Financial Calculus

Base Knowledge

Knowledge of Mathematics at the 9th grade level.

Teaching Methodologies

Classes will be taught in a face-to-face approach.

The teaching of the various Chapters will take place together with the resolution of a wide range of practical cases.

Mandatory attendance is not established, and the student must assume responsibility for deciding accordingly. However, attending classes and participating in them is strongly recommended, given the continuous nature of the subjects under study.

Learning Results


The main goal of this course is to provide the basic concepts in Finance, particularly those related with the value of money in time.


At the end of the course, students must be able to:

 – apply the calculation methods inherent to asset and liability financial transactions;

 – discuss and compare the various financing modalities available to private and public entities;

 – identify the determining factors of the financial cost inherent in the different types of financing;

 – produce and interpret maps and other documents relating to the various financing modalities.


Chapter I – Capitalization and discount

 1 – Return, financial transactions and interest rate

 2 – Capitalization

               2.1 – Simple interest

               2.2 – Compound interest

               2.3 – Continuous interest

3 – Calculation of interest in banking practice

4 – Confrontation between the various capitalization regimes

5 – Discount operations

               5.1 – Discount at simple interest

               5.2 – Discount at compound interest

Chapter II – Interest rates

1 – Kinds of interest rates

2 – Proportional and equivalent interest rate

3 – Nominal and effective interest rates

4 – Average interest rate

5 – The effect of taxation: gross and net interest rate

6 – Annual percentual rate of charge (APR)

Chapter III – Short-term Financing Sources

1 – Discount of credit securities

               1.1 – Concept and characteristics of bills

               1.2 – Bills’ discount

               1.3 – Concept and characteristics of promissory notes

2 – Effective cost of discount

3 – Bills’ roll-over

Chapter IV – Equivalence of capital

1 – Equations of value

2 – Evaluation rate

 Chapter V – Annuities

1 – Main concepts

2 – Kinds of annuities

3 – Two main cases

               3.1 – Discounted value of an annuity

               3.2 – Accumulated value of an annuity

4 – Annuities due

5 – Deferred annuities

6 – Fractional annuities

7 – Perpetual annuities of constant terms

8 – Contingent annuities: their specificities

Chapter VI – Long-term Financing Sources

1 – Loans

               1.1 – Notion and characteristics of loans

               1.2 – Amortization of loans

               1.3 – Amortization schedules

               1.4 – Periodic instalments and periodic repayments

2 – Debentures: their specificities

Curricular Unit Teachers




 1)    Quelhas, A. P. & Correia, F. (2017). Manual de Matemática Financeira, Coimbra: Almedina (4th edition reprinted).

 2)    Matias, R. (2018). Cálculo Financeiro – Teoria e Prática, Escolar Editora (6th edition).

 3)    Alves, C., Ribeiro, C., Farinha, J. & Alves, R. (2019). Cálculo Financeiro Aplicado. Coimbra: Almedina (2nd edition).

 4)    Nicolau, I. & Rodrigues, J. A. (2010). Elementos de Cálculo Financeiro. Áreas Editora (9th edition).

 5)    Laureano, R. & Santos, L. L. (2006). Fundamentos e Aplicações do Cálculo Financeiro. Lisboa: Edições Sílabo (2nd edition).

 6)    Quelhas, A. P. (2019). Mathematics of Finance. Almedina (e-book version / intended to Erasmus students).


Remark: without prejudice to the usefulness of the class support handouts, made available on the Nónio platform at the beginning of the semester, it is essential to use at least one of the mentioned manuals.