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 solve for the return on investment B, we need to break down the problem step-by-step:

### Known Information:
- The combined total value of investments A and B after 12 years is expected to be **$85,447**.
- **Investment A**: You will invest **$6,900** in 3 years, with an expected annual return of **13.69%**.
- **Investment B**: You will invest **$34,300** in 5 years, with an unknown return of **X%** per year.
- The future value of these two investments together after 12 years is **$85,447**.

We can calculate the future values of both investments using the compound interest formula:

\[
FV = PV \times (1 + r)^t
\]
where:
- $ FV $ is the future value,
- $ PV $ is the present value (initial investment),
- $ r $ is the annual return rate,
- $ t $ is the number of years.

### Step 1: Calculate the future value of investment A

- **Investment A** will start in 3 years, so it has **12 - 3 = 9 years** of growth.
- The annual return rate for investment A is **13.69%**, or $ 0.1369 $ as a decimal.

Using the formula for future value:
\[
FV_A = 6,900 \times (1 + 0.1369)^9
\]

### Step 2: Calculate the future value of investment B

- **Investment B** will start in 5 years, so it has **12 - 5 = 7 years** of growth.
- The annual return rate for investment B is unknown and is represented as **X%**, or $ r_B $.

Using the formula for future value:
\[
FV_B = 34,300 \times (1 + r_B)^7
\]

### Step 3: Combine the future values

The combined future value is given as **$85,447**. So:
\[
FV_A + FV_B = 85,447
\]
Substituting the expressions for $ FV_A $ and $ FV_B $:
\[
6,900 \times (1 + 0.1369)^9 + 34,300 \times (1 + r_B)^7 = 85,447
\]

Now let's calculate this step by step.The annual return rate for Investment B is approximately **9.21%**.

Would you like further clarification on any step or details? Here are some related questions:

1. How is compound interest calculated for different time frames?
2. What happens to the return rate if the investment amount changes?
3. How would the final total change if the return rate for Investment A was lower?
4. What is the difference between simple and compound interest?
5. How do delayed investments affect the overall return?

**Tip:** Always account for the time horizon when planning investments, as longer periods of compounding can significantly impact returns.

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.

Solve for the return rate of Investment B using compound interest formulas. You will learn how to calculate future values based on different investment time frames and returns. This financial math problem involves calculating the unknown return percentage for Investment B, given a combined future value of $85,447 over 12 years.

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