Course guide of Introduction to Financial Operations (2351114)

Not required

• Basic concepts: financial capital and operation.
• Classic financial theorems.
• Short-term operations.
• Annuity Theory.
• Constitution and amortization: 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.

Topic 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.

Topic 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.

Topic 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).

Topic 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.

Topic 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.

Topic 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.

Frías-Aceituno, J.V. (2025). Introducción Operaciones Financieras. Editorial: Técnica Avicam.

Frías-Aceituno, J.V. (2025). Introduction Financial Operations. Editorial: Técnica Avicam.

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

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. Docencia presencial en el aula 
• MD02. Estudio individualizado del alumno, búsqueda, consulta y tratamiento de información, resolución de problemas y casos prácticos, y realización de trabajos y exposiciones. 
• MD03. Tutorías individuales y/o colectivas y evaluación  

• MD01. Face-to-face teaching in the classroom.

The assessment system is primarily continuous. However, a single final assessment could be applied, which may when students are unable to comply with the continuous assessment method due to work commitments, health reasons, disability, mobility programmes or any other cause preventing them from following the continuous assessment regime. Students may apply for the Single Final Assessment in accordance with the Regulations on Student Assessment and Grading (Art. 8).

The continuous assessment system is based on:

• A ‘mid-term exam’, covering the first four units, will account for 40% of the course grade (4 points) and will consist of two parts: a theoretical section and a theoretical-practical section. Each part will have a maximum score of 10 points, with the theory section weighted at 30% (1.2 points) and the theory-and-practice section at 70% (2.8 points).

The theoretical section will consist of multiple-choice questions with a single correct answer. Incorrect answers will result in negative marks (students will be informed of the penalty); unanswered questions will neither add to nor deduct from the mark. The theoretical-practical section will consist of solving exercises.

To pass the mid-term exam, students must achieve a minimum mark of 4 out of 10 in each of its two parts: theory and theory-practice. Only if this minimum mark is achieved in both sections, the corresponding weighting will be applied to calculate the mid-term exam mark. Once the weighting has been applied, this requirement equates to obtaining at least 0.48 points in the theory section and 1.12 points in the theoretical-practical section.

If the minimum mark is not achieved in either part, the student must redo the exam again, during the ordinary examination period and on the date set by the Centre, solely for the part or parts in which they did not meet the minimum requirement. Furthermore, the student may choose to retake one or both parts of the partial exam, thereby waiving the mark previously obtained in the part or parts they are sitting. In such cases, the new mark obtained will replace the previous one for the relevant part.

• A ‘final exam’, to be held on the official date set by the Centre, which will consist of two parts: one covering the first four units and the other covering units 5 and 6.

The section covering the first four units – to be taken by students who have failed one or both parts of the mid-term exam or who wish to retake one or both parts to improve their mark – will have the same structure, weighting and requirements as the mid-term exam. If a student retakes one or both parts, the mark obtained will replace the previous mark for the relevant part.

Consequently, the section covering units 5 and 6 will account for 60% of the course grade (6 points) and will also consist of two parts: a theoretical part and a theoretical-practical part. Each part will have a maximum score of 10 points, with the theory section weighted at 30% (1.8 points) and the theory-and-practice section at 70% (4.2 points). The theory section will consist of multiple-choice questions with a single correct answer. Incorrect answers will result in negative marks (students will be informed of the penalty); unanswered questions will neither add to nor deduct from the total. The theoretical-practical section will consist of solving exercises.

To pass the section covering units 5 and 6, students must obtain a minimum of 4 points out of 10 in each of its constituent parts: theory and theory-practice. Only if this minimum mark is achieved in both sections, the corresponding weighting will be applied to calculate the mark for this test. Once the weighting has been applied, this requirement equates to obtaining at least 0.72 points in the theory section and 1.68 points in the theory-and-practical section.

