Cálculo Financeiro

Basic knowledge in mathematics.

The theoretical contents of the curricular unit will be presented making use of educational resources as Exposition, Explanation, Dialogue and Questioning and illustrated whenever possible with practical cases. Students are encouraged to apply the competences acquired through practical activities, including the analysis of practical cases and exercises.

The main objectives of the course unit are to:

• provide students with the fundamental knowledge of Financial Mathematics;
• develop their ability to relate time, capital and interest, understand the time value of money, and analyse the main accumulation and discounting regimes;
• understand and apply different interest rates and establish equivalence relationships between cash flows;
• apply methods for the valuation of annuities and loan repayment;
• develop the ability to formulate and solve financial problems, interpret the results obtained, and support decision-making in practical contexts.

Given the predominantly applied nature of the course unit, fundamental concepts and principles will be combined with problem-solving and practical exercises. Particular emphasis will be placed on the correct formulation of problems, the selection of appropriate calculation methods, and the analysis and interpretation of results.

Chapter I – Fundamentals of Financial Mathematics

1. Fundamental Concepts
1.1. Time, capital and interest
1.2. Interest and discount rates
1.3. Present value and accumulated value

2. Accumulation and Discounting
2.1. Accumulation regimes
2.1.1. Simple interest
2.1.2. Compound interest

3. Interest Rates
3.1. Proportional and equivalent rates
3.2. Nominal and effective rates
3.3. Gross and net rates
3.4. Nominal and real rates

4. Equivalence of Cash Flows
4.1. Equation of value
4.2. Common principal
4.3. Common maturity date
4.4. Average maturity date

Chapter II – Annuities

1. Concepts and Classification of Annuities
1.1. Definition and classification
1.2. Annuities with constant payments
1.3. Annuities with variable payments
1.4. Fractional annuities with constant payments
1.5. Fractional annuities with variable payments

Chapter III – Financing Operations

1. Commercial Calculations
1.1. Bank discount of bills of exchange

2. Loan Repayment
2.1. Concepts and characteristics
2.2. Loan repayment methods
2.3. Preparation of amortisation schedules

1) Periodic Assessment

Periodic assessment comprises the following components:

• Participation and completion of in-class exercises - 5%;
• Group assignment - 10%, in accordance with the rules set out in the course unit presentation document;
• First written test - 35%;
• Second written test - 50%.

The final grade for continuous assessment is calculated as the weighted average of the assessment components listed above.

To pass the course unit through continuous assessment, students must obtain a final grade of at least 9.5 out of 20.

2) Assessment by Examination

Assessment by examination consists of an individual, in-person written examination, accounting for 100% of the final grade.

To pass the course unit under this assessment method, students must obtain a grade of at least 9.5 out of 20.

3) Additional Provisions

• The tests and examination are individual and in-person assessments. The use of any materials, devices or other resources not expressly authorised by the lecturer is prohibited.
• The group assignment and activities undertaken as part of the participation and completion of in-class exercises must be submitted by the deadlines established by the lecturer.
• Late submissions may only be accepted where they are duly justified and the justification is accepted by the lecturer, in accordance with the Academic Regulations for First-Cycle Study Programmes of ESTGOH.
• Any other matters relating to assessment, including absences, exceptional circumstances and examination periods, are governed by the Academic Regulations for First-Cycle Study Programmes of ESTGOH.

NAO