Simple Interest – Find principal from change in rate: A sum was invested for 4 years. If the annual simple interest rate had been 2% higher, the total interest would have been ₹ 56 more. What is the principal?

Introduction / Context:
In simple interest, increasing the rate by a fixed percentage changes the total interest linearly with principal and time.

Given Data / Assumptions:

• Time t = 4 years
• Rate increase Δr = 2% = 0.02
• Extra interest ΔI = ₹ 56

Concept / Approach:
ΔI = P * Δr * t. Solve for P.

Step-by-Step Solution:
56 = P * 0.02 * 4 = 0.08 PP = 56 / 0.08 = 700

Verification / Alternative check:
At principal ₹ 700, extra per year = 2% of 700 = 14; over 4 years → ₹ 56 (matches).

Why Other Options Are Wrong:
₹ 680, ₹ 720, ₹ 820 give extra interest not equal to ₹ 56.

Common Pitfalls:
Using compound interest thinking or forgetting to convert 2% into decimal.

Final Answer:
₹ 700