Convert SI to CI at 4% for 2 years — same principal: Simple interest at 4% per annum for 2 years on a certain sum is ₹ 80. What is the compound interest on the same principal for the same period and rate?

Introduction / Context:
Given SI over a duration, we can determine the principal; then compute CI with annual compounding for the same rate and time. The CI will be slightly larger due to interest on interest in the second year.

Given Data / Assumptions:

• SI = ₹ 80 for 2 years at 4% p.a.
• r = 4% = 0.04; t = 2 years

Concept / Approach:
SI = P * r * t → P = SI / (r * t). CI uses A = P * (1 + r)^t; CI = A − P. Alternatively, CI − SI over 2 years equals P * r^2.

Step-by-Step Solution:
P = 80 / (0.04 * 2) = 80 / 0.08 = ₹ 1000A = 1000 * (1.04)^2 = 1000 * 1.0816 = ₹ 1081.60CI = 1081.60 − 1000 = ₹ 81.60

Verification / Alternative check:
CI − SI = P * r^2 = 1000 * 0.0016 = ₹ 1.60. Since SI was ₹ 80, CI must be ₹ 81.60 (consistent).

Why Other Options Are Wrong:
₹ 160 and ₹ 1081.60 confuse total amount or double the period incorrectly; ₹ 79.20 understates the compounding effect; “None” is unnecessary because we have an exact value.

Common Pitfalls:
Confusing amount A with CI, or forgetting that CI − SI for 2 years equals P * r^2 only when compounding annually at a fixed r.

Final Answer:
₹ 81.60