Compound Interest – Rate from consecutive-year amounts: A sum amounts to ₹ 12,960 in 2 years and to ₹ 13,176 in 3 years at the same compound rate (annual). Find the rate per cent per annum.

Introduction / Context:
Successive compound amounts differ by a factor of (1 + r). Thus, the ratio of 3-year to 2-year amounts immediately yields 1 + r.

Given Data / Assumptions:

• A(2 years) = ₹ 12,960
• A(3 years) = ₹ 13,176
• Compounded annually

Concept / Approach:
(1 + r) = A3 / A2.

Step-by-Step Solution:
1 + r = 13176 / 12960 = 1.016666…r = 0.016666… = 1 2/3 %

Verification / Alternative check:
Check: A3 = A2 * (1 + r) = 12960 * 1.016666… = 13176 (given).

Why Other Options Are Wrong:
3 2/3 %, 4 %, and 7 % are larger than the ratio implies.

Common Pitfalls:
Computing r from (A3 − A2)/P instead of from A3/A2.

Final Answer:
1 2/3 %