Context

Financial mathematics is an essential tool in modern life and serves as the basis for many decisions we make every day. It is present in our daily lives when we calculate the monthly budget, analyze the interest on a loan, decide when and how much to save, or even when considering the risk and return of an investment.

The job market, household economy, and business world are environments where financial mathematics is constantly applied. It allows people and companies to make short or long-term projections, consider investment and financing alternatives, as well as plan expenses and revenues.

Spreadsheets, such as Excel, are widely used tools for performing financial calculations. They allow the manipulation of a large volume of data in an organized way and the execution of complex calculations in an automated manner. Additionally, they enhance data visualization through graphs and other graphical representations.

Theoretical Introduction

The study of financial mathematics involves fundamental concepts such as: simple and compound interest, discounts, inflation, interest rates, uniform payment series, present value, and future value.

Interest is the price paid for the use of someone else's money for a certain period, and it can be simple or compound. In simple interest, the value is always calculated based on the initial amount, while in compound interest, each period is calculated on the value of the previous period, accumulating over time.

Spreadsheets, like Excel, are a powerful tool for dealing with these calculations and other financial operations. Understanding how to use these tools and apply them in real life is an asset in anyone's personal and professional life.

Practical Activity

Practical Activity: Personalized Financial Planning

Project Objective

This project aims to teach students essential principles of financial mathematics and how to apply them in everyday life using spreadsheets. For this, the groups will simulate a family budget and project an investment plan for a period of 3 years.

Project Description

The groups will use financial mathematics concepts, along with practice in spreadsheets, to create a detailed family budget, including calculations of simple and compound interest, expense planning, and investment analysis.

Necessary Materials

• Computers with internet access and the ability to use a spreadsheet application, such as Excel.
• Reference material for financial mathematics and spreadsheets.

Project Step-by-Step

1. Group Formation and Scenario Selection: Divide the class into groups of 3 to 5 students. Each group will choose a real-life financial scenario to simulate, such as a low-income family, a middle-income family, or an independent college student.

2. Research and Data Collection: The groups will research to collect relevant data for the chosen scenario. This may include, for example, average cost of living, inflation, interest rates for loans and investments.

3. Budget Development: Each group will use their collected data to create a detailed budget spreadsheet, including items such as income, fixed expenses (rent, tuition, taxes, etc.), and variable expenses (food, leisure, etc.).

4. Interest Calculation: Students will introduce the concepts of simple and compound interest in their spreadsheet. They can simulate a loan for the acquisition of a high-value asset, such as a house or car, or an investment plan.

5. Analysis and Optimization: Based on the collected information and calculations made, students should analyze their budget and propose optimization strategies. These strategies may include: expense reduction, income increase, investment adjustment, among others.

6. Work Presentation: Finally, each group must present their financial analysis and the conclusions they have reached. It is important that all group members participate in the presentation.

Project Delivery

After completing the practical part, each group must prepare a detailed report that should include:

1. Introduction: Contextualization of financial mathematics and motivations for using a spreadsheet in this project. Students should explain the chosen scenario and why it is relevant.

2. Development: A description of the methodology used, a detailed explanation of the mathematical theory involved, how the spreadsheet was built and used, and a step-by-step description of the decisions made by the group. Also include screenshots or images of your work to support your explanations.

3. Conclusions: In this section, groups should summarize their main points, discuss what they have learned, and the conclusions they have reached regarding financial planning. Include a critical evaluation of the work done and suggestions on how they could improve or expand the project.

4. Referenced Bibliography: A list of all references consulted during the project.

Finally, the groups must submit the written report and the spreadsheet they created for evaluation.