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

The Correct Option is C

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