Question
An 8% Rs. 100 face-value stock is quoted at Rs. 120 in
the market. The brokerage charged is 5% on the market price. If an investor wants to get an annual income of Rs. 6,048 from this stock, how much money must he pay in total (including brokerage) to buy the required shares?Solution
ATQ, Face value per share = Rs. 100 Dividend rate = 8% Dividend per share per year = 8% of 100 = Rs. 8 Let the number of shares purchased be n. Total annual income = n × 8 Given total income = 6,048 So, n × 8 = 6,048 ⇒ n = 6,048 / 8 = 756 shares Market price per share = Rs. 120 Brokerage = 5% of market price Brokerage per share = 5% of 120 = 0.05 × 120 = Rs. 6 Effective cost per share = 120 + 6 = Rs. 126 Total amount paid = number of shares × cost per share = 756 × 126 Compute: 756 × 126 = 756 × (100 + 20 + 6) = 756×100 + 756×20 + 756×6 = 75,600 + 15,120 + 4,536 = 95,256 So the investor must pay Rs. 95,256.
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