Financial Calculus

Knowledge of Mathematics at the 9th grade level.

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.

Goals:

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

 Skills:

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

NAO

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

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

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

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

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

6)    Quelhas, A. P. (2019). Mathematics of Finance. Almedina (e-book version).