The Financial Mathematics of Loans, Debts, and Compound Interest

2011 ◽  
pp. 581-600
Keyword(s):  
Financial Mathematics ◽  
Compound Interest

scholarly journals Teachers’ knowledge for teaching compound interest

Pythagoras ◽  
2013 ◽  
Vol 34 (2) ◽  
Author(s):  
Craig Pournara
Keyword(s):  
Financial Literacy ◽  
Teaching And Learning ◽  
Secondary Mathematics ◽  
School Curriculum ◽  
Teaching Mathematics ◽  
Financial Mathematics ◽  
Secondary Mathematics Teachers ◽  
Knowledge For Teaching ◽  
The World ◽  
Compound Interest

There is increasing acknowledgement that teachers’ knowledge for teaching mathematics is multifaceted and topic specific. Given the paucity of research on the teaching and learning of financial mathematics in general, little can be known about teachers’ knowledge for teaching compound interest. However, since financial mathematics is a component of the school curriculum in South Africa, and an important element of financial literacy more broadly, attention needs to be given to knowledge for teaching financial mathematics, and compound interest in particular. Drawing from a larger study in which the author taught a financial mathematics course to pre-service secondary mathematics teachers, a theoretical elaboration is provided of the underlying mathematics of compound interest, and connections with the world of banking. Based on findings from the study, two key student errors are identified: the over-generalisation of linear thinking in multiplicative scenarios, and the over-generalisation of reversible operations in percentage-change scenarios. Taken together, teachers’ knowledge of relevant mathematics, of the banking context and of learners’ conceptions will contribute to building a knowledge-base for teachers’ knowledge for teaching compound interest.

scholarly journals EDUCAÇÃO FINANCEIRA: APRENDIZAGEM DE PROGRESSÕES GEOMÉTRICAS APLICADAS AOS JUROS COMPOSTOS NA PERSPECTIVA DA EDUCAÇÃO MATEMÁTICA CRÍTICA

2020 ◽  
Vol 5 (1) ◽  
pp. 45-64
Author(s):  
Martielle Soledade Souza Santos ◽  
Alfredo Dib Nour
Keyword(s):  
Mathematics Education ◽  
Financial Education ◽  
Financial Mathematics ◽  
Mathematical Education ◽  
Teaching Sequence ◽  
Critical Mathematics ◽  
Master's Thesis ◽  
Geometric Progressions ◽  
The One ◽  
Compound Interest

Resumo: O presente artigo trata-se de um recorte de dissertação de mestrado em Educação Matemática. O problema surge da análise de duas tendências que tratamos de articular, por um lado os dados indicam eventuais falhas no aprendizado da matemática e por outro os indicadores superiores a 60% de endividamentos das famílias. O objetivo principal é analisar o desenvolvimento do conteúdo de juros compostos a partir de uma sequência de ensino, tendo como base o estudo das Progressões Geométricas (PG) a partir do movimento da Educação Financeira. O referencial teórico articula as ideias de Skovsmose, referente à Educação Matemática Crítica (EMC), que enfatiza a aprendizagem da matemática de forma política e consciente. O estudo foi aplicado com estudantes do 1° ano do Ensino Médio, de uma escola na região oeste da Bahia, Brasil, em julho de 2018, com a aplicação de uma sequência de ensino. A metodologia se fundamenta na pesquisa de natureza empírica, caráter exploratório e explicativo. As análises foram organizadas em três categorias tratando-se da concepção de dinheiro, do entendimento sobre PA e PG e as propagandas. As conclusões evidenciam a necessidade de ampliação do trabalho procurando contemplar todos os elementos pertencentes à Matemática Financeira, de modo que sejam tratados criticamente.Palavras-chave: Educação Matemática Crítica; Educação Financeira; Progressões Geométricas. Abstract: This article is an excerpt of a master's thesis in Mathematics Education. The problem arises from the analysis of two trends that we tried to articulate, on the one hand, the data indicate possible flaws in the learning of mathematics and on the other, the indicators above 60% of household indebtedness. The main objective is to analyze the development of the content of compound interest based on a teaching sequence, based on the study of Geometric Progressions (PG) from the Financial Education movement. The theoretical framework articulates the ideas of Skovsmose, referring to Critical Mathematical Education (EMC), which emphasizes the learning of mathematics in a political and conscious way. The study was applied to students of the 1st year of high school, from a school in the western region of Bahia, Brazil, in July 2018, with the application of a teaching sequence. The methodology is based on research of an empirical nature, exploratory and explanatory. The analyzes were organized into three categories, dealing with the concept of money, understanding of PA and PG and advertisements. The conclusions show the need to expand the work, seeking to contemplate all elements belonging to Financial Mathematics, so that they are treated critically.Keywords: Critical Mathematics Education. Financial education. Geometric progressions.

