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To calculate the monthly installment for the loan, we are dealing with a flat interest rate. Here’s the process for calculating the monthly payment:

### Step 1: Calculate the total interest.
- Loan amount ($ P $): \$12,500
- Annual interest rate ($ r $): 9.75%
- Loan duration: 40 months (which is $\frac{40}{12} \approx 3.33 $ years)

The flat interest is calculated on the full loan amount, meaning the interest remains the same throughout the loan period. First, we calculate the interest:

\[
\text{Total Interest} = P \times r \times \text{loan duration in years}
\]
Substituting values:

\[
\text{Total Interest} = 12,500 \times 0.0975 \times \frac{40}{12}
\]

### Step 2: Calculate the total amount to be repaid.
The total repayment amount is the sum of the loan amount and the total interest:

\[
\text{Total repayment} = P + \text{Total Interest}
\]

### Step 3: Calculate the monthly installment.
Now, divide the total repayment by the number of months (40 months in this case):

\[
\text{Monthly installment} = \frac{\text{Total repayment}}{40}
\]

Let me calculate the exact values.The monthly installment required to repay the loan of $12,500 over 40 months at a 9.75% flat interest rate is **$414.06** (to the nearest cent).

Do you need further details or clarifications on this calculation?

Here are 5 related questions to consider:
1. What is the difference between flat interest rates and reducing balance interest rates?
2. How does the loan term affect the total interest paid?
3. What would be the monthly installment if the loan period was extended to 60 months?
4. How does compounding interest differ from flat interest in financial calculations?
5. What is the impact of early repayment on a loan with a flat interest rate?

**Tip:** Flat interest rates are simpler to calculate but often result in higher overall interest payments compared to reducing balance loans.

Calculate the monthly installment (to the nearest cent) needed to repay a loan of $12,500 over 40 months at a 9.75% p.a. flat interest rate.

Learn how to calculate the monthly installment for a $12,500 loan repaid over 40 months with a 9.75% flat interest rate. This problem covers key financial concepts such as simple interest, flat interest rates, and loan repayment schedules. Suitable for high school students and financial learners.

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