Question

Students of an MBA school have got together to constitute a fund where each student has contributed Rs. 10000. This group of 20 students laid down certain rules for investment where it was agreed that 50 percent of the fund would be invested in riskless government securities while the rest 50 percent would be invested in equities. At the end of the year the group realizes that the crash in the stock market has left them with zero return on equities but 1 percent dividend gain on the shares bought. The return on the riskless government security has been 7.8 percent in the last year. If the gains are to be divided equally, the gain per student is

• A. 2.2 percent
• B. 4.4 percent
• C. 6.6 percent
• D. None of the option is correct

Answer 1

The Correct Option is B

Each of the 20 students contributed Rs. 10,000, so the total fund is:
\[ 20 \times 10,000 = Rs. 200,000 \]
Half of this fund is invested in riskless government securities and the other half in equities:
\[ \text{Investment in government securities} = \frac{200,000}{2} = Rs. 100,000 \]
\[ \text{Investment in equities} = \frac{200,000}{2} = Rs. 100,000 \]
The return on equities is zero, but the return on government securities is 7.8%:
\[ \text{Return on government securities} = 100,000 \times 0.078 = Rs. 7,800 \]
This gain is divided equally among the 20 students:
\[ \text{Gain per student} = \frac{7,800}{20} = Rs. 390 \]
The gain per student as a percentage of their initial contribution:
\[ \frac{390}{10,000} \times 100 = 3.9\% \]
Thus, the gain per student is 3.9%, which does not match any of the given options. Therefore,
Answer: D (None of the options is correct)

Answer 2

Since each student contributed equally and the fund is split equally between the two investments, the percentage gain per student equals the overall weighted-average return on the fund -- there is no need to compute rupee amounts first.

Half the fund earns 7.8% and the other half earns 1% (the dividend gain, since the equity price itself did not grow):
\[\text{Average return}=0.5\times7.8\%+0.5\times1\%=3.9\%+0.5\%=4.4\%\]

1. Option A (2.2 percent): Does not match the weighted average.
2. Option B (4.4 percent): Matches exactly.
3. Option C (6.6 percent): Does not match.
4. Option D (None of the option is correct): Ruled out since Option B matches.

The gain per student, as a percentage of their contribution, is 4.4%.

Hence, the correct answer is Option B: 4.4 percent.