and theoretical-practical), both in the exam corresponding to units 1 to 4 and in the exam corresponding to units 5 and 6, the overall final grade of the subject will be the sum of the marks obtained in the partial and final exam, with a maximum of 3 points. The student who does not appear for the final exam (Ordinary Call) will have the qualification of "Not presented".

In the Extraordinary Call, the assessment of the subject will be carried out entirely through an extraordinary exam, corresponding to the whole syllabus (Units 1 - 6), with a total score of 10 points, even if during the development of the subject the student had opted for the continuous evaluation system.

The exam in the Extraordinary Call will consist of three parts, one theoretical and two theoretical-practical. Thetheoretical part, corresponding to the whole syllabus, will consist of multiple-choice questions with only one correct answer. Wrong answers will be marked negatively (the student will be informed of the penalty), questions not answered neither add nor subtract. This part will account for 30% of the final grade for the subject (3 points). The two theoretical-practical parts will consist of solving exercises. The first theoretical-practical part will correspond to the first four units and the second one to units 5 and 6. The first theoretical-practical part will account for 28% of the final grade for the subject (2.8 points) and the second, the remaining 42% (4.2 points).

Additionally, the following requirements must be met by students to pass the exam:

1. Obtain a minimum of 4 points out of 10 in each of the parts, i.e. 1.20 points in the theoretical part, 1.12 points in the first theoretical-practical part and 1.68 points in the second theoretical-practical part.
2. The sum of the scores obtained in the three parts must be equal to or higher than 5 out of 10 points.

In those cases, in which the above requirements are not met, the overall mark of the exam and, therefore, the final grade of the subject will be a maximum of 3 points.

The student who does not appear for this final exam will have the qualification of "Not presented".

Being an extraordinary call, the previous qualifications obtained in the continuous assessment system or final single assessment will not be considered.

For those students who have not taken the partial exam and, therefore, have chosen the Single Final Assessment system, the evaluation of the theoretical and practical contents of the subject will be carried out entirely through a single exam, corresponding to the whole syllabus (Units 1 - 6), with a total score of 10 points.

This exam will consist of four parts: a) theoretical part corresponding to the units 1 to 4 weighting a 12% of final grade, b) theoretical part corresponding to units 5 and 6 with a weighting a 18% of final grade, c) theoretical-practical part corresponding to units 1 to 4 weighting a 28% of final grade, and d) theoretical-practical part corresponding to units 5 and 6 weighting a 42% of final grade.

To pass the subject, the student must obtain a minimum of 4 points out of 10 in each of the parts of the exam. In those cases, in which this last requirement is not met, the overall mark of the exam and, therefore, the final grade of the subject will be a maximum of 3 points. Likewise, to pass the subject, the total score must be equal to or higher than 5 points out of 10.

The theoretical part will consist of multiple-choice questions with only one correct answer. Wrong answers will be marked negatively (the student will be informed of the penalty), the questions not answered neither add nor subtract. The theoretical-practical part will consist of solving exercises.

The student who does not appear for this final exam will have the qualification of "Not presented".

Students must necessarily be provided with the respective D.N.I., driver's license or official passport to take any of the programmed exams.

INCLUSION and DIVERSITY. In the case of students with disabilities or other specific educational support needs (NEAE), the tutoring system will be adapted to these needs, in accordance with the recommendations of the area with powers in inclusion of the University of Granada, being the departments and centers the responsible for establishing appropriate measures so that tutoring takes place in accessible places. Likewise, at the request of the teaching staff, support may be requested from the competent unit of the UGR when special methodological adaptations are involved.

Información de interés para estudiantado con discapacidad y/o Necesidades Específicas de Apoyo Educativo (NEAE): Gestión de servicios y apoyos (https://ve.ugr.es/servicios/atencion-social/estudiantes-con-discapacidad).