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27 Dec 2025, 07:14
Kudos
Bookmarks
Bunuel
Here,
Net Gain from the investment = Interest from the treasury bond + change in market value of certificates
If the sum invested in the treasury bond is \(x\), the interest received for the 2 year duration = \(\frac{x*rate*time}{100} = \frac{x*3*2}{100} = \frac{6x}{100}\)
For the optimistic projection, change in market value over 2 years = \(\frac{2*2400*(+5)}{100} = +(24 * 10) = +240\)
For the pessimistic projection, change = \(\frac{2*2400*(-10)}{100} = -(24*20) = -480\)
Therefore,
For Optimistic Projection
\(600 = \frac{6x}{100} + 240\)
\(360 = \frac{6x}{100}\)
From here, we get x = 6000
For Pessimistic Projection
\(600 = \frac{6x}{100} - 480\)
\(1080 = \frac{6x}{100}\)
From here, we get x = 18000
27 Dec 2025, 07:17
Kudos
Bookmarks
We know that,
No interest certificate is purchased for 2400 and cant be sold for 2 yrs
Treasure bond earns 3% simple interest per year
Investor total combined netgain after 2 yrs = 600
Optimistic projection we see 5% increase of 2400$ purchase
Pessimistic projection we see 10% decrease of the 2400$ purchase
We need to know under optimistic and pessimistic projection, the amount invested in the bond
For no interest certificate,
Price = 2400
Time = 2 years
Optimistic projection: 5% increase every year
Total gain = (2400*0.05)*2 = 240
Pessimistic projection: 10% decrease every year
Total loss = (2400*0.1)*2 = 480
For bond
Let amount invested = x
Time = 2 years
Simple interest = 3%
Total gain = (x*0.03)*2 = 0.06x
We know investor goal is 600 gain in 2 years
Optimistic projection:
Amount to be gained from bond investment = 600 - 240 = 360
=> 360 = 0.06x
=> x = 6000
Pessimistic projection:
Amount to be gained from bond investment = 600 - (-480) = 1080
=> 1080 = 0.06x
=> x = 18000
Bond investment, optimistic = 6000
Bond investment, pessimistic = 18000
No interest certificate is purchased for 2400 and cant be sold for 2 yrs
Treasure bond earns 3% simple interest per year
Investor total combined netgain after 2 yrs = 600
Optimistic projection we see 5% increase of 2400$ purchase
Pessimistic projection we see 10% decrease of the 2400$ purchase
We need to know under optimistic and pessimistic projection, the amount invested in the bond
For no interest certificate,
Price = 2400
Time = 2 years
Optimistic projection: 5% increase every year
Total gain = (2400*0.05)*2 = 240
Pessimistic projection: 10% decrease every year
Total loss = (2400*0.1)*2 = 480
For bond
Let amount invested = x
Time = 2 years
Simple interest = 3%
Total gain = (x*0.03)*2 = 0.06x
We know investor goal is 600 gain in 2 years
Optimistic projection:
Amount to be gained from bond investment = 600 - 240 = 360
=> 360 = 0.06x
=> x = 6000
Pessimistic projection:
Amount to be gained from bond investment = 600 - (-480) = 1080
=> 1080 = 0.06x
=> x = 18000
Bond investment, optimistic = 6000
Bond investment, pessimistic = 18000
27 Dec 2025, 07:25
Kudos
Bookmarks
combined net gain = certificate gain + interest from bond
interest from bond = amount * bond interest * 2 years = amount * 3/100 * 2 = 0.06 * amount
certificate gain + 0.06 * amount = 600
amount = (600 - certificate gain)/0.06
optimistic case:
certificate gain = 2 * 5/100 * 2400 = 240
amount = (600 - 240)/0.06 = 6000
pessimistic case:
certificate gain = 2 * (-10/100) * 2400 = -480
amount = (600 - (-480))/0.06 = 18000
Bond investment, optimistic=6000 and Bond investment, pessimistic=18000
interest from bond = amount * bond interest * 2 years = amount * 3/100 * 2 = 0.06 * amount
certificate gain + 0.06 * amount = 600
amount = (600 - certificate gain)/0.06
optimistic case:
certificate gain = 2 * 5/100 * 2400 = 240
amount = (600 - 240)/0.06 = 6000
pessimistic case:
certificate gain = 2 * (-10/100) * 2400 = -480
amount = (600 - (-480))/0.06 = 18000
Bond investment, optimistic=6000 and Bond investment, pessimistic=18000
