João applied an amount in a financial investment that yields simple interest. After 8 months, the amount João applied increased by 60%. Considering that the bank uses the simple interest regime, what was the monthly interest rate used in this investment?

A farmer usually takes out loans from a financial company, always in the amount of R$ 5,000.00 under the simple interest modality, to be paid after six months in a single installment, at a rate of 2% per bimester. However, due to being in a tight budget situation, he asked the company to extend the payment deadline by another six months. In order to maintain the same amount obtained with the loan and the same total amount to be paid at the end of the deadline, this farmer must request the application of a new bi-monthly interest rate from the financial institution, as he is already an old client of the institution. The new rate will be

To solve this question, we first need to understand the original scenario and then the scenario with the extended deadline. Let's call the original bi-monthly interest rate i1 and the new bi-monthly interest rate i2. Original scenario: - Loan amount (P1): R$ 5,000.00 - Bi-monthly interest rate (i1): 2% (or 0.02) - Deadline: 6 months (3 bimesters) - Total amount to be paid at the end of the deadline (F1): P1 * (1 + i1 * n), where n is the number of bimesters. Scenario with extended deadline: - Loan amount (P2): R$ 5,000.00 - Bi-monthly interest rate (i2): unknown - Deadline: 12 months (6 bimesters) - Total amount to be paid at the end of the deadline (F2): P2 * (1 + i2 * n) The conditions given in the question are: 1) P1 = P2 2) F1 = F2 Step-by-step to solve the question: 1) Calculate F1: F1 = P1 * (1 + i1 * n) = 5000 * (1 + 0.02 * 3) = 5000 * (1 + 0.06) = 5000 * 1.06 = 5300 2) Now, using the condition F1 = F2, we have: F2 = 5300 = P2 * (1 + i2 * n) 3) Substitute P1 = P2 and n to find i2: 5300 = 5000 * (1 + i2 * 6) 4) Isolating i2: (5300/5000) - 1 = i2 * 6 0.06 = i2 * 6 5) Divide by 6 to get i2: i2 = 0.06 / 6 = 0.01 6) Converting i2 to percentage: i2 = 1.0% Therefore, the new bi-monthly interest rate to be requested by the farmer is 1.0% (correct alternative: "1.0%").

A loan of R$ 5,000.00 was granted at a simple interest rate of 2% per month. If the loan is to be repaid in 10 equal monthly installments, calculate the value of each installment and the total amount paid at the end of the 10th month. Consider that the interest is applied on the outstanding balance at the beginning of each month and that the installment does not include compound interest correction.

A farmer financed with a cooperative the inputs used in the crop in 2014. He paid $$\mathbf{20\%}$$ of the value of the inputs at the time of purchase, using part of the profit obtained in the previous year, and financed the rest in $$\mathbf{10}$$ months at a rate of $$\mathbf{2\%}$$ per month at simple interest. He noticed that he had spent the amount of $$\mathbf{R} \$ \mathbf{208.800,00}$$ with the financed part. In this case, the amount financed by the farmer for the inputs was:

A farmer financed with a cooperative the inputs used in the crop in 2014. He paid 

 of the value of the inputs at the time of purchase, using part of the profit obtained in the previous year, and financed the rest in 

 per month at simple interest. He noticed that he had spent the amount of 

 with the financed part. In this case, the amount financed by the farmer for the inputs was:

A loan of R$ 50,000.00 was contracted with a bank that charges simple interest of 3% per month. After 7 months, the debtor decided to make a partial payment of R$ 30,000.00. Considering that the partial payment was made at the end of the 7-month period, calculate the total interest paid by the debtor since the beginning of the loan. In addition, analyze the situation from the bank's point of view, highlighting how the early partial payment affected the profitability of the loan and explaining the concept of early payment discount.

Question bank: Financial Mathematics: Simple Interest

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