Explanation:

- Given Information:

- The sum becomes Rs 13,824 in 2 years.

- It is Rs 16,588.80 in 3 years.

- Compound interest annually.

- To Find:

- Amount at the end of the 4th year.

- Let's Calculate:

- From Rs 13,824 (2 years) to Rs 16,588.80 (3 years), the growth factor for 1 year is \( \frac{16,588.80}{13,824} \).

- Compute the growth factor: \( \frac{16,588.80}{13,824} \approx 1.20 \).

- Multiply Rs 16,588.80 by this growth factor for the 4th year:

- Rs 16,588.80 × 1.20 ˜ Rs 19,906.56.

- Answer Options:

- Option 1: Rs 20,238.

- Option 2: Rs 18,248.

- Option 3: Rs 19,907.

- Option 4: Rs 18,579.

- Conclusion:

- The amount after 4 years is approximately Rs 19,907.

- The closest option is Option 3: Rs 19,907.

Option 3: Rs 19,907 is the correct choice.