On the day established by the Centre for the Ordinary Call, all students sitting the examination will first be examined on the content corresponding to units 5 and 6. Subsequently, those students who have failed any part of the mid-term exam covering units 1, 2, 3 and 4, or who choose to retake one or both parts of that exam, thereby forfeiting the mark previously obtained, will sit the exam on the part or parts 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 cases where a student does not achieve a minimum mark of 4 out of 10 in each of the sections (theory and theory-practice), both in the examination covering the first four units and in that covering units 5 and 6, the overall final grade of the subject will be the sum of the marks obtained in the mid-term and final examinations, up to a maximum of 3 points. Students who do not sit this final examination will be awarded the grade ‘Not presented’.

Summary of weightings and minimum requirements

In the Extraordinary Call, the assessment of the subject will be carried out entirely through an extraordinary exam, covering the entire syllabus, with a total score of 10 points, even if the continuous assessment system had been used during the course.

This exam will consist of three parts: one theoretical and two theoretical-practical. The theoretical part, covering the entire syllabus, will consist of multiple-choice questions with a single correct answer. Incorrect answers will be marked negatively (students will be informed of the penalty); unanswered questions will neither add nor subtract from the mark. This part will account for 30% of the course mark (3 points).

The two theoretical-practical sections will consist of completing exercises. The first theoretical-practical section will cover the first four units, and the second will cover units 5 and 6 of the syllabus. The first theoretical-practical section will account for 28 % of the course mark (2.8 points), and the second for the remaining 42% (4.2 points).

Therefore, to pass the exam, students must meet the following requirements:

1. Obtain a minimum of 4 points out of 10 in each of the three parts of the exam: the theoretical part; the theoretical-practical part covering units 1, 2, 3 and 4; and the theoretical-practical part covering units 5 and 6. Only if this minimum mark is achieved in all parts the corresponding weighting will be applied to calculate the final mark. Once the weighting has been applied, this requirement is equivalent to obtaining at least 1.20 points in the theory section, 1.12 points in the theory-and-practical section covering units 1 to 4, and1.68 points in the theory-and-practical section covering units 5 and 6.
2. The sum of the marks obtained in the three parts must be equal to or greater than 5 out of 10.

In cases where the above requirements are not met, the overall mark for the examination and, therefore, the final grade of the subject will be the sum of the marks obtained in the various sections, up to a maximum of 3 points.

As this is an Extraordinary Examination Session, previous marks obtained in Continuous Assessment or the Single Final Assessment will not be considered.

Summary of weightings and minimum requirements

For those students who have been granted the single final assessment in accordance with the University of Granada’s Regulations on Student Assessment and Grading, the assessment of the course will be carried out entirely through a single examination, covering the entire syllabus, out of a total of 10 points.

This examination will consist of four parts:

1. A theoretical section covering the first four units, weighted at 12% of final grade (1.2 points).
2. A theoretical section covering units 5 and 6, accounting for 18% (1.8 points).
3. A theoretical-practical section covering the first four units, accounting for 28% (2.8 points).
4. A theoretical-practical section covering units 5 and 6, accounting for 42% (4.2 points).

The theoretical section will consist of multiple-choice questions with a single correct answer. Incorrect answers will be marked negatively (students will be informed of the penalty); unanswered questions will neither add to nor deduct from the mark. The theoretical-practical section will consist of solving exercises.

To pass the subject, students must obtain a minimum of 4 points out of 10 in each and every one of its constituent parts. Only if this minimum mark is achieved in all parts, the corresponding weighting will be applied to calculate the final grade. Once the weighting has been applied, this requirement equates to obtaining at least 0.48 point in part (a), 0.72 points in part (b), 1.12 points in part (c) and 1.68 points in part (d).

In cases where this latter requirement is not met, the overall mark for the exam and, therefore, the final grade of the subject will be the sum of the marks obtained in each section, up to a maximum of 3 points. Furthermore, to pass the subject, the total score must be equal to or higher than 5 points out of 10.

Students who do not sit this final examination will be marked as ‘Not presented’.

Summary of weightings and minimum requirements

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).

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).

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