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 $7,000 after 7 months.
PV = $ 

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

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

Where:
- $ PV $ = present value (what we're solving for),
- $ FV $ = future value ($7,000),
- $ r $ = annual interest rate (8% per year or 0.08 in decimal form),
- $ t $ = time in years.

Since the time is given in months, we need to convert it to years. $ t = \frac{7}{12} $ years.

Now, let's substitute the values into the formula:

\[
PV = \frac{7000}{(1 + 0.08)^{\frac{7}{12}}}
\]

Now, we compute this step-by-step:

1. Calculate the interest rate factor: $ 1 + 0.08 = 1.08 $.
2. Raise it to the power of $ \frac{7}{12} $: $ 1.08^{\frac{7}{12}} $.
3. Divide $7,000 by the result from step 2.

Let me calculate this for you.The present value (PV) of the investment is approximately **$6,692.69**.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How does the interest rate impact the present value over different time periods?
2. What happens to the present value if the investment period is longer than 7 months?
3. How would the present value change if the interest rate increased to 10% per year?
4. Can this formula be applied to continuous compounding interest? If so, how?
5. How can inflation affect the present value of future investments?

**Tip**: Always convert the time period into years when using annual interest rates for calculations!

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 $7,000 after 7 months.

Learn how to calculate the present value (PV) of an investment that earns 8% per year and is worth $7,000 after 7 months. This problem involves the compound interest formula and demonstrates how to convert months to years for accurate calculations. Suitable for college-level students or advanced high school learners.

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