Find the annual rate from two consecutive CI amounts: A sum grows to ₹ 578.40 in 2 years and to ₹ 614.55 in 3 years under compound interest with annual compounding. Determine the annual rate of interest.

Introduction / Context:
Two successive annual amounts let us take their ratio to get 1 + r immediately. This avoids principal calculations and provides a clean way to read off the annual rate under CI (annual compounding).

Given Data / Assumptions:

• A(2 years) = ₹ 578.40
• A(3 years) = ₹ 614.55
• Annual compounding

Concept / Approach:
(1 + r) = A(3)/A(2). Convert the decimal to a recognisable fraction/percentage if possible. Then r = (A3/A2 − 1) × 100% per annum.

Step-by-Step Solution:
1 + r = 614.55 / 578.40 = 1.0625r = 0.0625 = 6.25% = 6¼% p.a.

Verification / Alternative check:
1.0625 = 17/16. Over one year, that’s exactly 6.25% (since 16 grows to 17). Multiplying ₹ 578.40 by 1.0625 gives ₹ 614.55 exactly.

Why Other Options Are Wrong:
6%, 6½%, or 6¾% do not match the precise ratio; 5% is far too small.

Common Pitfalls:
Rounding the ratio too early and picking 6% or 6.5% by approximation rather than exact calculation.

Final Answer:
6¼%