The compound interest on Rs. 1,000 at 10% per annum for 3 years is to be found. What is the amount of compound interest (in rupees) earned over the 3 year period?

Introduction / Context:
This question focuses on calculating compound interest for a small principal over a moderate time period. It helps reinforce the difference between the final amount and the interest earned, an area where many learners confuse figures, especially when both are listed among the options.

Given Data / Assumptions:

• Principal P = Rs. 1,000.
• Annual interest rate r = 10% per annum.
• Time period n = 3 years.
• Interest is compounded annually.
• We must find the compound interest CI, not the final amount.

Concept / Approach:
The amount A after n years at rate r under annual compounding is A = P * (1 + r)^n. The compound interest CI is the difference between the amount and the principal, that is CI = A - P. Because both A and CI are sometimes used in options, it is important to identify which quantity the question is asking for and subtract correctly.

Step-by-Step Solution:
Step 1: Write the formula for the amount A = P * (1 + r)^n.Step 2: P = 1,000, r = 0.10, and n = 3.Step 3: Compute (1 + r) = 1 + 0.10 = 1.10.Step 4: Evaluate (1.10)^3 = 1.10 * 1.10 * 1.10 = 1.331.Step 5: Amount A = 1,000 * 1.331 = Rs. 1,331.Step 6: Compound interest CI = A - P = 1,331 - 1,000 = Rs. 331.

Verification / Alternative check:
We can verify by calculating interest year by year. After year 1, interest is 10% of 1,000, which is Rs. 100, so amount is 1,100. After year 2, interest is 10% of 1,100, which is Rs. 110, giving an amount of 1,210. After year 3, interest is 10% of 1,210, which is Rs. 121, giving a final amount of 1,331. Total interest is 100 + 110 + 121 = 331 rupees, which matches our earlier calculation.

Why Other Options Are Wrong:

• Rs. 1331: This is the final amount, not the interest. The question specifically asks for compound interest, so this is not correct.
• Rs. 300: This is the simple interest that would be earned at 10% for 3 years (100 per year), but compound interest is slightly higher because interest also earns interest.
• Rs. 1300: This is far too large to be the interest on only 1,000 rupees at 10% for 3 years.

Common Pitfalls:
Many students confuse the amount with the interest and choose the value of 1,331 instead of the actual interest of 331. Others apply the simple interest formula and compute 1,000 * 0.10 * 3 = 300, forgetting that compound interest is calculated on an increasing base each year. It is important to read the wording carefully and always double check whether the question asks for the total amount or just the interest portion.

Final Answer:
The compound interest earned on Rs. 1,000 at 10% per annum for 3 years is Rs. 331.