Investment size from income — 3.75% stock at 96: By investing in a 3 3/4% stock at 96, one earns ₹100 annually. What investment amount (in ₹) was made?

Introduction / Context:We must invert the income formula to get the investment. Knowing the coupon rate and quoted price allows direct computation of cash needed to secure a fixed dividend income.

Given Data / Assumptions:

• Coupon = 3.75% ⇒ Dividend ₹3.75 per ₹100 nominal.
• Quoted price = ₹96 per ₹100 nominal.
• Target income = ₹100 per year.

Concept / Approach:Let I be the investment. Number of ₹100-nominal units purchased = I / 96. Income = (I / 96) * 3.75. Set equal to 100 and solve for I.

Step-by-Step Solution:(I / 96) * 3.75 = 100.I = 100 * 96 / 3.75 = 9600 / 3.75 = ₹2560.

Verification / Alternative check:Units purchased = 2560 / 96 = 26.666…; income = 26.666… * 3.75 = 100, confirming the result.

Why Other Options Are Wrong:

• ₹3600, ₹4800, ₹36000 correspond to different income targets or different quotes; they do not yield exactly ₹100 here.

Common Pitfalls:

• Applying 3.75% to the investment I instead of to nominal value per unit.

Final Answer:Rs. 2560