Question

Diversifying Your Savings Portfolio 1.2

You saved $30,000.00 and want to diversify your monies. You invest 40% in a
Treasury bond for 3 years at 5.35% APR compounded annually You place 10% in a CD
at 4.75% APR for 3 years compounded annually 30% you invest in a stock plan and
the remainder is in a savings account at 3.90% APR compounded annually. The stock
plan increases 9% the first year, decreases in value by 5% the second year, and
increases by 7% the thind year.
1. What are the balances for each type of investment a
year?
2. What is your total gain from all of the investments combined?
of the thind
3. If you had invested 40% in stock and 30% in Treasury bonds, would you have
more or less of a gain after the three years?
Be sure to include in your response:
Detailed calculations for each type of investment.
Answers to the original questions.

Answer 1

ChatGPT

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