scholarly journals O regime de juros compostos segundo a dialética ferramenta-objeto

2020 ◽  
Vol 9 (2) ◽  
Author(s):  
DEJAIR FRANK BARROSO ◽  
CILEDA DE QUEIROZ E SILVA COUTINHO ◽  
MARCO AURÉLIO KISTEMANN JR
Keyword(s):  
Mathematics Teacher ◽  
Financial Literacy ◽  
Financial Education ◽  
Financial Mathematics ◽  
Mathematical Concepts ◽  
Mathematical Notion ◽  
Doctoral Research ◽  
De Se ◽  
Compound Interest ◽  
Didactics Of Mathematics

ResumoEste trabalho faz parte de uma pesquisa de doutorado em andamento que trata sobre o tema educação financeira e suas potencialidades para o letramento financeiro do professor de matemática na licenciatura. Pretendemos descrever brevemente as fases de organização para a construção de conceitos matemáticos segundo a dialética ferramenta-objeto introduzida por Régine Douady. Nosso objetivo  é apresentar um exemplo dessa organização no campo da matemática financeira, e mais precisamente, relativo ao regime de juros compostos. Esse tipo de organização enfatiza a importância de se alternar, no ensino, os aspectos ferramenta e objeto de uma dada noção matemática. No exemplo proposto foi desenvolvida uma sequência para articular a noção de juros compostos e sua mobilização numa nova situação. Palavras-chave: Didática da Matemática; Dialética ferramenta-objeto; Juros compostos.AbstractThis work is part of an ongoing doctoral research that deals with the theme of financial education and its potential for the financial literacy of the mathematics teacher in the degree. We intend to briefly describe the phases of organization for the construction of mathematical concepts according to the tool-object dialectic introduced by Régine Douady. Our goal is to present an example of this organization in the field of financial mathematics, and more precisely, regarding the compound interest regime. This type of organization emphasizes the importance of alternating, in teaching, the tool and object aspects of a given mathematical notion. In the proposed example, a sequence was developed to articulate the notion of compound interest and its mobilization in a new situation.Keywords: Didactics of Mathematics; Dialectic tool-object; Compound interest.   

scholarly journals Uma proposta interdisciplinar para o desenvolvimento de aplicativos de matemática financeira em um curso de graduação em Engenharia Elétrica

2018 ◽  
Vol 7 (1) ◽  
Author(s):  
Ana Paula de Andrade Janz Elias ◽  
Marcelo Souza Motta ◽  
Fabiana Roberta Gonçalves e Silva Hussein
Keyword(s):  
Computer Programming ◽  
Electrical Engineering ◽  
Great Influence ◽  
Financial Mathematics ◽  
Digital Tool ◽  
Interdisciplinary Work ◽  
Financial Applications ◽  
App Inventor ◽  
Compound Interest

