You own 2 investments, A and B, which are expected to be worth a  combined total value  of $85,447 in 12  years. You plan to invest $6,900 in 3 years in investment A, which has an expected return of 13.69 percent per year. You also plan to invest $34,300 in 5 years in investment B, which has an expected return  of X percent per year.  What is X? Round to  two decimal places and provide your answer as a percent 

To find the required return $ X $ for Investment B, we can use the time value of money concepts. Here are the steps to solve the problem:

### Step 1: Future Value of Investment A
You plan to invest $6,900 in 3 years into Investment A, which grows at 13.69% per year. We need to find the future value of Investment A after 12 years (i.e., 9 years of growth after the initial investment in year 3).

The future value of Investment A is given by the formula:

\[
FV_A = P_A \times (1 + r_A)^{t_A}
\]

Where:
- $ P_A = 6,900 $ is the amount invested in Investment A,
- $ r_A = 0.1369 $ is the annual return for Investment A (13.69%),
- $ t_A = 12 - 3 = 9 $ years is the period for Investment A to grow after the initial investment.

### Step 2: Future Value of Investment B
You plan to invest $34,300 in 5 years into Investment B, which grows at $ X $ percent per year. We need to find the future value of Investment B after 12 years (i.e., 7 years of growth after the initial investment in year 5).

The future value of Investment B is given by the formula:

\[
FV_B = P_B \times (1 + r_B)^{t_B}
\]

Where:
- $ P_B = 34,300 $ is the amount invested in Investment B,
- $ r_B = X $ is the annual return for Investment B (which we need to solve for),
- $ t_B = 12 - 5 = 7 $ years is the period for Investment B to grow after the initial investment.

### Step 3: Total Future Value
The total future value of both investments is expected to be $85,447 in 12 years. Therefore, we can set up the equation:

\[
FV_A + FV_B = 85,447
\]

Substituting the expressions for $ FV_A $ and $ FV_B $, we get:

\[
6,900 \times (1 + 0.1369)^9 + 34,300 \times (1 + X)^7 = 85,447
\]

Now, we can solve this equation for $ X $. Let's do the calculations.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, you can also try calculating the solution step by step using the formulas we've discussed!

Would you like any further assistance on the concept or approach?

Here are 5 related questions for deeper understanding:
1. How does the timing of investments affect their future value?
2. What would happen to the required return $ X $ if you invested more in Investment B?
3. How would changing the interest rate for Investment A impact the result?
4. What if both investments had different compounding frequencies?
5. How is the formula for future value

You own 2 investments, A and B, which are expected to be worth a combined total value of $85,447 in 12 years. You plan to invest $6,900 in 3 years in investment A, which has an expected return of 13.69 percent per year. You also plan to invest $34,300 in 5 years in investment B, which has an expected return of X percent per year. What is X? Round to two decimal places and provide your answer as a percent.

Find the required return rate (X) for Investment B given a combined future value of $85,447 in 12 years. This detailed solution walks through the application of future value and compound interest formulas for Investments A and B. Suitable for college-level students studying finance and algebra.

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