Name: THE MATHEMATICS OF FINANCIAL OPERATIONS
Code: 510201005
Type: Basic
ECTS: 6
Length of subject: Per term
Semester and course: 1st Year - First term
Speciality:
Language: English
Mode of study: On-site class
Lecturer data: RAMÓN LLORENS, MARÍA DEL CAMINO
Knowledge area: Economía Financiera y Contabilidad
Department: Economía, Contabilidad y Finanzas
Telephone: 868071045
Email: camino.ramon@upct.es
Office hours and location:
miércoles - 10:00 / 12:00
EDIFICIO CIM - FCCE, planta 1, Despacho FCE
Para quedar en un horario diferente mandar un correo electrónico: camino.ramon@upct.es
Tutorials will be carried out by request of the student sending an email to camino.ramon@upct.es
Qualifications/Degrees:
Academic rank in UPCT: Profesora Titular de Universidad
Number of five-year periods: 3
Number of six-year periods: 1 de investigación
Curriculum Vitae: Full Profile
Responsible for the groups: G1
RA36 ¿ Apply ethical and sustainability criteria in decision-making.
TYPE: Competencies
RA7 ¿ Describe and analyze the financial metrics of different investment and financing operations.
TYPE: Knowledge or content
Se desarrollan los conceptos básicos en el ámbito de las operaciones financieras, las leyes financieras que se aplican a la valoración de capitales financieros, la operativa con capitales financieros y su integración en las operaciones de ahorro y financiación más comunes.
UD.1: FUNAMENTAL CONCEPTS OF FINANCIAL MATHEMATICS
1.1.1. Financial Phenomenon
1.1.2. Financial Capital
1.1.3. Financial Space
1.2. Financial equivalence. Properties of equivalence
1.2.1. Financial Equivalence
1.2.2. Properties of equivalence
1.2.3 Financial preference
1.3. Financial laws. Properties
1.3.1. Financial laws
1.3.2. Properties of financial laws
1.4. The principle of capital equivalence
1.4.1. Properties of equivalence
1.4.2. Sum of financial capital
1.5. Financial operation. Classification
1.6. The financial factor
1.7. Mathematical reserve
UD.2: FINANCIAL LAWS OF CAPITALIZATION
2.1. Simple and compound capitalization
2.1.1. Introduction
2.1.2. Calculation of the total or final capital in simple capitalization
2.1.3. Calculation of the total or final capital end in compound capitalization
2.1.4. Graphic Representation
2.1.5. Analytic Justification
2.1.6. Interests for the commercial and calendar year in simple capitalization
2.1.7. Calculation of the duration of the operation
2.1.8. Calculation of the capital based on the previous one
2.1.9. Calculation of interest rate
2.2. Conventions for the calculation of the total in compound capitalization with split time
2.2.1. Exponential Convention
2.2.2. Linear Convention
2.2.3. Difference between both conventions
2.3. Calculation of time by linear convention
2.4. Calculation of the percentage by the linear convention
2.5. Inflation in financial operations
UD.3: FRACTIONED CAPITALIZATION
3.1. Simple fractional and compound capitalization
3.2. Equivalence amounts
3.3. T.A.E. or E.A.R (effective annual rate) and the nominal amount. Relations of equivalence between them
3.4. Relation between the nominal amount and the frecuency of capitalization
3.5. The anticipated annual interest rate. Equivalence with E.A.R
UD4: OPERATIONS IN CAPITALIZATION
4.1. Conversion of a capital in another multiple of itself
4.2. Displacement of capital
4.3. Equivalent capital units
4.3.1. Compound capitalization
4.3.2. Simple capitalization
4.4. Single capital. Common expiration
4.4.1. Single capital
4.4.2. Common Due Date
4.5. The average due date and the average amount
4.5.1. Average Due Date
4.5.2. Average Amount
D.U.5: THE FINANCIAL DISCOUNT OPERATION
5.1. The commercial discount operation
5.2. Simple update
5.2.1. Simple Rational Discount
5.2.2. Simple Commercial Discount
5.2.3. Both the equivalent interest to the discount
5.3. Compound update
5.3.1. Compound Rational Discount
5.3.2. Composed Commercial Discount
5.3.3.Both the equivalent interest to that of a discount
5.4. Comparison between simple rational discount and composed
rational discount
5.5. Equivalence of capital units and the discount
5.6. Bank commissions. Non-payment, return and overdue drafts re-exhange bill
D.U.6: INTRODUCTION OF FINANCIAL INCOMES
6.1. Concept of income
6.2. General income classification
6.3. Financial value of an income. Post-payability and pre-payability
6.3.1. Temporal, variable, immediate and post-payable income
6.3.2. Temporal, variable, immediate and pre-payable income
6.4. Calculation of the current value and the final of an immediate income
