Compound vs Simple Interest — small second-year lift at 5%: The difference between the compound interest and the simple interest on the same principal at 5% per annum for 2 years is ₹ 1.50. What is the principal (the original sum)?

Introduction / Context:
For the same principal and term, compound interest (CI) slightly exceeds simple interest (SI) because interest in the second year is earned on both principal and the first year’s interest. The excess for 2 years depends only on principal and rate.

Given Data / Assumptions:

• Annual rate r = 5% = 0.05
• Time t = 2 years
• CI − SI = ₹ 1.50
• Principal P = ?

Concept / Approach:
With annual compounding for 2 years, the well-known relationship is: CI − SI = P * (r^2). This is the “interest on interest” generated in the second year: first-year interest is P * r; interest on it next year is (P * r) * r = P * r^2.

Step-by-Step Solution:
CI − SI = P * r^21.50 = P * (0.05)^21.50 = P * 0.0025P = 1.50 / 0.0025 = ₹ 600

Verification / Alternative check:
At P = 600, SI for 2 years = 600 * 0.05 * 2 = ₹ 60. CI amount = 600 * (1.05)^2 = 600 * 1.1025 = ₹ 661.50 → CI = ₹ 61.50. Difference = 61.50 − 60 = ₹ 1.50 (matches).

Why Other Options Are Wrong:
₹ 500, ₹ 400, ₹ 300, or ₹ 750 produce differences different from ₹ 1.50 when substituted into P * r^2 at r = 5%.

Common Pitfalls:
Using r/100 twice incorrectly, forgetting that for 2 years CI − SI equals P * r^2 (not P * r * t adjustments).

Final Answer:
₹ 600