https://file.aiquickdraw.com/mathbot/file/172269777438287l7cqy8.jpg

To solve the problem, we need to determine the rate of interest using the given information:

1. **Principal (P)**: The initial amount borrowed by Ankit, which is \( P = \text{Rs.} 15,000 \).
2. **First Repayment**: After 6 years, Ankit returned \( \text{Rs.} 5,500 \).
3. **Total Payment**: After 10 years, Ankit settled the account by paying an additional \( \text{Rs.} 13,460 \).

Let's calculate the interest rate using the formula for simple interest:

\[ \text{SI} = \frac{P \times R \times T}{100} \]

Where:
- \( \text{SI} \) is the simple interest,
- \( P \) is the principal amount,
- \( R \) is the rate of interest, and
- \( T \) is the time in years.

The total amount paid after 10 years is the sum of the interest and the principal.

### Calculation

1. **Amount paid after 6 years**: \( \text{Rs.} 5,500 \) which includes partial repayment of principal and interest.

2. **Final Settlement after 10 years**: Additional \( \text{Rs.} 13,460 \).

#### Total Payment
- Total amount paid after 10 years: \( \text{Rs.} 5,500 + \text{Rs.} 13,460 = \text{Rs.} 18,960 \).

#### Calculation of Simple Interest
- Total amount due after 10 years: \( P + \text{SI} = 18,960 \)
- We know \( P = 15,000 \), so:
  \[ 15,000 + \text{SI} = 18,960 \]
  \[ \text{SI} = 18,960 - 15,000 \]
  \[ \text{SI} = 3,960 \]

#### Rate of Interest Calculation
- Using the simple interest formula:
  \[ 3,960 = \frac{15,000 \times R \times 10}{100} \]
  \[ 3,960 = 1,500R \]
  \[ R = \frac{3,960}{1,500} \]
  \[ R = 2.64\% \]

The rate of interest is approximately **2.64%**.

**Note**: The answer options in the image provided are not perfectly matching with the calculated rate, so ensure the problem data and options are accurate or check if any rounding or approximate consideration is allowed.

Would you like more details or have any questions?

### Related Questions:
1. How is simple interest different from compound interest?
2. What would be the total amount if the interest were compounded annually?
3. How does the time period affect the total interest paid?
4. What happens if the interest rate changes during the loan period?
5. Can the principal amount change during the loan period in such scenarios?
6. How does paying off part of the principal early affect the total interest paid?
7. What are some common factors that influence the rate of interest on loans?
8. How can one calculate the interest if payments are made monthly instead of at the end of the period?

### Tip:
Always double-check the final repayment terms in a loan agreement to ensure all components, like partial repayments, are correctly accounted for in interest calculations.

Learn how to calculate simple interest using Ankit's loan repayment problem. Understand the formula SI = (P * R * T) / 100 and see a step-by-step solution. Suitable for high school students studying financial mathematics.

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