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I need help with this Consumer Math B question. I have no idea where to start with this question.



You saved $20,000.00 and want to diversify your monies. You invest 45% in a Treasury bond for 3 years at 4.35% APR compounded annually. You place 15% in a CD at 3.75% APR for 3 years compounded annually. 20% you invest in a stock plan and the remainder is in a savings account at 2.90% APR compounded annually. The stock plan increases 8% the first year, decreases in value by 4% the second year, and increases by 6% the third year.

1. What are the balances for each type of investment at the end of the third year?
2. What is your total gain from all of the investments combined?
3. If you had invested 45% in stock and 20% in Treasury bonds, would you have more or less of a gain after the three years?

I need included the mathematical steps used to solve it! That way, I can learn to use those skills in further questions like this. Thanks!

Respuesta :

Aliwohaish12
20000*0.45 = 9000 in the bond
20000*0.15 = 3000 in the CD
20000*0.20 = 4000 in stocks
20000*0.029 = 580 in savings

A=9000(1 + 4.35%)^3 = 10,226.33
A=3000(1 + 2.90%)^3 = 3,268.64
A=4000 (1 + 8%) x (1 - 4%) x (1 + 6%) = 4,396.03
A=580(1 + 4.35%)^3 = 4,545.04
Total value = 22,436.04
Gain = 22,436.04 - 20,000 = 2,436.04
Lanuel
  1. The balances for each type of investment at the end of the third year are $10,226.7, $3,350.4, $4,396.032 and $4,358.4 respectively.
  2. The total gain from all of the investments combined is $2,331.532.
  3. If you had invested 45% in stock and 20% in Treasury bonds, we can deduce that you would have more of a loss after the three years.

Given the following data:

  • Principal = $20,000.00.
  • Time = 3 years.

1. To calculate the balances for each type of investment at the end of the third year:

How to calculate the balance.

For Treasury bond:

Note: Only 45% (0.45) of the principal was invested for 3 years at 4.35%.

Treasury bond = [tex]0.45 \times 20000[/tex] = $9,000.

For the bond's compound interest:

Mathematically, compound interest is given by this formula:

[tex]A = P(1+r)^t[/tex]

Where:

  • A is the future value.
  • P is the principal.
  • r is the interest rate.
  • t is the time measured in years.

Substituting the given parameters into the formula, we have;

[tex]A = 9000(1+0.0435)^3\\\\A = 9000(1.0435)^3\\\\A = 9000(1.1363)[/tex]

Bond's A = $10,226.7.

For CD:

Note: Only 15% (0.15) of the principal was invested for 3 years at 3.75%.

CD = [tex]0.15 \times 20000[/tex] = $3,000.

For the CD's compound interest:

[tex]A = 3000(1+0.0375)^3\\\\A = 3000(1.0375)^3\\\\A = 3000(1.1168)[/tex]

CD's A = $3,350.4.

For stock plan:

Note: Only 20% (0.20) of the principal was invested.

Stock plan = [tex]0.20 \times 20000[/tex] = $4,000.

For the stock plan's compound interest:

[tex]A=4000 (1 + 0.08) \times (1 - 0.04) \times (1 + 0.06)\\\\A=4000 (1.08) \times 0.96 \times 1.06[/tex]

Stock plan's A = $4,396.032.

For savings account:

Note: The remainder is 20% (0.20) of the principal at 2.90%.

Savings account = [tex]0.20 \times 20000[/tex] = $4,000.

For the savings account's compound interest:

[tex]A = 4000(1+0.0290)^3\\\\A = 4000(1.0290)^3\\\\A = 4000(1.0896)[/tex]

Savings account's A = $4,358.4.

Next, we would calculate the total balance:

[tex]Total\;balance=10226.7+3350.4+4396.032+4358.4[/tex]

Total balance = $22,331.532.

2. To calculate the total gain from all of the investments combined:

[tex]Total\;gain = 22331.532 - 20000[/tex]

Total gain = $2,331.532.

3. If you had invested 45% in stock and 20% in Treasury bonds, we can deduce that you would have more of a loss after the three years.

Read more on interest rate here: brainly.com/question/24341207