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To solve this problem, let's interpret the question and apply the simple interest formula.

### Problem Interpretation

Vitor made an agreement with the bank to repay a debt of R$5,000. The bank offered a simple interest plan with:
- An interest rate of 10% per month,
- Over a period of 10 months.

The task is to find the total amount Vitor will pay by the end of the 10 months.

### Solution

Using the simple interest formula:
\[
A = P \times (1 + i \times n)
\]
where:
- $ A $ is the total amount after $ n $ months,
- $ P = 5000 $ (the principal or initial amount of debt in R$),
- $ i = 0.10 $ (the monthly interest rate of 10%),
- $ n = 10 $ (the number of months).

Substitute the values into the formula:
\[
A = 5000 \times (1 + 0.10 \times 10)
\]
\[
A = 5000 \times (1 + 1)
\]
\[
A = 5000 \times 2
\]
\[
A = 10000
\]

### Answer

The total amount Vitor will pay at the end of 10 months is **R$10,000.00**.

Would you like more details or have any questions?

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Here are five related questions to expand on this topic:

1. How would the total amount change if the interest were compounded monthly instead of being simple interest?
2. What would be the amount if the interest rate were reduced to 5% per month?
3. How would the repayment amount change if the repayment period were extended to 12 months with the same interest rate?
4. What would be Vitor’s monthly payment if he paid in equal installments over the 10 months?
5. How does simple interest compare to compound interest in terms of the total payment?

**Tip:** Always check if an interest rate is compounded or simple, as it significantly affects the total repayment.

Vitor fez um acordo com o banco para pagar suas dívidas. Para isso, o banco ofereceu que o montante seja pago por meio de um parcelamento a juros simples, durante 10 meses, com uma taxa de 10% ao mês. O valor da dívida de Vitor é de R$ 5.000,00. O montante pago por Vitor ao final dos 10 meses será de quanto?

Understand how to calculate the total amount Vitor will pay after 10 months at a 10% simple interest rate per month on a R$5,000 debt. This example uses the simple interest formula to determine the final payment amount, ideal for Grades 9-10 students learning about interest calculations.

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