Future value (with changing interest rates). Jose has \( \$ 8,000 \) 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 \( 4 \% \). b. Bond fund at \( 8 \% \). c. Mutual stock fund at \( 15 \% \). d. New venture stock at \( 22 \% \). d. What would be the value of Jose's new venture stock investment if it earns an annual rate of return of \( 22 \% \) for 3 years? \( \$ \square \) (Round to the nearest cent.)

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.