We are given the formula for a future value (VF):

\[
VF = 500,000,000 \times (1 + 0.01)^{48}
\]

Here, we need to compute the future value by raising the term \((1 + 0.01)\) to the power of 48, then multiplying by 500,000,000.

### Step-by-step:

1. Simplify inside the parentheses:
   \[
   1 + 0.01 = 1.01
   \]

2. Raise 1.01 to the power of 48:
   \[
   1.01^{48} \approx 1.608
   \]

3. Multiply by 500,000,000:
   \[
   VF \approx 500,000,000 \times 1.608 = 804,000,000
   \]

Thus, the future value \(VF\) is approximately **804,000,000**.

Would you like more details or have any questions?

Here are five related questions for further exploration:
1. How does the value of \(VF\) change with a different interest rate (e.g., 2%)?
2. What would the future value be after 60 periods instead of 48?
3. How does the formula change if interest is compounded quarterly instead of annually?
4. How does the value of \(VF\) change if the initial amount is halved?
5. Can you derive the time it takes to double an investment with this formula?

**Tip:** Exponentiation in growth formulas often leads to compounding effects, making values increase exponentially over time.

Explore how to calculate the future value of an investment using the compound interest formula. This example computes the future value of 500,000,000 at 1% interest compounded annually over 48 periods. Suitable for high school students learning about exponential growth and interest calculations.

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