What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12% per annum, if interest is compounded annually?

Introduction / Context:
This is a direct compound interest computation with a constant rate and an integer number of years. You must find the interest, not the final amount, on a principal of Rs. 25,000 at 12% per annum over 3 years. Such questions are routine but important for building speed and accuracy in interest calculations.

Given Data / Assumptions:
- Principal P = Rs. 25,000.
- Annual rate r = 12% per annum.
- Time n = 3 years.
- Interest is compounded annually.
- We need the compound interest (C.I.), i.e., amount minus principal.

Concept / Approach:
We use the standard compound amount formula:
A = P * (1 + r/100)^n.
Once we find A, the compound interest is C.I. = A - P. For r = 12%, the growth factor per year is 1.12. Therefore, over 3 years, the factor is (1.12)^3.

Step-by-Step Solution:
Step 1: Write the amount formula: A = 25000 * (1 + 12/100)^3.Step 2: Simplify the inner term: 1 + 12/100 = 1.12.Step 3: Compute (1.12)^3 = 1.404928 (approximately).Step 4: Multiply: A ≈ 25000 * 1.404928 = 35123.20.Step 5: Compound interest C.I. = A - P = 35123.20 - 25000 = 10123.20.Step 6: Therefore, the compound interest on Rs. 25,000 for 3 years at 12% per annum is Rs. 10,123.20.

Verification / Alternative check:
Compute year by year: After 1 year: 25000 * 1.12 = 28000. After 2 years: 28000 * 1.12 = 31360. After 3 years: 31360 * 1.12 = 35123.20. Subtracting 25,000 again gives an interest of 10,123.20. Both methods yield the same result, confirming the calculation.

Why Other Options Are Wrong:
Rs. 12,100 or Rs. 12,552 and Rs. 12,665 are larger amounts that might be mistaken for final amounts or arise from confusion between amount and interest. Rs. 9,850 comes from simple interest or using the wrong rate or time period. Only Rs. 10,123.20 matches the correct compound interest for the given data.

Common Pitfalls:
Typical mistakes include stopping after computing the amount and forgetting to subtract the principal, or using the simple interest formula instead. Some learners also round intermediate values too early. Always keep sufficient precision until the final step and clearly distinguish between amount and interest.

Final Answer:
The compound interest on Rs. 25,000 after 3 years at 12% per annum is Rs. 10,123.20.