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Financial Mathematics

Code	14001
Year	2
Semester	S2
ECTS Credits	6
Workload	TP(60H)
Scientific area	Management
Entry requirements	None
Mode of delivery	Face-to-face
Work placements	None
Learning outcomes	This course intends to evidence the importance of financial calculus, as well as an integrated and detailed analysis of financial operations (financing and investing) and their relationships towards business management.
Syllabus	1 - Capitalization and Discount 1.1 - Introductory concepts 1.1.1 - Definition and objectives 1.1.2 - Basic variables 1.1.3 - Present value and accumulated value 1.1.4 - Interest and interest rate 1.1.5 - Discount and discount rate 1.1.6 - Axioms of financial calculation 1.2 - Interest 1.2.1 - System of simple interest 1.2.2 - System of compound interest 1.2.3 - Types of joint interest 1.2.4 - Differences and theory (zero-rate and retention without capitalization of interest) 1.3 - Asynchronous capitalization of interest 1.3.1 - Fees proportionate and nominal rates 1.3.2 - Fees equivalents and effective rates 1.4 - Update or discount 1.4.1 - Discount composed 1.4.2 - Interest rates in the evaluation 1.4.3 - Discount Rates in the evaluation 1.4.4 - Deviations to theory 1.5 - Equity capital 1.5.1 - Value Equation 1.5.2 - Possible unknowns in the value equation 1.5.3 - Single capital 1.5.4 - Basic single and average deadline 1.5.5 - Miscellaneous capitals 1.5.6 - Implications to the interest rate 2 - Rents 2.1 - Framework and definitions 2.2 - Whole and split rents with constant terms 2.2.1 - Temporary and immediate 2.2.2 - Temporary and deferred 2.2.3 - Perpetual and immediate 2.2.4 - Perpetual and deferred 2.3 - Whole and split rents with variable terms 2.3.1 - With variable terms of any kind 2.3.2 - With variable terms in arithmetic progression 2.3.3 - With variable terms in a geometric progression 2.4 - Whole and split rents in steps or levels 2.4.1 - Levels in the arithmetic progression 2.4.2 - Levels in a geometric progression 3 - Loans 3.1 - Debt service 3.2 - Repayment of loans 3.2.1 - Full refund at the end of the loan 3.2.1.1 - Single payment of interest on deadline 3.2.1.2 - Payment of interest only at the beginning of term 3.2.1.3 - Interest payments during the period 3.2.1.4 - Payment of interest only during the period 3.2.2 - Repayment of long-term, single payment of interest 3.2.2.1 - Single payment of interest on deadline 3.2.2.2 - Payment of interest only at the beginning of term 3.2.2.3 - Payment of interest only during the period 3.2.3 - Repayment of long-term, single payment of interest 3.2.3.1 - Single payment of interest on deadline 3.2.3.2 - Payment of interest only at the beginning of term 3.2.3.3 - Single payment of interest during the period 3.2.4 - Repayment over the term and interest payments over the term 3.2.4.1 - Assumptions 3.2.4.2 - Debt service map 3.2.4.3 - Constant Debt service 3.2.4.3 - Variable debt service with constant portions of refund 3.3 - Loan evaluation 3.3.1 - Background and definitions 3.3.2 - Loans with indexed rate 3.3.3 - Fixed-rate loans 3.3.4 - Full property 4 - Transaction costs and economic and fiscal effects 4.1 - Framework and definitions 4.2 - The effect of transaction costs in the study of rates 4.2.1 - Effective cost rates 4.2.2 - Effective yield rates 4.2.3 - Annual effective rate 4.2.4 - Global Annual effective rate 4.3 - The effects of inflation rates in the study of rates 4.3.1 - nominal interest rates (current prices) 4.3.2 - real interest rates (at constant prices) 4.4 - The tax effect in the study of rates 4.4.1 - Gross interest rates or 4.4.2 - Net interest rates
Main Bibliography	CADILHE, Miguel (1995) "Matemática Financeira Aplicada", Edições Asa, Porto, ISBN 972-41-1214-4, Capítulos 1, 3, 5 e 8 Biblioteca CSH: EG-4.5/000060 FERREIRA, Roberto G. (2000) "Matemática Financeira Aplicada", Ed. Universitária da UFPE, 5.ª Edição, Recife, Brasil, ISBN 85-7315-028-9 Biblioteca CSH: EG-4.5/000064 MATIAS, Rogério (2007) "Cálculo Financeiro - Teoria e Prática", Escolar Editora, 2.ª Edição, Lisboa, ISBN 978-972-592-210-1 Biblioteca CSH: Não disponível Site de apoio: http://www.calculofinanceiro.com MATIAS, Rogério, SILVA, Ilídio (2008) "Cálculo Financeiro - Exercícios Resolvidos e Explicados", Escolar Editora, Lisboa, ISBN 978-972-592-233-0 Biblioteca CSH: Não disponível Site de apoio: http://www.calculofinanceiro.com MATIAS, Rogério (2008) "Cálculo Financeiro - Casos Reais Resolvidos e Explicados", Escolar Editora, Lisboa, ISBN 978-972-592-234-7 Biblioteca CSH: Não disponível Site de apoio: http://www.calculofinanceiro.com MATEUS, Alves (1994) "Cálculo Financeiro", Edições Sílabo, 3.ª Edição, Lisboa, ISBN 972-618-112-3 Biblioteca CSH: EG-4.5/000009 Site informativo: http://www.silabo.pt/livros.asp?tit=&aut=mateus&is=&ano=&Submit=Procurar&num=32 (5.ª Edição) MATEUS, Alves (1994) "Exercícios Práticos de Cálculo Financeiro", Edições Sílabo, 2.ª Edição, Lisboa, ISBN 972-618-103-8 Biblioteca CSH: EG-4.5/000042 Site informativo: http://www.silabo.pt/livros.asp?tit=&aut=mateus&is=&ano=&Submit=Procurar&num=83 (4.ª Edição) SILVA, Armindo Neves (1993) "Matemática das Finanças - Volume I", McGraw-Hill, 2.ª Edição, Lisboa, ISBN 972-9241-36-6 Biblioteca CSH: EG-4.5/000010
Teaching Methodologies and Assessment Criteria	Teaching Methodology: Oral presentation of concepts. Resolution of consolidation exercises. EEA (The evaluation dates will be announced in the second semester) T1 - 5v - xx/xx/2025 T2 - 5v - xx/xx/2025 T3 - 5v - xx/xx/2025 T4 - 5v - xx/xx/2025 The indicated dates should always be confirmed, in order to check for possible changes
Language	Portuguese. Tutorial support is available in English.