Find the principal amount if the compound interest earned at the rate of 10% per annum for 2 years, compounded annually, is Rs. 420.

Introduction / Context:
This question tests your ability to work backwards from the compound interest amount to the original principal. You are given the interest earned over 2 years at a fixed annual compound rate and must determine how much was originally invested.

Given Data / Assumptions:

Rate of interest r = 10% per annum.
Time t = 2 years.
Compound interest (CI) for 2 years = Rs. 420.
Compounding is annual (once per year).
Principal is denoted by P, and amount by A.

Concept / Approach:
For annual compounding: A = P * (1 + r/100)^t Compound interest is: CI = A - P We are given CI and r and t, so we first express A in terms of P, then set A - P = 420, and solve for P. For r = 10% and t = 2 years, the amount factor is (1.10)^2 = 1.21.

Step-by-Step Solution:
Step 1: Write the amount in terms of P. A = P * (1.10)^2 = P * 1.21. Step 2: Express compound interest. CI = A - P = P * 1.21 - P = P * (1.21 - 1) = P * 0.21. Step 3: Use the given CI to find P. P * 0.21 = 420. P = 420 / 0.21 = 2000.

Verification / Alternative check:
Check the result by recomputing the amount. With P = Rs. 2000: A = 2000 * 1.21 = Rs. 2420. Compound interest = A - P = 2420 - 2000 = Rs. 420, which matches the given CI. Hence, the principal is verified as Rs. 2000.

Why Other Options Are Wrong:
If P = 2100, CI for 2 years at 10% would be 2100 * 0.21 = 441, not 420. Similarly, for 1900 or 2150, the calculated CI does not equal 420. Only P = 2000 satisfies the condition.

Common Pitfalls:
Some students mistakenly use the simple interest formula or forget that compound interest for 2 years is not simply 2 * P * r / 100. Others may incorrectly apply the percentage or ignore the power when dealing with (1 + r/100)^t. Always compute the amount correctly and then subtract the principal to get CI.

Final Answer:
The principal amount is Rs. 2000.