Compound vs Simple Interest — Find the difference (rounded to 2 decimals) between compound interest and simple interest on ₹ 16,200 for 3 years at 25% per annum.

Introduction / Context:
The excess of compound interest over simple interest across multiple years can be computed directly from rate and time without first finding the principal from amounts.

Given Data / Assumptions:

• P = ₹ 16,200
• r = 25% = 0.25 per annum
• t = 3 years

Concept / Approach:
For 3 years, CI − SI = P * (3r^2 + r^3) = P * r^2 * (3 + r). This comes from expanding (1 + r)^3 − 1 = 3r + 3r^2 + r^3 and subtracting 3r (the SI part).

Step-by-Step Solution:
r^2 = 0.25^2 = 0.0625; (3 + r) = 3.25Multiplier = 0.0625 * 3.25 = 0.203125Difference = 16,200 * 0.203125 = 3,290.625 ⇒ ₹ 3,290.63 (rounded to 2 decimals)

Verification / Alternative check:
Compute SI and CI separately and subtract; the above closed form should match exactly, saving time.

Why Other Options Are Wrong:
They correspond to using a wrong formula such as P*r^2 (valid only for 2 years) or arithmetic slips when multiplying.

Common Pitfalls:
Using 2-year difference formula P*r^2 for a 3-year case, or forgetting to round to 2 decimals.

Final Answer:
₹ 3,290.63