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The problem is asking for the present value that should be invested now to reach a future value of $3000, compounded semiannually at a 3% interest rate for 5 years. 

To solve this, we can use the **present value formula** for compound interest:

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

where:
- $ PV $ is the present value (the amount we want to find),
- $ FV = 3000 $ is the future value,
- $ r = 0.03 $ is the annual interest rate (3%),
- $ n = 2 $ is the number of compounding periods per year (semiannual),
- $ t = 5 $ is the number of years.

### Step-by-Step Calculation:
1. **Calculate the interest per compounding period:** $\frac{r}{n} = \frac{0.03}{2} = 0.015$.
2. **Calculate the total number of compounding periods:** $nt = 2 \times 5 = 10$.
3. **Plug into the formula:**

   \[
   PV = \frac{3000}{(1 + 0.015)^{10}}
   \]

4. **Compute the result:**

   \[
   PV = \frac{3000}{(1.015)^{10}}
   \]

Using a calculator, we find:

\[
(1.015)^{10} \approx 1.1609
\]

Thus,

\[
PV \approx \frac{3000}{1.1609} \approx 2583.07
\]

### Answer:
The present value that should be invested now is approximately **$2583.07**.

Would you like further clarification on any of these steps?

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Here are five related questions to deepen understanding:

1. How would the present value change if the interest was compounded quarterly instead of semiannually?
2. What is the future value if the present value of $2583.07 is invested at the same rate for 5 years compounded semiannually?
3. How does an increase in the interest rate affect the present value required?
4. What would the present value be if the time period was extended to 10 years instead of 5?
5. How is the present value formula derived from the future value formula?

**Tip:** Remember, the more frequently the interest compounds, the higher the amount accumulated over the same period.

Find the present value (the amount that should be invested now to accumulate the following amount) if the money is compounded as indicated: $3000 at 3% compounded semiannually for 5 years.

Learn how to determine the present value required to accumulate $3000, with 3% interest compounded semiannually over 5 years. This step-by-step solution uses the compound interest formula to find the amount to invest now.

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