6.4.1. Current value of a constant, immediate and post-payable income
6.4.2. Current value of an immediate, constant and pre-payable income
6.4.3. Final value of a constant income, immediate and post-payable
6.4.4. Final value of a constant income, immediate and pre-payable
6.4.5. Relation between current value and final value
6.5. Deferred incomes
6.5.1. Current value of a constant income, post-payable and deferred
6.5.2. Current value of a constant income, pre-payable and deferred
6.5.3. Final value of a constant income, post-payable and deferred
6.5.4. Final value of a constant income, pre-payable and deferred
6.6. Anticipated incomes
6.6.1. Current value of a constant income, post-payable and anticipated
6.6.2. Final value of a constant income, post-payable and anticipated
6.7. Perpetual incomes
6.7.1. Current value of a constant, immediate, perpetual and
post-payable income
6.7.2. Current value of a constant, immediate, perpetual and
pre-payable income
6.7.3. Current value of a constant, deferred, perpetual and
pre-payable income
6.7.4. Current value of a constant, immediate, perpetual and
pre-payable income
6.8. Calculate the time in the post-payable immediate incomes
D.U. 7: CONSTANT FRACTIONAL INCOMES WITH HIGH PERIODICITY IN THE YEAR AND CONTINUOUS
7.1. Fractional, immediate, post-payable income
7.1.1. Current value
7.1.2. Final value
7.2. Fractional, immediate, pre-payable income
7.2.1. Current value
7.2.2. Final value
7.3. Deferred fractional income
7.3.1. Post-payable income. Current value
7.3.2. Pre-payable income. Current value
7.4. Anticipated fractional income
7.4.1. Post-payable income. Final value
7.4.2. Pre-payable income. Final value
7.5. Perpetual fractional income
7.5.1. Post-payable income. Current value
7.5.2. Deferred and post-payable income. Current value
7.5.3. Pre-payable income. Current value
7.5.4. Deferred and pre-payable income. Current value
7.6. Fractional incomes according to the equivalent amount
7.7. Periodicity incomes greater than a year: Immediate, deferred, anticipated and perpetual
7.7.1. Post-payable immediate income
7.7.2. Pre-payable immediate income
7.7.3. Deferred income
7.7.4. Anticipated income
7.7.5. Perpetuate income
7.7.6. Periodicity incomes greater than a year according to the equivalent amount
7.8. Continuous incomes
7.9. Incomes fractioned by annual block
D.U. 8: VARIABLE INCOMES IN GEOMETRIC AND ARITHMETIC PROGRESSION
8.1. Variable annual income in geometric progression
8.1.1. Post-payable income
8.1.2. Pre-payable income
8.1.3. Deferred income
8.1.4. Particular case of indetermination:
8.1.5. Perpetual Rent
8.2. Variable annual income in arithmetic progression
8.2.1. Post-payable terms
8.2.2. Pre-payable terms
8.2.3. Perpetual rent
8.3. Fractioned variable income
8.4. Fractioned variable incomes by annual blocks
8.5. Variable fractioned perpetual incomes by annual blocks
8.6. Continuous variable incomes
D.U. 9: AMORTIZATION OPERATION: GENERAL CASE. LOANS WITH SINGLE REIMBURSEMENT
9.1. The amortization operation. General concepts
9.2. Loan classification
9.3. General case
9.3.1. Post-payable interest
9.3.2. Pre-payable interest
9.4. Amortizable loans through single reimbursement
9.4.1. Amortizable loans through comprehensive single reimbursement of capital and interest: elemental loan operation
9.4.2. Amortization through single reimbursement of the capital, and interest paid periodically: American Loan Operation
D.U. 10: LOAN AMORTIZATION WITH CONSTANT INCOMES
10.1. French or progressive amortization system
10.2. German amortization system on anticipated interests
10.3. Particular case: Deferment (lack)
10.3.1. French Method
10.4. Loans with fractioned interest and annual amortization: French method
10.4.1. According to the Fractioned Amount
10.4.2. According the Nominal Amount
10.5. Loan with fractioned amortization and interest: French method
10.5.1. According to the Nominal Amount
GENERAL
During the course, activities related to the teaching-learning process will be carried out, as well as practical exercises to monitor the student's progress. These activities and final reports from the student in resolving practical exercises, for those who follow the continuous evaluation process (SEC) and wish to complete them, are valued up to 20% of the final grade (10% activities, 10% final report exercises). The grade obtained by the student in the voluntary completion of these participation activities and exercises will be retained during the academic year.
