Compound vs Simple Interest – Difference over 3 years: Find the difference between compound interest and simple interest on ₹ 10,000 for 3 years at 5% per annum (annual compounding).

Introduction / Context:
Over 3 years, CI grows as P(1 + r)^3 − P, while SI is P * r * t. Their difference quantifies the extra “interest on interest”.

Given Data / Assumptions:

• P = ₹ 10,000
• r = 5% per annum
• t = 3 years

Concept / Approach:
Compute SI and CI separately, then subtract: (CI − SI) = P[(1 + r)^3 − 1] − P * r * t.

Step-by-Step Solution:
SI = 10000 * 0.05 * 3 = ₹ 1,500CI = 10000[(1.05)^3 − 1] = 10000(1.157625 − 1) = ₹ 1,576.25Difference = 1576.25 − 1500 = ₹ 76.25

Verification / Alternative check:
Year-wise addition confirms the same excess due to compounding in years 2 and 3.

Why Other Options Are Wrong:
₹ 76, ₹ 76.50, ₹ 76.75 are near but not exact.

Common Pitfalls:
Using the 2-year shortcut P * r^2 / 10000 (only valid for exactly 2 years).

Final Answer:
₹ 76.25