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To find the future amount after 7 years for an investment of $11,000 at 4% compounded quarterly, we can use the compound interest formula:

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

where:
- $ P $ is the principal amount (initial investment), which is $11,000,
- $ r $ is the annual interest rate (4%, or 0.04 as a decimal),
- $ n $ is the number of times interest is compounded per year (quarterly, so $ n = 4 $),
- $ t $ is the time in years (7 years).

### Step-by-Step Solution:
1. **Plugging in the values**:

   \[
   A = 11000 \left(1 + \frac{0.04}{4}\right)^{4 \times 7}
   \]

2. **Simplifying the terms**:

   - $ \frac{0.04}{4} = 0.01 $,
   - $ 4 \times 7 = 28 $.

   So,

   \[
   A = 11000 \left(1 + 0.01\right)^{28}
   \]

3. **Calculating**:

   \[
   A = 11000 \times (1.01)^{28}
   \]

4. **Finding $ (1.01)^{28} $**:

   - $ (1.01)^{28} \approx 1.319 $ (using calculator approximation).

   \[
   A \approx 11000 \times 1.319
   \]

5. **Final Amount**:

   \[
   A \approx 14509
   \]

So, the amount after 7 years is approximately **$14,509**.

Would you like further details or have any questions?

### Related Questions
1. How would the amount change if the compounding were monthly instead of quarterly?
2. What would be the final amount if the investment duration was 10 years instead of 7?
3. How does the interest rate affect the future amount if it's increased to 5%?
4. What would happen if interest were compounded continuously instead?
5. How much interest is earned over the 7 years?

### Tip
When working with compound interest, increasing the frequency of compounding (e.g., from annually to quarterly) increases the final amount due to more frequent application of interest.

If $11,000 is invested at 4% compounded quarterly, what is the amount after 7 years?

Learn how to calculate the future value of $11,000 invested at a 4% interest rate, compounded quarterly over 7 years. This solution uses the compound interest formula, providing a step-by-step guide for high school students (Grades 10-12).

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