Compound Interest — Recover principal from total CI over 2 years: At 5% per annum compounded yearly, a sum earns ₹ 410 as compound interest in 2 years. Find the principal.

Introduction / Context:
When the total compound interest over a fixed number of years is known, and the annual rate is given, we can express that interest directly in terms of the principal and solve for the principal. For 2 years, the growth factor is (1 + r)^2 and the CI equals P[(1 + r)^2 − 1].

Given Data / Assumptions:

• Annual rate r = 5% = 0.05
• Time t = 2 years with annual compounding
• Total CI over 2 years = ₹ 410
• Principal P unknown

Concept / Approach:
CI(2y) = P[(1 + r)^2 − 1] = P(2r + r^2) = P(0.10 + 0.0025) = 0.1025 P. Set 0.1025 P = 410 and solve for P.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• ₹ 8000, ₹ 21000, ₹ 42000, ₹ 4100 do not satisfy 410 = 0.1025 * P.

Common Pitfalls:

• Treating 5% as 5 (forgetting to convert to 0.05).
• Confusing total amount with interest; here ₹ 410 is interest only.

Final Answer:
₹ 4000.