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 $6,000 after 8 months.

To find the present value (PV) of an investment that grows at 8% per year, we can use the formula for the present value in terms of future value (FV):

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

Where:
- $ PV $ is the present value (what we are solving for),
- $ FV $ is the future value, which is $6,000,
- $ r $ is the annual interest rate, which is 8% or 0.08,
- $ t $ is the time period in years. Since we are given 8 months, we convert it to years: $ \frac{8}{12} = \frac{2}{3} \text{ years}. $

Now, substitute the values into the formula:

\[
PV = \frac{6,000}{(1 + 0.08)^{2/3}}
\]

Let me calculate that for you.The present value (PV) of the investment is approximately **$5,699.92**.

Would you like further details or explanations? Here are five related questions for further exploration:

1. How would the present value change if the interest rate were 10%?
2. What would the present value be if the investment period were 1 year instead of 8 months?
3. How does the present value formula differ for continuous compounding interest?
4. What is the future value formula for this type of investment?
5. How does inflation affect the real present value of money?

**Tip:** When converting months to years, always divide the number of months by 12 to get an accurate time period.

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 $6,000 after 8 months.

Learn how to calculate the present value (PV) of an investment with an 8% annual interest rate, given that the future value is $6,000 after 8 months. This detailed solution covers the present value formula and key financial concepts. Ideal for high school or college-level students.

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