Question

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

• A. Rs. 19642
• B. Rs. 10784
• C. Rs. 10504
• D. Rs. 15000

Answer 1

Answer: (C)

Rs. 10504

Answer 2

The correct option is (C): Rs. 10504
To determine how much money 'A' should invest to secure an annual income of Rs. 1500 from 15% debentures, we can follow these steps:

Step 1: Calculate the Effective Yield of the Debentures
1. Face Value of Debenture: Rs. 100
2. Interest Rate: 15% of face value = $0.15 \times 100 = Rs. 15$
3. Cost of Debenture: Rs. 104
4. Brokerage: 1% of the cost = $0.01 \times 104 = Rs. 1.04$
5. Total Cost per Debenture:
$104 + 1.04 = Rs. 105.04$

Step 2: Calculate the Effective Return
- The effective annual return on the investment is given by:
$\text{Effective Return} = \frac{\text{Annual Interest}}{\text{Total Cost}} \times 100$

Using the figures we have:
$\text{Effective Return} = \frac{15}{105.04} \times 100 \approx 14.26\%$

Step 3: Determine Required Investment
To achieve an annual income of Rs. 1500 with an effective return of approximately 14.26%, the required investment can be calculated using:
$\text{Required Investment} = \frac{\text{Desired Income}}{\text{Effective Return}} \times 100$
$\text{Required Investment} = \frac{1500}{14.26} \times 100 \approx 10504.20$

Final Step: Conclusion
The closest option to Rs. 10504.20 is: Rs. 10504