Promoting the continuous improvement of working and study conditions of the entire university community is one the basic principles and goals of the Universidad Politécnica de Cartagena. Such commitment to prevention and the responsibilities arising from it concern all realms of the university: governing bodies, management team, teaching and research staff, administrative and service staff and students. The UPCT Service of Occupational Hazards (Servicio de Prevención de Riesgos Laborales de la UPCT) has published a "Risk Prevention Manual for new students" (Manual de acogida al estudiante en materia de prevención de riesgos), which may be downloaded from the e-learning platform ("Aula Virtual"), with instructions and recommendations on how to act properly, from the point of view of prevention (safety, ergonomics, etc.), when developing any type of activity at the University. You will also find recommendations on how to proceed in an emergency or if an incident occurs. Particularly when carrying out training practices in laboratories, workshops or field work, you must follow all your teacher's instructions, because he/she is the person responsible for your safety and health during practice performance. Feel free to ask any questions you may have and do not put your safety or that of your classmates at risk.
Class in conventional classroom: theory, problems, case studies, seminars, etc
Described in the training program section. According to the subject's training program, instructional sessions will be conducted through lectures based on concepts and theories, with an estimated duration of 33 hours.
During the course, problem-solving classes will be held in instructional sessions aimed at developing practical knowledge, based on the resolution of exercises. The estimated duration of these sessions is 24 hours.
Achieved learning outcomes: RA36, RA7
57
100
Assessment activities (continuous assessment system)
Described in the evaluation activities section.
During the course, there will be 2 written tests corresponding to the 2 partial exams scheduled in the SEC (the 1st partial exam covering topics 1 to 5 with a weight of 30% of the final grade, and the 2nd partial exam covering topics 6 to 10 with a weight of 50% of the final grade), some participation activities in the teaching-learning process (weighting 10% of the final grade); a report on the practical exercises carried out during the course to monitor their learning (10% of the final grade). The minimum score to pass each of the partial exams will be 40% of its maximum score. The subject will be passed when the minimum scores in the partial exams are met, and the final grade is higher than 5 points out of 10 in the sum of the parts completed in the SEC.
Achieved learning outcomes: RA36, RA7
3
100
Assessment activities (final assessment system)
In the final evaluation system (SEF), a written test with a maximum duration of 120 minutes will be conducted (for those being examined on 100% of the material), structured in the same parts as the SEC (continuous evaluation system). Students can retain the grade obtained in the partial exam that meets the minimum required score, as well as the activities or the report of practical exercises they completed during the course, and will only need to be examined in the final evaluation for the partial exam not passed.
Achieved learning outcomes: RA36, RA7
3
100
Tutorials
Described in the tutoring section (15 hours), these sessions are aimed at resolving doubts, providing guidance, and monitoring the participation activities in the student's teaching-learning process.
15
50
Student work: study or individual or group work
It includes the completion of participation activities in the teaching-learning process and the submission of a course practical report (2 hours) by the student to develop practical knowledge of the subject (2 hours).
This study will enable the student to achieve all the learning outcomes.
Time dedicated to studying the subject.