Resumo: Este artigo tem como objetivo apresentar uma proposta de trabalho interdisciplinar entre as disciplinas de Programação de Computadores e Matemática Financeira em um curso de graduação em Engenharia Elétrica. A ferramenta utilizada foi o software App Inventor. Inicialmente, no percurso metodológico, a Matemática Financeira foi trabalhada de forma “tradicional” para, posteriormente, apresentarmos a possibilidade de programar aplicativos financeiros para o cálculo de Juros simples e Compostos. Os estudantes responderam a dois questionários. Apresentaremos aqui como se deu a aceitação dos estudantes em relação a proposta de trabalho interdisciplinar, bem como a análise de suas respostas aos questionários propostos. Fica evidenciado que a integração das disciplinas teve grande influência no processo de construção do conhecimento de Matemática Financeira.Palavras chave: Interdisciplinaridade. Matemática Financeira. Programação. App Inventor. AN INTERDISCIPLINARY PROPOSAL FOR THE DEVELOPMENT OF FINANCIAL MATHEMATICS APPLICATIONS IN ELECTRICAL ENGINEERING UNDERGRADUATION COURSEAbstract: This article aims to present a proposal of interdisciplinary work between the disciplines of Computer Programming and Financial Mathematics in an Electrical Engineering undergraduate course. The digital tool used was App Inventor software. In the methodological course, initially, "Financial Mathematics" was worked in a "traditional" way to later present the possibility of programming financial applications for the calculation of simple and compound interest. The students answered two questionnaires. We present here how students were accepted in relation to the interdisciplinary work proposal, as well as the analysis of their answers to the questionnaires proposed. It is evidenced that the integration of the disciplines had great influence in the process of construction of the knowledge of Financial Mathematics.Keywords: Interdisciplinarity. Financial Mathematics. Programming. App Inventor. 

Using R for teaching financial mathematics and statistics

2011 ◽  
Vol 11 (1) ◽  
pp. 7-11
Author(s):  
Julian Stander ◽  
John Eales
Keyword(s):  
Financial Mathematics

scholarly journals Special Issue “Interplay between Financial and Actuarial Mathematics”

Risks ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 139
Author(s):  
Corina Constantinescu ◽  
Julia Eisenberg
Keyword(s):  
Machine Learning ◽  
Control Theory ◽  
Option Pricing ◽  
Interest Rates ◽  
Financial Mathematics ◽  
Special Issue ◽  
Actuarial Mathematics ◽  
Mortality Models ◽  
Low Interest Rates

The Special Issue aims to highlight the interaction between actuarial and financial mathematics, which, due to the recent low interest rates and implications of COVID-19, requires an interlace between actuarial and financial methods, along with control theory, machine learning, mortality models, option pricing, hedging, unit-linked contracts and drawdown analysis, among others [...]

Compound Interest

2014 ◽  
pp. 142-151
Author(s):  
Jeremy Bentham
Keyword(s):  
Compound Interest

scholarly journals Lie Symmetries of (1+2) Nonautonomous Evolution Equations in Financial Mathematics

Mathematics ◽  
2016 ◽  
Vol 4 (2) ◽  
pp. 34 ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Richard Morris ◽  
Peter Leach
Keyword(s):  
Evolution Equations ◽  
Lie Symmetries ◽  
Financial Mathematics

scholarly journals On the First Passage time for Brownian Motion Subordinated by a Lévy Process

2009 ◽  
Vol 46 (1) ◽  
pp. 181-198 ◽  
Author(s):  
T. R. Hurd ◽  
A. Kuznetsov
Keyword(s):  
Brownian Motion ◽  
Approximation Scheme ◽  
First Passage Time ◽  
Gaussian Model ◽  
Passage Time ◽  
Financial Mathematics ◽  
First Passage ◽  
Financial Modeling ◽  
Motion Time ◽  
Normal Inverse Gaussian

In this paper we consider the class of Lévy processes that can be written as a Brownian motion time changed by an independent Lévy subordinator. Examples in this class include the variance-gamma (VG) model, the normal-inverse Gaussian model, and other processes popular in financial modeling. The question addressed is the precise relation between the standard first passage time and an alternative notion, which we call the first passage of the second kind, as suggested by Hurd (2007) and others. We are able to prove that the standard first passage time is the almost-sure limit of iterations of the first passage of the second kind. Many different problems arising in financial mathematics are posed as first passage problems, and motivated by this fact, we are led to consider the implications of the approximation scheme for fast numerical methods for computing first passage. We find that the generic form of the iteration can be competitive with other numerical techniques. In the particular case of the VG model, the scheme can be further refined to give very fast algorithms.

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