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This problem describes a scenario where you're making regular quarterly deposits into an annuity with interest compounded quarterly. The goal is to find how much you will have saved after 8 years and determine the interest.

This is a future value of an annuity problem. The formula for the future value of an annuity compounded periodically is:

\[
A = P \times \frac{(1 + r/n)^{nt} - 1}{r/n}
\]

Where:
- $A$ is the future value of the annuity.
- $P$ is the regular payment (quarterly in this case).
- $r$ is the annual interest rate (as a decimal).
- $n$ is the number of times the interest is compounded per year (quarterly means $n = 4$).
- $t$ is the number of years.

### Step-by-step:
1. **Given values:**
   - $P = 1500$ (quarterly deposit)
   - $r = 4.5\% = 0.045$ (interest rate)
   - $n = 4$ (compounded quarterly)
   - $t = 8$ (years)

2. **Plug values into the formula:**
   \[
   A = 1500 \times \frac{(1 + \frac{0.045}{4})^{4 \times 8} - 1}{\frac{0.045}{4}}
   \]
   Simplifying:
   \[
   A = 1500 \times \frac{(1 + 0.01125)^{32} - 1}{0.01125}
   \]
   \[
   A = 1500 \times \frac{(1.01125)^{32} - 1}{0.01125}
   \]

3. **Calculate $ (1.01125)^{32} $:**
   \[
   (1.01125)^{32} \approx 1.423297
   \]
   So:
   \[
   A = 1500 \times \frac{1.423297 - 1}{0.01125}
   \]
   \[
   A = 1500 \times \frac{0.423297}{0.01125}
   \]
   \[
   A = 1500 \times 37.626
   \]
   \[
   A \approx 56439.45
   \]

4. **Total amount saved at the end of 8 years:**
   \[
   A \approx 56439 \, (\text{rounded to the nearest dollar})
   \]

5. **To find the interest:**
   The total interest earned is the difference between the future value and the total deposits made. The total deposits made are:
   \[
   1500 \times 32 = 48000
   \]
   Interest:
   \[
   \text{Interest} = 56439 - 48000 = 8439
   \]

### Final Answer:
- **Amount saved:** \$56,439
- **Interest earned:** \$8,439

Would you like a more detailed breakdown of any step, or do you have further questions?

Here are five related questions:
1. How would the total amount change if the interest rate were 5%?
2. What happens to the future value if the compounding frequency is changed to monthly?
3. How does increasing the number of years impact the total savings?
4. What would be the impact of reducing the deposit amount to $1,000 quarterly?
5. Can you calculate the present value of this annuity given the same conditions?

**Tip:** Always check whether interest is compounded periodically or continuously, as this can significantly affect the outcome.

Suppose that you earned a bachelor's degree and now you're teaching middle school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit $1500 at the end of every three months in an annuity that pays 4.5% compounded quarterly. How much will you have saved at the end of 8 years? Find the interest.

Calculate the future value of an annuity with $1500 quarterly deposits over 8 years at 4.5% interest compounded quarterly. Find out how much is saved and the total interest earned using the future value of annuity formula.

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