Back out the annual rate from consecutive CI amounts: A sum becomes ₹ 9680 in 2 years and ₹ 10648 in 3 years under compound interest (annual compounding). What is the annual rate of interest?

Introduction / Context:
When two successive-year amounts are known under annual compounding, their ratio directly gives (1 + r). This avoids computing the principal and provides a quick path to the annual rate.

Given Data / Assumptions:

• A(2 years) = ₹ 9680
• A(3 years) = ₹ 10648
• Annual compounding at fixed r

Concept / Approach:
A(3) / A(2) = (P * (1 + r)^3) / (P * (1 + r)^2) = 1 + r. Hence r = (A3 / A2) − 1.

Step-by-Step Solution:
1 + r = 10648 / 9680 = 1.10r = 0.10 = 10% per annum

Verification / Alternative check:
If r = 10%, then A(3) = A(2) * 1.10 = 9680 * 1.10 = ₹ 10648 (exact).

Why Other Options Are Wrong:
5%, 15%, and 20% do not satisfy the observed ratio; 12% would give 1.12 rather than 1.10.

Common Pitfalls:
Attempting to solve for P first, or confusing CI with SI where amounts grow linearly rather than multiplicatively.

Final Answer:
10%