By investing in 16⅔ percent stock at Rs 64, one earns Rs 1,500 per year in dividends. What is the investment amount?

Given data

• Coupon rate = 16⅔ percent = 50/3 per Rs 100 face
• Market price = Rs 64 per Rs 100 face
• Annual dividend received = Rs 1,500

Concept / Approach

• Dividend per rupee invested = (Dividend per 100 face) / Market price.
• Investment = Total dividend ÷ Dividend per rupee.

Step-by-step calculation

Dividend per rupee invested = (50/3) / 64 = 50/192 = 25/96Investment = 1,500 ÷ (25/96) = 1,500 × 96 / 25 = Rs 5,760

Verification

At Rs 5,760 invested, face value bought = 5,760/64 × 100 = 9,000; dividend = 16⅔ percent of 9,000 = 1,500.

Common pitfalls

• Multiplying by 64 instead of dividing when converting from face to market.
• Using 16⅔ percent of investment directly, which ignores the price premium or discount.

Final Answer

Rs 5,760