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13 Jan 2026, 13:01
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Bond investment, optimistic: 6,000
Bond investment, pessimistic: 18,000
An investor purchases a no interest certificate that he cannot sell for 2 years. He buys certificates with a total purchase price of $2,400. At the same time, he invests an additional sum in a treasury bond that earns 3% simple interest per year.
The investor’s goal is a combined net gain of $600 from the two investments after 2 years.
Two analysts give different projections for how the certificate’s market value will change over the two years. Under the optimistic projection, each year the market value increases by a fixed amount equal to 5% of the original $2,400 purchase price. Under the pessimistic projection, each year the market value decreases by a fixed amount equal to 10% of the original $2,400 purchase price.
In the table, select for Bond investment, optimistic the amount the investor must invest in the bond to reach the $600 goal under the optimistic scenario, and select for Bond investment, pessimistic the amount the investor must invest in the bond to reach the $600 goal under the pessimistic scenario. Make only two selections, one in each column.
The investor’s goal is a combined net gain of $600 from the two investments after 2 years.
Two analysts give different projections for how the certificate’s market value will change over the two years. Under the optimistic projection, each year the market value increases by a fixed amount equal to 5% of the original $2,400 purchase price. Under the pessimistic projection, each year the market value decreases by a fixed amount equal to 10% of the original $2,400 purchase price.
In the table, select for Bond investment, optimistic the amount the investor must invest in the bond to reach the $600 goal under the optimistic scenario, and select for Bond investment, pessimistic the amount the investor must invest in the bond to reach the $600 goal under the pessimistic scenario. Make only two selections, one in each column.
| Bond investment, optimistic | Bond investment, pessimistic | |
| 6,000 | ||
| 8,000 | ||
| 12,000 | ||
| 14,000 | ||
| 18,000 | ||
| 36,000 |
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Official Answer
Bond investment, optimistic: 6,000
Bond investment, pessimistic: 18,000
13 Jan 2026, 13:01
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Bookmarks
Official Solution:
Optimistic scenario:
Each year the certificate gains 5% of 2,400, which is 120. Over 2 years, the gain is 240.
So the bond must provide the remaining gain: 600 − 240 = 360.
At 3% simple interest per year, the bond earns 6% over 2 years, so 0.06 × Bond investment = 360.
Bond investment = 360/0.06 = 6,000.
Pessimistic scenario:
Each year the certificate loses 10% of 2,400, which is 240. Over 2 years, the loss is 480.
So the bond must cover 600 + 480 = 1,080 in gain.
With 6% total simple interest over 2 years, 0.06 × Bond investment = 1,080.
Bond investment = 1,080/0.06 = 18,000.
Correct answer:
Bond investment, optimistic "6,000"
Bond investment, pessimistic "18,000"
Bunuel
Optimistic scenario:
Each year the certificate gains 5% of 2,400, which is 120. Over 2 years, the gain is 240.
So the bond must provide the remaining gain: 600 − 240 = 360.
At 3% simple interest per year, the bond earns 6% over 2 years, so 0.06 × Bond investment = 360.
Bond investment = 360/0.06 = 6,000.
Pessimistic scenario:
Each year the certificate loses 10% of 2,400, which is 240. Over 2 years, the loss is 480.
So the bond must cover 600 + 480 = 1,080 in gain.
With 6% total simple interest over 2 years, 0.06 × Bond investment = 1,080.
Bond investment = 1,080/0.06 = 18,000.
Correct answer:
Bond investment, optimistic "6,000"
Bond investment, pessimistic "18,000"
