By investing Rs. 1,620 in an 8% stock, Michael earns Rs. 135 as annual dividend. At what market value per Rs. 100 nominal is the stock quoted?

Introduction / Context:
This is another yield and market price question based on the same data as a previous example, but with different distractor options. The investor's total dividend and total investment are known, and we must determine the market value of an 8% stock that results in the observed income.

Given Data / Assumptions:

• Michael invests Rs. 1,620 in an 8% stock.
• Annual dividend income = Rs. 135.
• Dividend rate = 8% on nominal value, so Rs. 8 per Rs. 100 nominal.
• No brokerage is mentioned.

Concept / Approach:
If P is the market price per Rs. 100 nominal, then investing P rupees buys Rs. 100 nominal and yields Rs. 8 in dividend. For an investment of 1,620 rupees, the number of hundreds of nominal value purchased is 1620 / P, and the total dividend is (1620 / P) * 8. We equate this to the known income of Rs. 135 and solve for P.

Step-by-Step Solution:
Step 1: Let P be the market price per Rs. 100 nominal. Step 2: Dividend from Rs. 1,620 investment = (1620 / P) * 8. Step 3: Given this dividend equals Rs. 135, so (1620 / P) * 8 = 135. Step 4: Multiply both sides by P: 1620 * 8 = 135 * P. Step 5: Compute the left side: 1620 * 8 = 12,960. Step 6: Therefore P = 12,960 / 135 = Rs. 96. Step 7: Hence the stock is quoted at Rs. 96 per Rs. 100 nominal.

Verification / Alternative check:
At P = 96, nominal value purchased = (1620 / 96) * 100 = Rs. 1,687.50. Dividend at 8% = 0.08 * 1687.5 = Rs. 135, which matches the given income. This confirms that Rs. 96 is the correct market value.

Why Other Options Are Wrong:
Rs. 75 or Rs. 80 would lead to a higher nominal value and hence a higher dividend than Rs. 135. Rs. 145 and Rs. 245.10 are too high; buying at those prices would reduce nominal holdings far below the level needed to generate Rs. 135 at 8%. Only Rs. 96 matches exactly with the stated investment and income.

Common Pitfalls:
Students may misinterpret 8% as yield on investment rather than on nominal value or attempt to divide 135 directly by 0.08 ignoring the market price relationship. Always use the proper formula linking investment, market price, nominal value, and dividend rate to avoid such errors.

Final Answer:
The stock is quoted at a market value of Rs. 96 per Rs. 100 nominal.