Financial Calculus


At the end of this course the student will have acquired the knowledge, skills and competences that will allow them to:

Learn introductory concepts related to Mathematics of Finance;

Understand the concepts of time value of money, interest rates and interest rate;

Calculate Current Value and Value Accumulated capital in different moments in time;

Understand the concept of Financial Annuities and apply it in various scenarios;

Build and analyse Classic Loans and Bond Loans;

Analysis of the viability of an investment by the NPV and IRR;

Identify some Risk Measures of Interest Rate.

This course will also provide the foundations to develop expertise in the areas of Actuarial Studies and Finance.

General characterization





Responsible teacher

Inês Jorge da Silva Sequeira, Rui Manuel Rodrigues Cardoso


Weekly - 4

Total - 60

Teaching language



Students should have knowledge at the level of mathematical analysis (sequences in arithmetic progression and geometric sums, series, differentiation and integration) and probabilities.


McCutcheon, J. and Scott, W.. An Introduction to the Mathematics of Finance. The Institute of Actuaries and the Faculty of Actuaries, 1998. 

Broverman, S.A.. MathematicsofInvestment and Credit, 7thEdition, ACTEXAcademic Series, 2017.

Barroso, M.N., Couto, E. e Crespo, N.. Cálculo e Instrumentos Financeiros: da prática para a teoria, Escolar Editora 2009.

Nicolau I. e Rodrigues J.A.. Elementos de Cálculo Financeiro, 9ª Edição, Áreas Editora, 2010.

Mateus, J.. Cálculo financeiro, 5ª Edição, Edições Sílabo, 2002.

Matias, R.. Cálculo financeiro: teoria e prática, 6ª Edição, Escolar Editora, 2018.

Teaching method

The teacher presents the themes using slides and privileging the exchange of ideas to reach the goal of each lesson. Students perform exercises and practical applications of the concepts acquired in class throughout the semester. Whenever possible the matter is illustrated with real examples from financial activity. Classes take place in a computing laboratory solving exercises using proper software.

Evaluation method


Attendance at the course is given to students who attended, at least, at 2/3 of the classes.

Continuous Evaluation

The continuous assessment is composed of 2 tests. Let T1 and T2 the grades obtained in each test by chronological order. Let AC=0.5*T1+0.5*T2. The student succeed if AC>=9.5

Evaluation by exam

Let ER be the grade obtained in the Exam. The student succeed if ER>=9.5

Grades Improvements and Defenses

The student wishing to improve the grade must register for this purpose at the Academic Office.

If the student obtains a final grade higher than 18 , you can choose between staying with the classification of 18 values or performing a complementary test for the defense of note.


a. Each test is written, individual and with consultation of a form, if it is needed.

b. Each test is evaluated of 0 the 20 values, with rounding to tenth.

c. It does not have daily pay-registration in the tests.

d. It is necessary to take a notebook, calculator and a document of identification with photograph (e.g., Identity or Student cards) to the examination.

e. Any student involved in fraud fails the course.

Subject matter

1 – Basic concepts

2 - Capitalization Regimes

3 - Equity Capitals

4 - Financial Annuities

5 - Reimbursement of Loans

6 - Bond Loans

7 - Calculus and Financial Applications Capital