To find the present value $PV$ of the investment, we use the formula for the present value of a future amount:

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

Where:

• $FV$ is the future value (given as $3,000),
• $r$ is the annual interest rate (5%, or 0.05 as a decimal),
• $t$ is the time in years.

Given that the investment is worth $3,000 after 7 months, we need to convert 7 months into years. Since there are 12 months in a year:

$t = \frac{7}{12} \approx 0.5833 \text{ years}.$

Now, plug the values into the formula:

$PV = \frac{3000}{(1 + 0.05)^{0.5833}}.$

First, calculate the denominator:

$1 + 0.05 = 1.05,$ $1.05^{0.5833} \approx 1.0285.$

Now, calculate the present value:

$PV = \frac{3000}{1.0285} \approx 2917.28.$

Thus, the present value $PV$ is approximately $2,917.28.

Do you need further details or clarifications?

Here are some related questions you might want to explore:

1. What is the formula for future value if we are given the present value?
2. How does compounding frequency affect the present value?
3. What happens to the present value if the interest rate increases?
4. How can we compute the present value for continuous compounding?
5. How do you adjust this formula for varying interest rates over time?

Tip: Always double-check whether the interest rate is annual and adjust the time period accordingly when it's given in months or days.