Required investment for target income: To produce an annual income of ₹500 from a 4% stock quoted at 90, how much money must be invested (market investment)?

Introduction / Context:
You want a fixed income from a stock that pays a fixed percentage on nominal value but trades at a market price. The investment required depends on the relation between coupon rate and quoted price.

Given Data / Assumptions:

• Target annual income = ₹500.
• Stock rate = 4% paid on nominal ₹100 ⇒ ₹4 dividend per ₹100 nominal.
• Market price = ₹90 per ₹100 nominal.

Concept / Approach:
Let I be the total investment. Then the number of ₹100-nominal units purchased is I / 90. Annual income = (I / 90) * 4. Set equal to ₹500 and solve for I.

Step-by-Step Solution:
(I / 90) * 4 = 500.I = 500 * 90 / 4 = 500 * 22.5 = ₹11250.

Verification / Alternative check:
At I = ₹11250, number of units = 11250 / 90 = 125. Income = 125 * 4 = ₹500, confirming the requirement.

Why Other Options Are Wrong:

• ₹12500, ₹18000, ₹20000 yield incomes different from ₹500 at 4% with price 90.

Common Pitfalls:

• Using 4% on the investment directly (which would be wrong since 4% applies to nominal, not market price).

Final Answer:
Rs. 11250