ISMAT 154

Financial Calculus

• ApresentaçãoPresentation

  The Financial Calculus course unit gives Business Management students the tools to measure the value of money over time: what a loan costs, what savings earn and what a payment due later is worth today. It starts from interest and the interest rate and goes through capitalisation regimes, rates, equivalence of capitals and annuities. It ends with loans and the effective cost of credit. It is a decision-making tool. A manager who cannot tell a nominal rate from an effective rate, or who cannot read an APRC (TAEG), compares financing offers badly and pays for the mistake. This is why every topic ends in a decision grounded in the result, worked with real data such as Euribor, published credit offers and savings certificates. The spreadsheet accompanies the unit from the first sessions rather than being a separate subject.
• ProgramaProgramme

  S1 - Fundamentals of the time value of money: timeline and signs; interest and rate; rate-period consistency. S2 - Capitalisation regimes: simple and compound interest; present and future value; rate and term; commercial and exact interest. S3 - Interest rates: TAN and TAE; equivalent and proportional rates; real rate and inflation; CAGR. S4 - Equivalence of capitals and discounting: focal date; substitution and consolidation; rational and commercial discount. S5 - Annuities: classification; present and accumulated value; fractional; perpetuities; payment and periods. S6 - Loans and effective cost of credit: amortisation schedule; French, constant and American systems; grace period and prepayment; fixed and indexed rate; APRC (TAEG) and MTIC. S7 - Applications to management decisions: credit offers; leasing and ALD; saving; NPV (VAL) and IRR (TIR). S8 - Digital tools (transversal): financial functions; auditable schedule; scenarios; critical use of AI.
• ObjectivosObjectives

  LO1 - Explain and apply the fundamental concepts of the time value of money, interest and the interest rate. LO2 - Calculate and interpret capitalisation, updating and discounting operations and establish the equivalence of capitals referred to different dates. LO3 - Identify, distinguish and calculate the values of certain, constant, fractional and perpetual annuities. LO4 - Build and interpret loan amortisation schedules and compare financing options by their effective cost. LO5 - Apply financial calculus to everyday saving, credit and investment decisions, grounding the choice in the result obtained. LO6 - Use spreadsheets and digital tools to solve, audit and test financial calculus problems, critically checking results assisted by artificial intelligence.
• BibliografiaBibliography

  Alves, C., Alves, R., Ribeiro, C., & Farinha, J. (2023). Cálculo financeiro aplicado (3.ª ed.). Edições Almedina. Wang, S. (2024). Mathematics of finance. eCampusOntario Pressbooks. https://ecampusontario.pressbooks.pub/mathematicsfinance/  
• MetodologiaMethodology

  ME1 - Theoretical-practical exposition with double resolution: guided examples solved by hand and in the spreadsheet, side by side, within the exposition. ME2 - Applied problem solving with decisions and real data: each exercise ends in a decision, using verifiable data (Euribor, published APRC, savings certificates, Bank of Portugal customer portal). ME3 - Peer teaching with public demonstration of the solution: in each group presentation session, a group solves at the board the problem the class worked on, submits an auditable file and answers questions. ME4 - Digital resources and artificial intelligence: supervised use of the spreadsheet and generative AI, with mandatory, declared manual verification. ME5 - Spaced retrieval practice with immediate correction: nine mini-tests (30% of the grade) on the previous session, with the answer key straight afterwards.
• LínguaLanguage

  Português
• TipoType

  Semestral
• ECTS

  5
• NaturezaNature

  Mandatory
• EstágioInternship

  Não