Contextualization

Introduction

Financial Mathematics is a comprehensive and relevant area for various everyday situations, and one of its most important concepts is Compound Interest. But what are compound interests after all? Compound interests are the application of interests on interests. This happens when the yield of one period is incorporated into the capital to calculate the interest of the following period. This feature is widely used by the financial system for consumer goods financing.

We can consider Compound Interests as a universal phenomenon in the world of investments and financing. They represent one of the most common ways of increasing the initial value of an investment or debt over time. In the business world, it is practically impossible not to use this concept.

One of the first to be attributed to the concept of compound interests is the great mathematician and physicist Isaac Newton, who created the formula for calculating compound interests that is used to this day. In summary, Newton's formula for calculating compound interests is: A = P(1 + r/n)^(nt), where A is the future value, P is the principal value, r is the interest rate, n is the number of times the interest is applied per period of time, and t is the time in years.

Contextualization

Compound interests are extremely important both for personal life and for the business world. In the personal aspect, they affect loans, car financing, mortgages, among other situations. In the business world, they are the main driver of long-term investments, retirements, and savings. Understanding them is essential for efficient financial management.

Furthermore, compound interests have broad application in the global economy. For example, they are present in the calculation of a country's GDP, in inflation rates, in investment returns, and in the evaluation of investment projects. Therefore, understanding the concept of compound interests is of vital importance, not only for daily activities but also to understand the world economy.

Atividade Prática

Activity Title: "Unraveling the Mysteries of Compound Interest"

Project Objective

The project's objective is to provide students with a clear and practical understanding of the concept and application of Compound Interests, challenging them to solve practical problems and explain their reasoning.

Detailed Project Description

Form groups of 3 to 5 students and challenge them to simulate a real investment and loan scenario using the concept of Compound Interests. They should compare different investment and loan scenarios to fully understand the impact of Compound Interests in each situation.

Required Materials

• Computer with Internet access
• Calculator
• Paper and Pen for notes

Step by Step

Step 1: Each group chooses a hypothetical situation to apply Compound Interests. It can be an investment, a loan, a mortgage, etc.

Step 2: The groups must research to understand and define the real terms and conditions for their chosen situation, such as: what would be the principal value, what would be the annual interest rate, what would be the compounding frequency, etc.

Step 3: Based on these conditions, students must calculate the final value after a certain period, using the Compound Interests formula. This calculation should be done for different time periods (for example, 1, 3, 5, and 10 years) in order to observe the impact of time on the growth of the principal value.

Step 4: Students must compare the results obtained with the base case of Simple Interests for the same parameters and time periods. This will help understand the difference between Simple and Compound Interests.

Step 5: The groups must record all their findings and observations, paying special attention to the clear explanation of their processes, calculations, and results.

Project Deliverables

• Project Report: Each group must present their findings in the form of a report containing the following topics:

  1. Introduction: Contextualize the chosen situation and explain why you chose this situation. Describe the relevance and application of the "Compound Interests" theme for this situation.

  2. Development: Explain the theory behind Compound Interests, the activity carried out in detail, the methodology used, present the calculations, and discuss the results obtained. Contextualize the calculation results with the chosen situation.

  3. Conclusion: Conclude the work by summarizing your main points, explaining the learnings obtained, how the knowledge of compound interests helped understand the chosen situation, and the conclusions drawn from the project.

  4. Bibliography: Indicate the sources you relied on to work on the project such as books, web pages, videos, etc.

• Oral Presentation: Each group must make an oral presentation of their work to the classroom, sharing their findings and answering questions from classmates and the teacher.