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To solve this problem, we need to find the present value $ P $ of a future sum $ F = 6302496 $ that is needed in 2 years. Given:

- Future Value, $ F = 6302496 $
- Time, $ t = 2 $ years
- Nominal interest rate, $ r = 5\% $
- Compounding period: semi-annual (twice a year).

For semi-annual compounding, we use the formula:

\[
P = \frac{F}{(1 + \frac{r}{n})^{nt}}
\]

where:
- $ n = 2 $ (compounding periods per year),
- $ t = 2 $ years,
- $ r = 0.05 $ (or 5%).

### Step-by-Step Calculation:

1. **Adjust the interest rate per compounding period:**
   \[
   \text{Interest per period} = \frac{r}{n} = \frac{0.05}{2} = 0.025
   \]

2. **Calculate the total number of compounding periods:**
   \[
   \text{Total periods} = n \times t = 2 \times 2 = 4
   \]

3. **Apply the formula:**
   \[
   P = \frac{6302496}{(1 + 0.025)^4}
   \]

4. **Calculate the denominator:**
   \[
   (1 + 0.025)^4 = 1.025^4 \approx 1.1038
   \]

5. **Final calculation:**
   \[
   P \approx \frac{6302496}{1.1038} \approx 5709750.32
   \]

### Answer:
The correct answer is **$ 5709750.32 $**, which corresponds to option (a).

Would you like a further breakdown or have any questions?

---

1. What is the formula for calculating present value with different compounding periods?
2. How would the answer change if compounding were annual instead of semi-annual?
3. What happens to the present value if the interest rate increases?
4. How would you calculate the future value if the present value were known?
5. What effect does compounding frequency have on investment growth?

**Tip:** Always check the compounding frequency, as it significantly affects the amount you need to invest.

Assume that a company will have to spend $6,302,496 on a new construction 2 years from now, and the current investment rates are 5% nominal. What single sum (P) should be invested by the company (approximate sum), if the compounding period is semi-annual?

Learn how to calculate the present value of a future investment requirement of $6,302,496 with a semi-annual compounding period and a 5% nominal interest rate. This problem involves concepts like present value calculation, compounding interest, and semi-annual compounding, suitable for finance or business studies students.

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