Future value (with changing interest rates). Jose has to invest for a 3 -year period. He is
looking at four different investment choices. What will be the value of his investment at the end of 3
years for each of the following potential investments?
a. Bank CD at .
b. Bond fund at .
c. Mutual stock fund at .
d. New venture stock at .
d. What would be the value of Jose’s new venture stock investment if it earns an annual rate of return of
for 3 years?
(Round to the nearest cent.)

Ask by Watkins Valdez. in the United States

Jan 22,2025

Question

Future value (with changing interest rates). Jose has to invest for a 3 -year period. He is
looking at four different investment choices. What will be the value of his investment at the end of 3
years for each of the following potential investments?
a. Bank CD at .
b. Bond fund at .
c. Mutual stock fund at .
d. New venture stock at .
d. What would be the value of Jose’s new venture stock investment if it earns an annual rate of return of
for 3 years?
(Round to the nearest cent.)

Ask by Watkins Valdez. in the United States

Jan 22,2025

UpStudy AI · Accepted Answer

To calculate the future value of Jose's investment for each of the four different investment choices, we can use the formula for compound interest:

$$ FV = PV \times (1 + r)^n $$

where:
- $$ FV $$ is the future value of the investment
- $$ PV $$ is the present value of the investment (initial amount)
- $$ r $$ is the annual interest rate
- $$ n $$ is the number of years

Let's calculate the future value for each investment choice:

a. Bank CD at $$ 4\% $$:
$$ FV = \$8,000 \times (1 + 0.04)^3 $$

b. Bond fund at $$ 8\% $$:
$$ FV = \$8,000 \times (1 + 0.08)^3 $$

c. Mutual stock fund at $$ 15\% $$:
$$ FV = \$8,000 \times (1 + 0.15)^3 $$

d. New venture stock at $$ 22\% $$:
$$ FV = \$8,000 \times (1 + 0.22)^3 $$

Now, let's calculate the future value for each investment choice.
Calculate the value by following steps:
- step0: Calculate:
  $$8000\left(1+0.04\right)^{3}$$
- step1: Add the numbers:
  $$8000\times 1.04^{3}$$
- step2: Convert the expressions:
  $$8000\left(\frac{26}{25}\right)^{3}$$
- step3: Evaluate the power:
  $$8000\times \frac{17576}{15625}$$
- step4: Multiply:
  $$\frac{1124864}{125}$$
The future value of Jose's investment in the Bank CD at $$ 4\% $$ for 3 years is approximately $8,998.91.

Now, let's calculate the future value for the other investment choices.
Calculate the value by following steps:
- step0: Calculate:
  $$8000\left(1+0.08\right)^{3}$$
- step1: Add the numbers:
  $$8000\times 1.08^{3}$$
- step2: Convert the expressions:
  $$8000\left(\frac{27}{25}\right)^{3}$$
- step3: Evaluate the power:
  $$8000\times \frac{19683}{15625}$$
- step4: Multiply:
  $$\frac{1259712}{125}$$
The future value of Jose's investment in the Bond fund at $$ 8\% $$ for 3 years is approximately $10,077.69.

Now, let's calculate the future value for the Mutual stock fund at $$ 15\% $$.
Calculate the value by following steps:
- step0: Calculate:
  $$8000\left(1+0.15\right)^{3}$$
- step1: Add the numbers:
  $$8000\times 1.15^{3}$$
- step2: Convert the expressions:
  $$8000\left(\frac{23}{20}\right)^{3}$$
- step3: Evaluate the power:
  $$8000\times \frac{12167}{8000}$$
- step4: Multiply:
  $$12167$$
The future value of Jose's investment in the Mutual stock fund at $$ 15\% $$ for 3 years is $12,167.

Finally, let's calculate the future value for the New venture stock at $$ 22\% $$.
Calculate the value by following steps:
- step0: Calculate:
  $$8000\left(1+0.22\right)^{3}$$
- step1: Add the numbers:
  $$8000\times 1.22^{3}$$
- step2: Convert the expressions:
  $$8000\left(\frac{61}{50}\right)^{3}$$
- step3: Simplify:
  $$8000\times \frac{61^{3}}{50^{3}}$$
- step4: Rewrite the expression:
  $$50\times 160\times \frac{61^{3}}{50^{3}}$$
- step5: Reduce the numbers:
  $$160\times \frac{61^{3}}{50^{2}}$$
- step6: Rewrite the expression:
  $$10\times 16\times \frac{61^{3}}{50^{2}}$$
- step7: Rewrite the expression:
  $$10\times 16\times \frac{61^{3}}{10^{2}\times 5^{2}}$$
- step8: Reduce the numbers:
  $$8\times \frac{61^{3}}{5\times 5^{2}}$$
- step9: Multiply:
  $$\frac{8\times 61^{3}}{5^{3}}$$
- step10: Simplify:
  $$\frac{8\times 61^{3}}{125}$$
The future value of Jose's investment in the New venture stock at $$ 22\% $$ for 3 years is approximately $14,526.78.

Therefore, the value of Jose's new venture stock investment if it earns an annual rate of return of $$ 22\% $$ for 3 years is approximately $14,526.78.
The future value of Jose's investment after 3 years is: - Bank CD at 4%: \$8,998.91 - Bond fund at 8%: \$10,077.69 - Mutual stock fund at 15%: \$12,167.00 - New venture stock at 22%: \$14,526.78

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