What is the compound interest earned on Rs. 1000 at 10% per annum for 3 years, if the interest is compounded annually?

Introduction / Context:
This is a classic compound interest calculation. We are given the principal, the annual interest rate and the time in years. We must compute the compound interest, not the final amount. Many candidates confuse these two, so it is important to distinguish the interest portion from the total amount accumulated.

Given Data / Assumptions:

Principal P = Rs. 1000
Rate of interest r = 10% per annum
Time t = 3 years
Compounding frequency = annually (once a year)
We are asked for compound interest (CI), not for the full amount A

Concept / Approach:
For annual compounding, the amount after t years is:
A = P * (1 + r/100)^t. The compound interest is:
CI = A − P. We will compute the amount using the factor (1.10)^3, then subtract the principal to obtain the interest earned over 3 years.

Step-by-Step Solution:
Step 1: Compute the growth factor. 1 + r/100 = 1 + 10/100 = 1.10. Step 2: Raise it to the power of 3 (for 3 years). (1.10)^3 = 1.1 * 1.1 * 1.1 = 1.331. Step 3: Find the amount A. A = 1000 * 1.331 = Rs. 1331. Step 4: Find the compound interest. CI = A − P = 1331 − 1000 = Rs. 331.

Verification / Alternative check:
We can calculate year by year. Year 1: interest = 1000 * 10% = 100; amount = 1100. Year 2: interest = 1100 * 10% = 110; amount = 1210. Year 3: interest = 1210 * 10% = 121; amount = 1331. Total interest over three years = 100 + 110 + 121 = 331, which confirms our earlier result.

Why Other Options Are Wrong:
Rs. 1331 is the final amount, not the interest. Rs. 300 would be the simple interest for 3 years (1000 * 10% * 3 / 100), not the compound interest. Rs. 1300 is close to the final amount but not correct for either CI or A. Only Rs. 331 corresponds to the actual compound interest earned.

Common Pitfalls:
The most common mistake is to give the total amount instead of the interest, or to use the simple interest formula when the question clearly states compound interest. Another error is to forget that each year's interest is calculated on the increased amount, not the original principal alone. Always check whether the question is asking for CI or for the final accumulated amount.

Final Answer:
The compound interest earned is Rs. 331.