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To solve this problem, we’ll use the formula for compound interest:

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

where:
- $ A $ is the final amount of money.
- $ P $ is the initial principal (starting amount), which is $4,500.
- $ r $ is the annual interest rate (expressed as a decimal), so 4% becomes 0.04.
- $ n $ is the number of times interest is compounded per year. Since it’s compounded quarterly, $ n = 4 $.
- $ t $ is the number of years the money is invested, which is 7 years.

### Step-by-Step Solution

1. **Substitute the values into the formula**:

   \[
   A = 4500 \left(1 + \frac{0.04}{4}\right)^{4 \times 7}
   \]

2. **Calculate inside the parentheses**:

   \[
   A = 4500 \left(1 + 0.01\right)^{28}
   \]
   \[
   A = 4500 \times (1.01)^{28}
   \]

3. **Calculate $ (1.01)^{28} $**:

   \[
   (1.01)^{28} \approx 1.319
   \]

4. **Multiply by the principal**:

   \[
   A \approx 4500 \times 1.319 = 5935.5
   \]

### Answer
The final amount is approximately **$5935.50** when rounded to two decimal places.

Would you like further clarification or have additional questions?

---

1. What happens if the interest is compounded monthly instead of quarterly?
2. How would the answer change if the interest rate were 5% instead of 4%?
3. How do we adjust the formula if compounding is continuous?
4. What if the money is left for 10 years instead of 7?
5. How does increasing the compounding frequency affect the final amount?

**Tip**: When dealing with compound interest, remember that more frequent compounding leads to higher returns.

Find the final amount of money in an account if $4,500 is deposited at 4% interest compounded quarterly (every 3 months) and the money is left for 7 years. Round answer to 2 decimal places.

Learn how to calculate the final amount in an account with a principal of $4,500 at a 4% interest rate, compounded quarterly over 7 years. Includes a step-by-step guide using the compound interest formula. Suitable for high school students.

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