Engenharia Econômica e Financeira - Aula 07 - Matemática Financeira

Summary

In this lecture on Financial Mathematics for Engineering students, the instructor covers the concept of payment series, focusing on calculating both present and future values of these payments. The class explores how to determine the amount needed to accumulate a specific future sum through regular deposits, and how to calculate the equivalent lump sum for a series of payments. Examples include calculating monthly payments for loan repayments and investment accumulation, using formulas for capital flow analysis. The session emphasizes practical applications using financial tools like calculators and Excel, aiming to build expertise in engineering economics and financial decision-making.

Takeaways

• 😀 Understanding the concept of **payment series** is crucial for managing financial transactions in both personal and professional contexts.
• 😀 A **uniform payment series** involves equal payments made at fixed intervals, and it's essential for calculating future value and present value of these payments.
• 😀 The **future value** of a series of payments can be calculated using a specific formula, considering factors like interest rates and time periods.
• 😀 Present value calculations are key to determining the current worth of future payments, and they help convert a series of payments into a lump sum equivalent.
• 😀 A **practical example** showed how depositing 500 monthly for 4 years at a 3% monthly interest rate would accumulate 53,570.83 by the end of the period.
• 😀 To accumulate a specific amount in the future (e.g., 200,000 in 5 years), one can calculate the required monthly deposit, such as 1,719.21 with a 2% monthly interest rate.
• 😀 **Capital equivalence** involves understanding how a series of payments can be replaced by a single lump-sum payment, making it easier to compare different payment structures.
• 😀 Financial calculations in **loan repayments** were discussed, showing how to determine the monthly installment for a 30,000 loan with a 3.5% interest rate over 12 months.
• 😀 The formulae for calculating **present value** and **future value** involve the systematic substitution of known variables and solving for the unknowns.
• 😀 The main objective of the class was to ensure students can confidently use financial formulas in real-world engineering and production scenarios to make informed decisions.
• 😀 Practice exercises are essential for reinforcing the theoretical concepts of **financial mathematics**, helping students become more adept at handling financial decisions in their future careers.

Q & A

What is the main topic of the class discussed in the script?

The main topic of the class is financial mathematics, specifically focusing on the concepts of series of payments and how they are used in various financial transactions.

What does the script describe about a series of payments?

The script discusses a series of payments where the first payment occurs at the time of agreement, and subsequent payments are made periodically according to the terms agreed upon. The payments are uniform, meaning each payment is the same, and it also covers the calculation of the future value and present value of such series.

What is the formula for calculating the future value of a series of uniform payments?

The formula involves applying the payment amount, the interest rate, and the number of periods to calculate the future value. The script mentions that this formula will give us the accumulated value at the end of the period, considering the payment sequence.

How is the future value of a series of payments calculated in the script's example?

In the example, the script calculates the future value of applying a monthly payment of 500 for 48 months with an interest rate of 3% per month. The result is 53,570.83 after four years, demonstrating how periodic payments accumulate over time with interest.

What is the purpose of determining the monthly deposit for a future fund?

The purpose is to find out how much needs to be deposited every month in order to accumulate a specific amount (in this case, 200,000) at the end of a defined period (five years). The script shows that with a 2% interest rate per month, the monthly deposit required would be 1,719.21.

What concept does the script introduce when discussing the present value of a payment series?

The script introduces the concept of the present value of a series of payments, which is the value today of a series of future payments. It emphasizes the use of a formula to determine the current equivalent of future payments, factoring in the interest rate.

How is the present value of 24 monthly payments calculated in the script's example?

The script calculates the present value of 24 monthly payments of 3,500 each at a 4% interest rate per month. The present value is determined by discounting the future payments back to today's value, which is the amount that would be equivalent to the series of payments.

What is the key takeaway from the discussion of value equivalents?

The key takeaway is that the present value of a series of future payments can be represented as a single lump sum amount today. This concept is crucial in understanding how to compare or substitute periodic payments for a one-time payment.

What does the script say about the use of electronic devices in financial calculations?

The script mentions that financial calculations, such as those for present value and future value of payment series, are commonly done using electronic devices like calculators and Excel spreadsheets. These tools simplify the application of the formulas discussed in the class.

What are the differences between payments made at the beginning and the end of a period in this context?

The script explains that there are variations in the formulas depending on whether payments are made at the beginning (as in an 'annuity due') or at the end of a period (as in an 'ordinary annuity'). These differences impact the calculations of both present and future values.