Aula 74 - Paralisação - Juros e Juros Simples (1ª série)

Summary

This video tutorial explains the concept of interest, focusing on its role as a remuneration for borrowed or invested capital. The instructor provides examples of simple interest, installment payments, and the impact of interest rates on loans. Key concepts, such as calculating interest, understanding the difference between cash and installment payments, and how to avoid hidden interest costs, are highlighted. Additionally, the instructor emphasizes the importance of evaluating interest rates carefully in daily transactions and the difference between cash discounts and actual interest charges. The session also touches on simple interest formulas and encourages students to engage with class activities and ask questions for clarification.

Takeaways

• 😀 Interest is the remuneration for the use of capital, and it can either be a gain or loss depending on whether you're lending or borrowing money.
• 😀 Interest can be earned from investments like a savings account or paid on loans. For example, a bank pays interest on deposited money, while a borrower pays interest on loans.
• 😀 When calculating interest, it's important to remember that rates are often presented as a percentage (like 14%) and need to be converted into decimals for calculations (0.14).
• 😀 A 14% interest rate on a capital amount can yield a set profit over a given period, like R$14 from an initial amount, helping us understand the profitability of an investment.
• 😀 In Brazil, average interest rates on investments are less than 5%, but higher yields (like 10%) are considered very attractive.
• 😀 Installment payments come with interest, and the total amount paid in installments is often more than the original price due to added interest.
• 😀 When evaluating installment options, it's important to calculate the true interest rate to understand the cost of buying on credit (e.g., a 40% rate on a 60 reais debt results in a significant increase in payment).
• 😀 A store offering a discount for cash payments is often still charging implicit interest when paying in installments, even if no interest is overtly mentioned.
• 😀 Simple interest is calculated using the formula: Interest = Principal × Rate × Time. The rate must be expressed in decimal form, and time should be in consistent units (usually years).
• 😀 The final value of an investment or loan can be calculated using formulas for simple interest or future value (e.g., Future Value = Present Value × (1 + Rate × Time)).

Q & A

What is the definition of interest mentioned in the video?

Interest is the remuneration paid for the use of capital over a certain period of time. It can be earned in savings accounts or paid when borrowing money.

What is the meaning of the acronyms 'A' and 'KM' as described in the video?

'A' stands for 'per year', while 'KM' refers to 'Almir' in the context provided, though the exact meaning of 'KM' is unclear from the script.

How is interest calculated in the example involving a 14% interest rate for 14 days?

In this case, the interest is calculated by multiplying the original amount (R$100) by 0.14 (14% rate). This gives R$14 as the interest earned over 14 days.

What is the significance of the 25% interest rate calculated in the installment payment example?

The 25% interest rate is calculated based on the difference between the installment plan price (R$100) and the original cash price (R$90). This demonstrates that even seemingly interest-free installment plans may include hidden interest.

Why is it important to calculate the interest rate in installment purchases?

Calculating the interest rate in installment purchases helps to understand the real cost of the product and avoid being misled by promotional offers that may appear to have no interest.

What is the formula for calculating simple interest?

The formula for calculating simple interest is: Interest (I) = Principal (P) × Rate (r) × Time (t), where 'P' is the initial amount, 'r' is the interest rate, and 't' is the time period.

How do interest and time units need to match when calculating simple interest?

Interest and time must be in the same unit. For example, if the interest rate is given annually, the time should be expressed in years as well, or converted to years.

What is the difference between simple interest and compound interest, based on the video's focus on simple interest?

Simple interest is calculated on the initial principal only, while compound interest is calculated on both the initial principal and the accumulated interest over time. The video focuses on simple interest, where interest is only applied to the initial amount.

What is the total amount paid if an initial loan of R$5,000 is subject to a 5% annual interest rate over 3 years?

The total amount paid can be calculated using the simple interest formula. For an initial amount of R$5,000, a 5% interest rate, and a 3-year period, the interest is R$5,000 × 0.05 × 3 = R$750. Therefore, the total amount paid is R$5,000 + R$750 = R$5,750.

Why does the store’s offer of a 10% discount for cash payments hide an effective interest rate in installment plans?

The store’s offer of a 10% discount for cash payments hides the effective interest rate in installment plans because the total paid in installments is higher than the cash price. Even though the store claims no interest, the cost difference between the cash and installment payments effectively includes interest.