Find the present value *PV* of the given investment (in dollars). (Round your answer to the nearest cent.)

An investment earns 8% per year and is worth $9,000 after 8 months.

*PV* = $

To find the present value ($ PV $) of an investment, we can use the formula:

\[
PV = \frac{FV}{(1 + r)^{t}}
\]

where:
- $ FV $ is the future value of the investment (in this case, $9,000),
- $ r $ is the annual interest rate (8%, or 0.08),
- $ t $ is the time in years.

Since the investment is worth $9,000 after 8 months, we need to convert 8 months into years. 

1. **Convert months to years:**
   \[
   t = \frac{8}{12} = \frac{2}{3} \approx 0.6667 \text{ years}
   \]

2. **Substitute values into the formula:**
   \[
   PV = \frac{9000}{(1 + 0.08)^{0.6667}}
   \]

3. **Calculate the present value:**

   \[
   PV \approx \frac{9000}{(1.08)^{0.6667}}
   \]

Using a calculator for the exponent and division:

\[
PV \approx \frac{9000}{1.0520} \approx 8555.67
\]

**Answer:**
\[
PV \approx 8555.67
\]

The present value of the investment is approximately **$8,555.67**.

Would you like further clarification or details?

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### Related Questions

1. How would the present value change if the interest rate was compounded monthly instead of annually?
2. What would be the present value if the investment period was extended to 1 year?
3. How does the frequency of compounding impact the present value calculation?
4. Can the formula be modified for investments with variable interest rates over time?
5. How would inflation impact the effective value of this investment?

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**Tip:** For short-term investments, converting time units precisely (like months to years) is essential to ensure accurate results.

Find the present value PV of the given investment (in dollars). (Round your answer to the nearest cent.) An investment earns 8% per year and is worth $9,000 after 8 months. PV = $

Calculate the present value (PV) of an investment worth $9,000 after 8 months, with an 8% annual interest rate. This example illustrates the concept of the time value of money using the present value formula, suitable for high school students in Grades 11-12.

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