CI known for 2 years at 5% — find corresponding SI for 2 years: If the compound interest on a certain principal for 2 years at 5% per annum is ₹ 328, what is the simple interest on the same principal for the same time at the same rate?

Introduction / Context:
We can convert CI over 2 years into the principal using the compounding factor, then compute the equivalent SI over the same period from the recovered principal. CI exceeds SI because of the interest-on-interest term.

Given Data / Assumptions:

• CI (2 years, 5% p.a.) = ₹ 328
• Annual compounding, fixed rate

Concept / Approach:
For 2 years, A = P * (1.05)^2 = 1.1025P; CI = A − P = 0.1025P. Hence P = 328 / 0.1025. Once P is known, SI over 2 years is P * 0.05 * 2 = 0.10P.

Step-by-Step Solution:
P = 328 / 0.1025 = ₹ 3200SI (2 years) = 3200 * 0.10 = ₹ 320

Verification / Alternative check:
CI − SI for 2 years equals P * r^2 = 3200 * 0.0025 = ₹ 8. Thus, CI = SI + 8 → SI = 328 − 8 = ₹ 320 (consistent).

Why Other Options Are Wrong:
₹ 322, ₹ 325, or ₹ 326 do not fit the exact factors (1.1025 and 0.10).

Common Pitfalls:
Using 2 * 5% as a compounded rate; failing to invert 0.1025 correctly when solving for P.

Final Answer:
₹ 320