Interest-rate hike and annual income increase: If the annual simple interest rate on an investment rises from 6.5% to 8%, a person’s yearly interest income increases by ₹ 4050. Find the invested capital (principal).

Introduction / Context:
When a bank increases its annual simple interest rate, the investor’s yearly interest income changes in direct proportion to the principal. The difference in income equals principal times the difference in rates.

Given Data / Assumptions:

• Old rate r1 = 6.5% p.a.
• New rate r2 = 8% p.a.
• Increase in yearly interest ΔI = ₹ 4050
• Principal P = ?

Concept / Approach:
Annual simple interest = P * r / 100. The increment ΔI = P * (r2 - r1) / 100. Solve for P.

Step-by-Step Solution:
Δr = 8 - 6.5 = 1.5%ΔI = P * Δr / 1004050 = P * 1.5 / 100P = 4050 * 100 / 1.5 = ₹ 270000

Verification / Alternative check:
At 6.5%: interest = 270000 * 0.065 = ₹ 17550. At 8%: interest = 270000 * 0.08 = ₹ 21600. Increase = ₹ 4050 (matches).

Why Other Options Are Wrong:
Other amounts do not yield exactly ₹ 4050 when multiplied by 1.5% per annum.

Common Pitfalls:
Forgetting the /100 factor or miscomputing the percentage difference (1.5% as 0.015 is essential).

Final Answer:
₹ 270000