The compound interest on Rs. 8,000 for 3 years at 10% per annum, compounded annually, is to be calculated. What is the value of this compound interest?

Introduction / Context:
This is a straightforward compound interest calculation with a constant annual rate and whole number of years. It checks your ability to apply the standard compound interest formula repeatedly over multiple years and then subtract the principal to get the interest earned.

Given Data / Assumptions:
- Principal P = Rs. 8,000.
- Rate of interest r = 10% per annum.
- Time n = 3 years.
- Interest is compounded annually.
- We must find the compound interest over the 3-year period.

Concept / Approach:
For compound interest with annual compounding, the amount after n years is given by:
A = P * (1 + r/100)^n.
Once the amount A is computed, the compound interest is simply A - P. For r = 10%, the factor (1 + r/100) becomes 1.10, and for 3 years we use (1.10)^3.

Step-by-Step Solution:
Step 1: Use the formula A = P * (1 + r/100)^n.Step 2: Substitute P = 8000, r = 10, n = 3: A = 8000 * (1.10)^3.Step 3: Compute (1.10)^3 = 1.331.Step 4: Multiply: A = 8000 * 1.331 = 10648.Step 5: Compound interest = A - P = 10648 - 8000 = 2648.Step 6: Therefore, the compound interest on Rs. 8,000 for 3 years at 10% per annum is Rs. 2,648.

Verification / Alternative check:
You can also compute year by year: After 1 year, amount = 8000 * 1.10 = 8800. After 2 years, amount = 8800 * 1.10 = 9680. After 3 years, amount = 9680 * 1.10 = 10648. Subtracting the original 8000 again gives interest = 2648, confirming the result.

Why Other Options Are Wrong:
Rs. 2,145 and Rs. 2,587 correspond to errors like using simple interest or miscomputing the power (1.10)^3. Rs. 2,784 and Rs. 2,400 come from incorrectly applying the rate or number of years. Only Rs. 2,648 is consistent with correct compounding for 3 years at 10% per annum.

Common Pitfalls:
Common mistakes include using the simple interest formula P * r * n / 100, which would give 8000 * 10 * 3 / 100 = 2400, not accounting for interest-on-interest. Others miscalculate 1.1^3 or round at intermediate steps. Always apply the full power and do not subtract the principal until after computing the final amount.

Final Answer:
The compound interest on Rs. 8,000 for 3 years at 10% per annum is Rs. 2,648.