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

Rui Manuel Rodrigues Cardoso


Weekly - 4

Total - 62

Teaching language



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


MATIAS, R. (2007) Cálculo financeiro: teoria e prática; Escolar Editora.

Vaaler, L. and Daniel, J. (2002). Mathematical Interest Theory. Mathematical Association of America

Jorion, Philippe (2006) Value at Risk, 3rd Ed.: The New Benchmark for Managing Financial Risk; McGraw-Hill

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

Continuous Evaluation:

a. The continuous assesment is composed of 2 tests and one practical assignment.

b. Let T1 and T2 the grades obtained in each test by cronological order.
c. Let NN=0.5*T1+0.5*T2+
d. The student succeed if NN>=9.5

Evaluation by exam
a. Let ER be the grade obtained in the Exam.
b. The student succed if ER>=9.5

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 fraud implies to fail.

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


Programs where the course is taught: