A wants to secure an annual income of ₹ 1500 by investing in 15% debentures of face value ₹ 100 each and available for ₹ 104 each. If the brokerage is 1%, then the sum of money he should invest is

### Concept & Total Investment Strategy To find the total investment required to secure a specific income, first determine how many shares/debentures are needed. Then, multiply that number by the actual cost price per share (including brokerage). $$ \text{Total Investment} = \text{Number of Shares} \times \text{Cost per Share} $$ ### Step-by-Step Solution * **Given:** Target Income = ₹ 1500, Dividend Rate = 15%, Face Value = ₹ 100, Market Value = ₹ 104, Brokerage = 1%. * **Step 1: Find Income per Debenture.** Income per debenture = 15% of ₹ 100 = ₹ 15. * **Step 2: Find Number of Debentures Needed.** Number of debentures = $\frac{\text{Target Income}}{\text{Income per Debenture}} = \frac{1500}{15} = 100$. * **Step 3: Calculate Cost per Debenture.** Brokerage is given as 1% of the market value (standard modern practice unless noted, let's calculate: 1% of 104 = 1.04). Cost per debenture = Market Value + Brokerage = $104 + 1.04 = 105.04$. * **Step 4: Calculate Total Investment.** Total Investment = $100 \times 105.04 = 10504$. ### Exam Strategy & Shortcut Find the number of debentures instantly by dividing the total required income by the per-debenture income ($1500 \div 15 = 100$). Because you need exactly 100 debentures, you just shift the decimal point of the true cost per debenture ($104 + 1.04 = 105.04$) two places to the right. ### Common Pitfall Calculating the brokerage as 1% of the Face Value (₹ 1) instead of the Market Value, which would lead to a cost per share of ₹ 105 and a total of ₹ 10500, an incorrect answer not represented in the options. ### Final Answer Therefore, the correct answer is **₹ 10504**.