To calculate the present value (PV) of an investment that earns 5% interest per year and is worth $4,000 after 7 months, we can use the formula for the present value:

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

Where:

• $PV$ is the present value.
• $FV$ is the future value, which is $4,000.
• $r$ is the annual interest rate (5% or 0.05).
• $t$ is the time in years (7 months = $\frac{7}{12}$ years).

Now, let's compute the PV.

$PV = \frac{4000}{(1 + 0.05)^{\frac{7}{12}}}$

Let me calculate that.The present value (PV) of the investment is approximately $3,887.76, rounded to the nearest cent.

Do you want further details or have any questions?

Here are some related questions:

1. How is the present value affected by changes in the interest rate?
2. What happens to the PV if the investment duration is shortened to 5 months?
3. Can this formula be applied to investments with variable interest rates?
4. What is the impact of compounding more frequently than annually on the present value?
5. How would inflation affect the real value of the present value?

Tip: Always ensure that the time duration in the present value formula is converted to years for accuracy in calculations.