Simple vs Compound Interest — The simple interest on a certain sum for 2 years at 4% p.a. is ₹ 80. What is the compound interest on the same sum for 2 years at 4% p.a.?

Introduction / Context:
From the stated simple interest, we can infer the principal, then compute the corresponding compound interest over the same time at the same rate.

Given Data / Assumptions:

• SI = ₹ 80 for 2 years at 4% p.a.
• Need CI for 2 years at 4% p.a. on the same principal.

Concept / Approach:
SI = P * r * t ⇒ P = SI / (r * t) = 80 / (0.04 * 2) = 1,000. CI (2 years) = P * [(1 + r)^2 − 1].

Step-by-Step Solution:
P = 1,000(1 + 0.04)^2 − 1 = 1.0816 − 1 = 0.0816CI = 1,000 * 0.0816 = ₹ 81.60

Verification / Alternative check:
Compute yearwise: Year-1 interest 40; Year-2 interest on amount 1,040 is 41.60; total 81.60.

Why Other Options Are Wrong:
₹ 80 equals SI, not CI; others come from arithmetic slips.

Common Pitfalls:
Assuming SI and CI are equal over 2 years; they only match for t = 1 year.

Final Answer:
₹ 81.60