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.
Correct Answer: 6¼%
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%