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!