Difference CI vs SI — The difference between compound interest and simple interest on a sum at 5% p.a. for 2 years is ₹ 1.50. Find the principal.

Introduction / Context:
Over 2 years, the excess of compound interest (CI) over simple interest (SI) at rate r equals P * r^2. This compact result follows from expanding (1 + r)^2 and comparing with linear SI.

Given Data / Assumptions:

• r = 5% = 0.05 per annum.
• Time = 2 years.
• CI − SI = ₹ 1.50.

Concept / Approach:
For 2 years: CI = P[(1 + r)^2 − 1] = P(2r + r^2); SI = P(2r); thus CI − SI = P * r^2.

Step-by-Step Solution:
P * r^2 = 1.50 ⇒ P * (0.05)^2 = 1.50.P * 0.0025 = 1.50 ⇒ P = 1.50 / 0.0025 = 600.

Verification / Alternative check:
At P = 600: r^2 P = 0.0025 * 600 = 1.5, matches difference.

Why Other Options Are Wrong:
500, 400, 300, 800 do not satisfy P * 0.0025 = 1.50.

Common Pitfalls:
Using 2 years formula incorrectly or computing CI − SI for the wrong duration.

Final Answer:
Rs. 600