72
0
Spoken or written exams
To pass the course through continuous assessment, students must take both midterm exams and achieve at least the minimum required score on each (40% of their respective weight in the final grade). The first midterm (covering topics 1 to 5) will be worth up to 3 out of 10 points of the final grade. The second midterm (covering topics 6 to 10) will be worth up to 5 out of 10 points of the final grade. The grade of any passed midterm may be retained for the entire academic year.
Achieved learning outcomes: RA36, RA7
80 %
Participation and involvement in the teaching-learning process
During the course, at least two participation activities related to the teaching-learning process will be carried out, which the student must submit in writing. These activities will have a total weight of up to 1 out of 10 points of the final grade and will be added to the other scheduled assessment activities.
Achieved learning outcomes: RA36, RA7
10 %
Presentation and defence of assignments
The activities included in SE2 will also be assessed through the student's in-class presentations, which will account for up to 10% of the final grade.
Achieved learning outcomes: RA36, RA7
10 %
Spoken or written exams
The exam corresponding to the final assessment system will be structured in the same parts as those included in the continuous assessment system.
Achieved learning outcomes: RA36, RA7
80 %
Participation and involvement in the teaching-learning process
The participation activities in the teaching-learning process will be assessed in the final exam through one or more practical exercises in which the student will perform financial calculations based on real cases (worth up to 1 out of 10 points).
Achieved learning outcomes: RA36, RA7
10 %
Evaluation of assignments and reports on practical sessions (final product, follow-up and contribution in the case of group work)
The activities related to the evaluation of assignments and reports will be assessed in the final exam through one or more theoretical questions based on real financial practices (worth up to 1 out of 10 points).
Achieved learning outcomes: RA36, RA7
10 %
If the overall grade for the course is equal to or higher than 5 but the minimum required score in the midterms has not been achieved, the student will be awarded a final grade of 4.5.
Author: Ramón Pintado, Tomás
Title: Fundamental Concepts of Financial Mathematics theory and practice
Editorial: Universidad Politécnica
Publication Date: 2011
ISBN: 9788496997707
Author: Ramón Pintado, Tomás
Title: Problemas de matemáticas financieras
Editorial: Universidad Politécnica de Cartagena
Publication Date: 2009
ISBN: 9788496997257
Author: Ramón Pintado, Tomás
Title: Matemáticas financieras
Editorial: Universidad Politécnica de Cartagena
Publication Date: 2009
ISBN: 9788496997264
Author: Pintado Ramón, Tomás
Title: Fundamental concepts of financial mathematics: theory and practice
Editorial: Universidad, Servicio de Documentación
Publication Date: 2011
ISBN: 9788496997707
Author: Levi, Eugenio
Title: Curso de matemática financiera y actuarial
Editorial: Bosch
Publication Date: 1973
ISBN: 8471626055
Author: Ferruz Agudo, Luis
Title: Operaciones financieras: descripción, análisis y valoración
Editorial: Ariel
Publication Date: 1994
ISBN: 843442097
Author: González Velasco, María del Carmen
Title: Análisis de las operaciones financieras (150 supuestos resueltos)
Editorial: Civitas
Publication Date: 2001
ISBN: 8447016188
Author: González Velasco, María del Carmen
Title: Análisis de las operaciones financieras
Editorial: Civitas,
Publication Date: 2008
ISBN: 9788447028931
Author: Navarro, Eliseo
Title: Fundamentos de matemáticas financieras
Editorial: Antoni Bosch
Publication Date: 2001
ISBN: 8495348012
Author: Gil Peláez, Lorenzo
Title: Matemáticas de las operaciones financieras: problemas resueltos
Editorial: Ac
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ISBN: 8472881229
Author: Lóbez Urquía, J.
Title: Matemática financiera: con nociones de cálculo actuarial
Editorial: s.n.
Publication Date: 1968
ISBN:
Author: Gil Peláez, Lorenzo
Title: Matemática de las operaciones financieras
Editorial: AC
Publication Date: 1987
ISBN: 8472881237
Author: Meneu, Vicente
Title: Operaciones financieras en el mercado español
Editorial: Ariel
Publication Date: 1994
ISBN: 8434420910