You are scheduled to receive $18,000 in two years. When you receive it, you will invest it for eight more years at 9 percent per year. How much will you have in ten years?

To solve this problem, we'll first determine the future value of the $18,000 after it is invested for 8 years at an interest rate of 9% per year.

### Step-by-Step Solution

1. **Understand the timeline:**
   - You are scheduled to receive $18,000 in 2 years.
   - Once you receive it, you will invest it for an additional 8 years.
   - This means the total time from now until the end of the investment is 10 years, but the $18,000 will only be invested for 8 years.

2. **Future Value Formula:**
   The future value $ FV $ of an investment can be calculated using the formula:

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

   where:
   - $ PV $ is the present value (the initial amount of money).
   - $ r $ is the annual interest rate (as a decimal).
   - $ n $ is the number of years the money is invested.

3. **Apply the values to the formula:**
   - $ PV = 18,000 $ (the amount to be invested in 2 years)
   - $ r = 0.09 $ (9% interest rate per year)
   - $ n = 8 $ (the number of years the money is invested)

   \[
   FV = 18,000 \times (1 + 0.09)^8
   \]

4. **Calculate the future value:**

   First, compute $ (1 + 0.09)^8 $:

   \[
   (1 + 0.09)^8 = 1.09^8 \approx 1.9926
   \]

   Now, compute the future value:

   \[
   FV = 18,000 \times 1.9926 \approx 35,866.80
   \]

### Final Answer

You will have approximately **$35,866.80** in 10 years.

Would you like more details on any of the steps, or do you have any questions?

### Related Questions

1. How would the future value change if the interest rate were 10% instead of 9%?
2. What would the future value be if the investment period were 10 years instead of 8?
3. How much interest would you earn in total over the 8-year investment period at 9%?
4. What if you received the $18,000 after 3 years instead of 2? How would that affect the calculation?
5. How does compound interest differ from simple interest in terms of future value calculation?

### Tip

Always remember to adjust the timeline properly when calculating the future value of investments to account for the exact period the money is actually invested.

Learn how to calculate the future value of an $18,000 investment over 10 years at a 9% annual interest rate. Understand the compound interest formula and step-by-step solution. Suitable for high school students and anyone interested in financial calculations.

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