Target income → find investment at a premium: What sum must be invested in 10% stock quoted at 102 to obtain an annual income of ₹400?

Introduction / Context:
To achieve a fixed annual income from a stock with a given coupon and quote, the necessary investment equals the income divided by the yield per rupee at the given price. This is a straightforward rearrangement of the income formula.

Given Data / Assumptions:

• Desired income = ₹400 per year.
• Coupon rate = 10% ⇒ ₹10 per ₹100 nominal.
• Quoted price = 102 ⇒ ₹102 per ₹100 nominal.

Concept / Approach:
If investment is I, the number of ₹100-nominal units purchased = I / 102. Annual income = (I / 102) * 10. Set equal to 400 and solve for I.

Step-by-Step Solution:
(I / 102) * 10 = 400.I = 400 * 102 / 10 = 40 * 102 = ₹4080.

Verification / Alternative check:
Units purchased = 4080 / 102 = 40. Income = 40 * 10 = ₹400. Exact match confirms the calculation.

Why Other Options Are Wrong:

• ₹4800, ₹8040, ₹8400 correspond to different combinations and would not yield exactly ₹400 at the quoted price.

Common Pitfalls:

• Applying 10% to the investment directly without accounting for the premium price.

Final Answer:
Rs. 4080