Successive-year CI known — find the principal (annual compounding): A sum is invested at compound interest payable annually. The interest in two successive years is ₹ 500 and ₹ 540. What is the principal?

Introduction / Context:
Under annual compounding, the second-year interest equals first-year interest multiplied by (1 + r). From the ratio of successive interests, we can find r, and then recover P from I1 = P * r.

Given Data / Assumptions:

• I1 = ₹ 500 (Year-1 interest)
• I2 = ₹ 540 (Year-2 interest)
• Annual compounding at fixed r

Concept / Approach:
I2 / I1 = 1 + r → 540 / 500 = 1.08 → r = 8%. Then use I1 = P * r to get the principal P.

Step-by-Step Solution:
1 + r = 540 / 500 = 1.08 → r = 8%P = I1 / r = 500 / 0.08 = ₹ 6250

Verification / Alternative check:
Year-1 interest on ₹ 6250 at 8% is ₹ 500. Amount after Year-1 = 6250 + 500 = ₹ 6750. Year-2 interest = 6750 * 8% = ₹ 540 (checks).

Why Other Options Are Wrong:
₹ 3750, ₹ 5000, or ₹ 5600 do not produce the given pair (500, 540) at 8%.

Common Pitfalls:
Using I2 = P * r directly without accounting for growth in the amount from year 1 to year 2 under compounding.

Final Answer:
₹ 6250