Future value​ (with changing interest​ rates).  Jose has ​$2 comma 000 to invest for a 6​-year period.  He is looking at four different investment choices.  What will be the value of his investment at the end of 6 years for each of the following potential​ investments?
a.  Bank CD at 3.5​%.
b.  Bond fund at 8​%.
c.  Mutual stock fund at 12​%.
d.  New venture stock at 25​%.
Question content area bottom
Part 1
a.  What will be the value of​ Jose's bank CD investment that offers an annual rate of return of 3.5​% for 6 ​years?
​$
  
enter your response here  ​(Round to the nearest​ cent.)
Part 2
b.  What will be the value of​ Jose's bond fund investment that offers an annual rate of return of 8​% for 6 ​years?
​$
  
enter your response here  ​(Round to the nearest​ cent.)
Part 3
c.  What would be the value of​ Jose's mutual stock fund investment if it earns an annual rate of return of 12​% for 6 ​years? 
​$
  
enter your response here  ​(Round to the nearest​ cent.)
Part 4
d.  What would be the value of​ Jose's new venture stock investment if it earns an annual rate of return of 25​% for 6 ​years?
​$
  
enter your response here  ​(Round to the nearest​ cent.)

To calculate the future value (FV) of Jose's investment, we will use the **future value formula for compound interest**:

\[
FV = P(1 + r)^t
\]

Where:
- $FV$ = future value of the investment
- $P$ = principal amount (initial investment)
- $r$ = annual interest rate (expressed as a decimal)
- $t$ = time in years

Given:
- Principal $P = 2000$
- Time $t = 6$ years

Now, let's calculate the future value for each investment choice:

### Part 1: Bank CD at 3.5%
\[
FV = 2000(1 + 0.035)^6
\]

\[
FV = 2000(1.035)^6
\]

\[
FV \approx 2000(1.233006)
\]

\[
FV \approx 2466.01
\]

So, the future value of the bank CD investment will be approximately **$2,466.01**.

---

### Part 2: Bond fund at 8%
\[
FV = 2000(1 + 0.08)^6
\]

\[
FV = 2000(1.08)^6
\]

\[
FV \approx 2000(1.586874)
\]

\[
FV \approx 3173.75
\]

So, the future value of the bond fund investment will be approximately **$3,173.75**.

---

### Part 3: Mutual stock fund at 12%
\[
FV = 2000(1 + 0.12)^6
\]

\[
FV = 2000(1.12)^6
\]

\[
FV \approx 2000(1.973823)
\]

\[
FV \approx 3947.65
\]

So, the future value of the mutual stock fund investment will be approximately **$3,947.65**.

---

### Part 4: New venture stock at 25%
\[
FV = 2000(1 + 0.25)^6
\]

\[
FV = 2000(1.25)^6
\]

\[
FV \approx 2000(3.052856)
\]

\[
FV \approx 6105.71
\]

So, the future value of the new venture stock investment will be approximately **$6,105.71**.

---

Do you need any more details or have questions about these calculations? 

Here are some related questions:
1. How does the interest rate affect the future value of investments?
2. What is the formula for continuous compounding, and how does it compare to annual compounding?
3. How would Jose's investment grow if compounded quarterly instead of annually?
4. What risks are associated with higher-return investments like new venture stock?
5. How does inflation impact the real value of the future investment returns?

**Tip:** The power of compound interest is significant over time; higher interest rates exponentially increase the final amount.

Jose has $2,000 to invest for a 6-year period. He is looking at four different investment choices. What will be the value of his investment at the end of 6 years for each of the following potential investments? a) Bank CD at 3.5%, b) Bond fund at 8%, c) Mutual stock fund at 12%, d) New venture stock at 25%.

Learn how to calculate the future value of an investment over 6 years with different interest rates. This problem includes scenarios such as a Bank CD at 3.5%, Bond fund at 8%, Mutual stock fund at 12%, and New venture stock at 25%. Detailed step-by-step solution provided, suitable for high school students.

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