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 $4,000 after 9 months.

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

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

Where:
- $ FV $ is the future value, which is $4,000.
- $ r $ is the annual interest rate, which is 8% or 0.08.
- $ t $ is the time in years. Since 9 months is $\frac{9}{12} = 0.75$ years, $ t = 0.75 $.

Substituting the values into the formula:

\[
PV = \frac{4000}{(1 + 0.08)^{0.75}}
\]

Let me calculate that for you.The present value (PV) of the investment is approximately **$3,775.65**.

Would you like more details or have any questions? 

Here are some related questions you might find helpful:
1. How does the present value change if the interest rate increases?
2. How is compound interest different from simple interest?
3. What is the effect of time duration on the present value of an investment?
4. How do I calculate future value for investments longer than one year?
5. Can you explain how interest is calculated when compounded monthly?

**Tip:** The present value is inversely proportional to both the interest rate and the time period. The higher the interest or the longer the time, the lower the present value.

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 $4,000 after 9 months.

Learn how to calculate the present value (PV) of a $4,000 investment that earns 8% annually over 9 months. This step-by-step guide covers the formula PV = FV / (1 + r)^t and explains the Time Value of Money theorem. Suitable for high school students in Grades 10-12.

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