Compound Interest – Find principal from amounts at 2 and 3 years: A sum amounts to ₹ 2,916 in 2 years and ₹ 3,149.28 in 3 years at compound interest (annual). What is the principal?

Introduction / Context:
Given two consecutive annual amounts under compounding, the ratio A(3yr) / A(2yr) equals (1 + r). This quickly yields the rate; dividing either amount by the appropriate power then recovers the principal. This is an efficient two-step method without solving simultaneous equations.

Given Data / Assumptions:

• A(2yr) = 2,916
• A(3yr) = 3,149.28
• Annual compounding at constant rate

Concept / Approach:
Compute r from ratio: 3,149.28 / 2,916 = 1.08 ⇒ r = 8%. Then P = A(2yr) / (1.08)^2. With (1.08)^2 = 1.1664, we get P = 2,916 / 1.1664 = 2,500.

Step-by-Step Solution:
Find rate: (A3/A2) − 1 = 1.08 − 1 = 0.08 = 8%Compute (1.08)^2 = 1.1664Principal P = 2,916 / 1.1664 = 2,500

Verification / Alternative check:
Forward: 2,500 → 2,700 (Year 1) → 2,916 (Year 2) → 3,149.28 (Year 3). All values align exactly with the problem statement.

Why Other Options Are Wrong:
₹ 1,500, ₹ 2,000, and ₹ 3,000 do not reproduce the provided amounts at 8% compounding; ₹ 2,400 is close but still inconsistent when forward-compounded.

Common Pitfalls:
Using simple interest or averaging the amounts leads to incorrect principals. Always divide by the appropriate compound factor to back out P.

Final Answer:
₹ 2,500