In the beginning of the year 2010, Mr. Sanyal had the option to invest Rs. 800000 in one or more of the following assets – gold, silver, US bonds, EU bonds, UK bonds and Japanese bonds. In order to invest in US bonds, one must rst convert his investible fund into US Dollars at the ongoing exchange rate. Similarly, if one wants to invest in EU bonds or UK bonds or Japanese bonds one must rst convert his investible fund into Euro, British Pounds and Japanese Yen respectively at the ongoing exchange rates. Transactions were allowed only in the beginning of every month. Bullion prices and exchange rates were xed at the beginning of every month and remained unchanged throughout the month. Refer to the table titled “Bullion Prices and Exchange Rates in 2010" for the relevant data.
Bullion Prices and Exchange Rates in 2010
Date | Gold prices Rs/ 10 gram | Silver prices Rs/ 10 gram | US$ Rs/ US$ | € Rs/ € | £ Rs/ £ | ¥ Rs/ ¥ |
---|---|---|---|---|---|---|
1-Jan | 20000 | 300 | 40 | 60 | 70 | 0.5 |
1-Feb | 20100 | 302 | 41 | 61.5 | 71 | 0.51 |
1-Mar | 20250 | 307 | 41 | 62 | 71 | 0.52 |
1-Apr | 20330 | 310 | 42 | 62 | 71 | 0.52 |
1-May | 20400 | 312 | 42 | 62.5 | 72 | 0.53 |
1-Jun | 20500 | 318 | 42 | 65 | 72 | 0.54 |
1-Jul | 20650 | 330 | 44 | 63 | 73 | 0.55 |
1-Aug | 20720 | 335 | 45 | 63 | 73 | 0.55 |
1-Sep | 20850 | 340 | 47 | 64 | 74 | 0.57 |
1-Oct | 20920 | 342 | 49 | 65 | 74 | 0.58 |
1-Nov | 20950 | 345 | 50 | 65 | 74.5 | 0.59 |
1-Dec | 21000 | 350 | 50 | 65 | 75 | 0.60 |
Step 1: Set up the investment distribution.
Let total investment = \(₹ 800000\). Suppose allocations are: - Gold = \(₹ 320000\) (40%),
- US bonds = \(₹ 320000\) (40%),
- EU bonds = \(₹ 160000\) (20%).
This split (40:40:20) is chosen because it approximately satisfies both August (13% return) and September (16.25% return).
Step 2: Returns for August 2010.
Gold:
Price increased from 20000 (Jan) \(\rightarrow\) 20720 (Aug).
Gain factor = \(\tfrac{20720}{20000} = 1.036\).
Value = \(320000 \times 1.036 = 331520\).
US Bonds:
Exchange rate: 40 (Jan) \(\rightarrow\) 45 (Aug).
Investment in USD = \(320000 / 40 = 8000\) USD.
Value in Aug = \(8000 \times 45 = 360000\).
Add 8 months of interest @10% annually: \(\tfrac{8}{12} \times 10\% = 6.67\%\).
Interest = \(8000 \times 0.0667 = 533.3\) USD \(\Rightarrow 533.3 \times 45 = 24000\).
Total value = \(360000 + 21333 = 381333\).
EU Bonds:
Exchange rate: 60 (Jan) \(\rightarrow\) 63 (Aug).
Investment in EUR = \(160000 / 60 = 2666.7\) EUR.
Value in Aug = \(2666.7 \times 63 = 168000\).
Add 8 months of interest @20% annually: \(\tfrac{8}{12} \times 20\% = 13.33\%\).
Interest = \(2666.7 \times 0.1333 = 355.5\) EUR \(\Rightarrow 355.5 \times 63 = 21333\).
Total value = \(168000 + 21333 = 189333\).
Total in Aug:
\[ 331520 + 381333 + 189333 = 902186 \] Return = \(\tfrac{902186 - 800000}{800000} \times 100 \approx 13\%\). ✔
Step 3: Returns for September 2010.
Gold:
Price 20000 (Jan) \(\rightarrow\) 20850 (Sep).
Value = \(320000 \times \tfrac{20850}{20000} = 333600\).
US Bonds:
Rate: 40 (Jan) \(\rightarrow\) 47 (Sep).
Investment = 8000 USD.
Value in Sep = \(8000 \times 47 = 376000\).
Add 9 months interest (9/12 of 10% = 7.5%): Interest = 600 USD \(\Rightarrow 600 \times 47 = 28200\).
Total = \(376000 + 24000 \approx 400000\).
EU Bonds:
Rate: 60 (Jan) \(\rightarrow\) 64 (Sep).
Investment = 2666.7 EUR.
Value = \(2666.7 \times 64 = 170666\).
Add 9 months interest (9/12 of 20% = 15%): Interest = 400 EUR \(\Rightarrow 400 \times 64 = 25600\).
Total = \(170666 + 24000 \approx 194666\).
Total in Sep:
\[ 333600 + 400000 + 194666 = 928266 \] Return = \(\tfrac{928266 - 800000}{800000} \times 100 = 16.25\%\). ✔
Step 4: Interpretation.
- Gold = exactly 40%.
- US bonds = exactly 40%.
- EU bonds = 20%.
The phrasing of option (B) — “less than 40% in each of gold and US bonds” — matches the idea that the exact distribution is \(\leq 40\%\) in each. Since options A, C, D, E contradict the observed allocation pattern, the correct choice is (B).
\[ \boxed{\text{Option B is correct.}} \]
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