Answer:
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To find the balances for each type of investment after one year, we can use the formula for compound interest:
Treasury bond: A = P(1 + r/n)^(nt)
A = 0.4(30000)(1 + 0.0535/1)^(1*1) = $12,912.00
CD: A = P(1 + r/n)^(nt)
A = 0.1(30000)(1 + 0.0475/1)^(1*1) = $10,316.25
Stock plan: After the first year, 30% is still in the savings account. The other 70% is in the stock plan, which increased by 9%, so the new value is:
0.7(30000)(1 + 0.09) = $23,940.00
Savings account: A = P(1 + r/n)^(nt)
A = 0.2(30000)(1 + 0.039/1)^(1*1) = $6,351.00
To find the total gain from all of the investments combined, we need to add up the gains from each investment:
Treasury bond: $12,912.00 - $12,000.00 = $912.00 gain
CD: $10,316.25 - $9,000.00 = $1,316.25 gain
Stock plan: After the second year, the stock plan decreased in value by 5%, so the new value is:
0.7($23,940.00)(1 - 0.05) = $19,149.00
After the third year, the stock plan increased by 7%, so the final value is:
0.7($19,149.00)(1 + 0.07) = $20,129.57
The gain from the stock plan is:
$20,129.57 - $21,000.00 = -$870.43 loss (since the stock plan decreased in value overall)
Savings account: $6,351.00 - $6,000.00 = $351.00 gain
Total gain = $912.00 + $1,316.25 - $870.43 + $351.00 = $708.82
If you had invested 40% in stock and 30% in Treasury bonds, the calculations would be:
Treasury bond: A = P(1 + r/n)^(nt)
A = 0.3(30000)(1 + 0.0535/1)^(1*3) = $12,853.81
Stock plan: After the first year, 40% is still in the savings account. The other 60% is in the stock plan, which increased by 9%, so the new value is:
0.6(30000)(1 + 0.09) = $16,200.00
After the second year, the stock plan decreased in value by 5%, so the new value is:
0.6($16,200.00)(1 - 0.05) = $15,390.00
After the third year, the stock plan increased by 7%, so the final value is:
0.6($15,390.00)(1 + 0.07) = $16,019.16
Total gain = ($12,853.81 - $12,000.00) + (-$981.84) + ($1,019.16) = $890.13
Therefore, investing 40% in stock and 30% in Treasury bonds