Compound vs Simple Interest – Given difference to find SI: On a certain principal, the difference between compound interest and simple interest at 5% per annum for 2 years is ₹ 16. Find the simple interest for 2 years.

Introduction / Context:
For exactly 2 years, CI − SI = P * r^2 / 10000 (r in percent). Using this, we recover P, then compute SI = P * r * t / 100.

Given Data / Assumptions:

• CI − SI = ₹ 16
• r = 5%
• t = 2 years

Concept / Approach:
16 = P * 5^2 / 10000 = P * 25 / 10000 = 0.0025 P → P = 6400. SI = P * r * t / 100.

Step-by-Step Solution:
P = 16 / 0.0025 = 6400SI = 6400 * 5 * 2 / 100 = 6400 * 0.10 = ₹ 640

Verification / Alternative check:
CI for 2 years at 5% on 6400 is 640 + 16 = 656; difference is 16, as given.

Why Other Options Are Wrong:
₹ 520, ₹ 840, ₹ 932 arise from using wrong r or t.

Common Pitfalls:
Applying the 2-year shortcut to other durations, or mixing percent with decimal.

Final Answer:
₹ 640