S = 7500 * [(1 + 0.020833)^8 - 1] / 0.020833

Let's solve the given expression step by step:

The formula is:

\[
S = 7500 \times \left[\frac{(1 + 0.020833)^8 - 1}{0.020833}\right]
\]

### Step 1: Calculate \( (1 + 0.020833) \)
\[
1 + 0.020833 = 1.020833
\]

### Step 2: Raise \( 1.020833 \) to the power of 8
\[
1.020833^8 \approx 1.177416
\]

### Step 3: Subtract 1 from the result
\[
1.177416 - 1 = 0.177416
\]

### Step 4: Divide by 0.020833
\[
\frac{0.177416}{0.020833} \approx 8.515036
\]

### Step 5: Multiply by 7500
\[
7500 \times 8.515036 \approx 63862.77
\]

Thus, the value of \( S \) is approximately:

\[
S \approx 63862.77
\]

Let me know if you'd like further details or clarifications.

---

Here are some related questions for further exploration:

1. How does the value change if the interest rate changes slightly?
2. Can you explain why exponentiation is important in compound interest?
3. How would this calculation change if the number of periods increased to 10?
4. What real-life scenarios could apply this type of formula?
5. How do you derive the compound interest formula?

**Tip:** When working with financial formulas, carefully track how small changes in interest rates or periods affect the total result.

Discover how to solve the compound interest problem using the formula S = 7500 * [(1 + 0.020833)^8 - 1] / 0.020833. This detailed solution explores exponential growth and the compound interest theorem, suitable for students in Grades 10-12.

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