Compare SI vs CI — Extra interest earned at 6% over 3 years: A person invests at 6% per annum. The simple interest over 3 years is ₹ 900. If interest were compounded annually at the same rate for 3 years on the same principal, how much more interest would be earned?

Introduction / Context:
Simple interest (SI) grows linearly with time, whereas compound interest (CI) includes interest on previously earned interest. The “extra” comes from this compounding effect. With the same rate and time, comparing SI and CI on the same principal cleanly quantifies that extra amount.

Given Data / Assumptions:

• SI over 3 years = ₹ 900 at 6% p.a.
• Thus P * 0.06 * 3 = 900 ⇒ P = 900 / 0.18 = ₹ 5000
• CI rate r = 6% per annum, t = 3 years (annual compounding)

Concept / Approach:
Compute CI over 3 years: CI = P[(1 + r)^3 − 1]. The extra interest = CI − SI. Plug P = 5000, r = 0.06, t = 3 to get the numeric difference.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• ₹ 38.13, ₹ 25.33, ₹ 35.30, ₹ 45.00 do not match the computed extra at 6% over 3 years on ₹ 5000.

Common Pitfalls:

• Using 6 as 6% (0.06) confusion; always convert to decimal.
• Forgetting to subtract SI from CI to isolate the “extra”.

Final Answer:
Rs. 55.08.