Introduction

The concept of interest is one of the fundamental pillars of financial mathematics and permeates many strategic business decisions, investments, and even everyday personal decisions. In its essence, interest refers to the compensation charged for lending money (or another item) and is expressed as a percentage of the amount borrowed.

Interest can be classified into two main types: simple interest and compound interest. In the case of simple interest, it is calculated only on the principal amount, that is, the amount that was actually borrowed. Compound interest, on the other hand, is calculated not only on the principal amount but also on the accumulated interest from previous periods. This leads to what we call "interest on interest," which results in exponential growth of the amount borrowed.

The main difference between the two types of interest is that, while simple interest results in linear growth of the amount borrowed, compound interest results in exponential growth. In other words, while the amount of simple interest generated in each period is always the same, the amount of compound interest generated in each period increases over time.

Context

The concept of interest is a fundamental aspect of the modern economy. Without the existence of interest, there would be little incentive to lend money, which would make it difficult or impossible for many people and companies to finance major purchases or make investments. They play a crucial role in sectors such as stock and bond markets, the real estate industry, personal loans, and many others.

Furthermore, the concept of the time value of money is a crucial aspect of understanding interest. R$1.00 today is not the same as R$1.00 in the future. For example, if a person lends R$100.00 to a friend with the promise of receiving the same amount back in a year, they are actually losing money. This is because the value of money changes over time due to factors such as inflation and lost investment opportunities.

As part of this project, you will simulate scenarios involving both simple and compound interest and compare them. In addition, you will learn about the importance of the interest phenomenon in the economy and in everyday life.

Resources for further study:

1. Khan Academy: Simple and Compound Interest
2. Just Math: Simple Interest and Compound Interest
3. Financial Mathematics Course with Excel, Prof. Alberto Leandro: Video Lessons

Practical Activity

Activity Title: "Simple Interest vs. Compound Interest: A Practical Simulation"

Project Objective

Understand the difference between simple and compound interest through a practical simulation. Develop financial planning skills by analyzing and comparing different situations involving interest.

Project Description

This project consists of creating a financial simulation where groups will compare the outcome of investments and loans using simple and compound interest. Each group of students must develop a presentation that explains their results and conclusions.

Materials Needed

• Paper and pen for notes.
• Calculator.
• Computer with internet access for research.
• Spreadsheet software (e.g., Microsoft Excel, Google Sheets).

Activity Step-by-Step

Step 1: Form groups of 3-5 students.

Step 2: Each group should choose three different situations to simulate: one investment scenario, one loan scenario, and one installment purchase scenario. For example, an investment of R$5,000.00 for 2 years, a loan of R$10,000.00 for 3 years, and a purchase of R$1,000.00 in 12 monthly installments.

Step 3: For each scenario, the groups should research on the internet real interest rates that would be applied to each chosen situation. These rates must be justified and referenced in the final presentation.

Step 4: Using spreadsheet software, the groups should simulate each situation twice: once using simple interest, and once using compound interest. The goal is to visualize the difference between the two types of interest in practice.

Step 5: The groups should prepare a written presentation of their simulations, explaining the situations chosen, the interest rates used, the difference in results between simple and compound interest, and their conclusions about which type of interest is more advantageous in each situation.

Project Delivery

The project deliverable will consist of a written report, including graphs of the simulations and a presentation of the conclusions in the following sections:

1. Introduction: Should include an explanation of what simple and compound interest are, the importance of interest in the economy, and the relevance and purpose of this project.

2. Development: Should describe in detail the three simulated situations, present the mathematical formulas used to calculate interest, inform the interest rates researched and applied, and present the results obtained in the simulation. In addition, it should contain graphs illustrating the difference between simple interest and compound interest in each situation.

3. Conclusions: Should summarize the main learnings obtained in the project, including an understanding of the difference between simple and compound interest and the practical application of this difference in the context of the simulated scenarios. It should also contain reflections on the importance of financial planning and the implications of interest in everyday life.

4. Bibliography: Should contain all sources of information used in the project, including websites from which interest rates were obtained, books, explanatory videos, and any other references consulted.