Financial Mathematics

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 Math

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The teaching of the course is based on recent bibliography and on experience gained through practice. The course’s pedagogy is strongly interactive. It seeks substantial student participation and know-how-based learning. Emphasis is placed on helping students report concepts, ideas and theories to current practice.

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

– Apply the methods of calculation related to financial transactions and lending;

– Identify the various possibilities of financing available to private and public entities;

– Identify the determinants of the financial costs inherent to the various forms of financing;

– Produce and interpret maps and other kinds of documents related with the sources of financing.

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PART I – BASIC CONCEPTS

I – Capitalization and discount operations

1 –Interest, financial transaction and interest rate

2 – Capitalization schemes

         2.1 – Simple capitalization scheme

         2.2 – Compound capitalization scheme

         2.3 – Continuous capitalization regime

3 – Calculation of interest in banking practice

4 – Confrontation between the various capitalization schemes

5 – Forms discount

         5.1 – Desconto por dentro

         5.2 – Desconto por fora

         5.3 – Desconto composto

II – Interest rates

1  – General inquiries

   2 – Proportional and equivalent rates

3 – Nominal and effective rates

4 – Average rate of application

5 – The effect of taxation: gross rates and net rates

6 – Annual effective rate of charge

 III – Equivalência de capitais

1 – Equation of equivalence

2 – Assessment rate

 PART II – Short-term financing sources

1 – Bill notes discount

         1.1 – Concept and characteristics of letters

         1.2 – letter discount

         1.3 – Concept and characteristics of promissory notes

2 – Effective cost of discount

3 – Reform operations

 PART III – Annuities

1 – Concept and characteristics of annuities

2 – Kinds of annuities

3 – Two key cases

         3.1 – Constant terms amortization annuities

         3.2 – Constant terms accumulation annuities

4 – Anticipated annuities

5 – Deferred annuities

6 – Fractional annuities

7 – Perpetuities of constant terms

 PART IV – Sources long-term financing

1 – Classic loans

         1.1 – Notion and characteristics of classic loans

         1.2 – Loan amortization systems (one-off amortization and periodic repayments)

         1.3 – Construction of amortization tables

         1.4 – Confrontation between amortization systems with periodic repayments

NAO

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FUNDAMENTAL

1. Ana Paula Quelhas e Fernando Correia. (2017). Manual de Matemática Financeira, Coimbra, Editora Almedina

ADDITIONAL

1. Alves Mateus. (2004). Exercícios Práticos de Cálculo Financeiro, Edições Sílabo 3ª Edição.

2. Azevedo Rodrigues e Isabel Nicolau. (2010). Elementos de Cálculo Financeiro, Rei dos Livros, 9ª Edição.

3. Fernanda Matias, Ana Martins, Carlos Monteiro  e Telma Correia . (2020). Matemática Financeira – Teoria e Prática. Edições Sílabo

4. Natália Canadas. (1998). A Matemática do Financiamento e das Aplicações de Capital, Plátano Editora

5. Rogério Matias. (2018). Cálculo Financeiro – Teoria e Prática, Escolar Editora, 6ª Edição.