Stocks and Shares — Net yield with market discount and brokerage What effective annual yield (rate of return in %) is obtained by investing in a 7% stock quoted at a 5% discount, when brokerage is 1/4% on purchase?

Introduction / Context:
This question from stocks and shares tests how to compute the investor’s effective yield (also called rate of return) when the market price differs from par (due to premium or discount) and when brokerage applies. Yield compares the annual dividend actually received to the total cash paid to acquire the stock.

Given Data / Assumptions:

• Coupon/Dividend rate = 7% per Rs. 100 nominal.
• Quoted at 5% discount ⇒ market price = Rs. 95 per Rs. 100 nominal.
• Brokerage on purchase = 1/4% = 0.25% of market value.
• No tax and no other charges are considered.

Concept / Approach:
Yield (%) = (Annual dividend per 100 nominal / Total cost per 100 nominal) * 100. Total cost includes quoted market price plus purchase brokerage. Dividend is always calculated on nominal value, not on the market price.

Step-by-Step Solution:
Market price per 100 nominal = 100 * (1 − 0.05) = Rs. 95.Brokerage on purchase = 0.25% of 95 = 95 * 0.0025 = Rs. 0.2375 ≈ Rs. 0.24 (keep exact in formula).Total cost per 100 nominal = 95 + 0.2375 = Rs. 95.2375.Annual dividend per 100 nominal = 7% of 100 = Rs. 7.Yield = (7 / 95.2375) * 100 ≈ 7.35%.

Verification / Alternative check:
A common quick check is to first compute yield ignoring brokerage: 7/95 * 100 = 7.3684%. Adding brokerage slightly increases cost and reduces yield to about 7.35%, which is consistent with the precise calculation above.

Why Other Options Are Wrong:
7.55% and 8.00% are too high and would correspond to a lower cost than actually paid.7.05% and 6.80% are too low; they would require a higher all-in purchase price than given.

Common Pitfalls:
Students often forget that brokerage on purchase is added to cost (reducing yield) and that the dividend is on nominal (par) value, not on the market price. Mixing those two bases causes systematic errors.

Final Answer:
7.35%