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The image shows a compound interest problem where you are given the following parameters:

- Principal $ P = 15,000 $
- Time $ t = 6 $ years
- Interest rate $ r = 4\% $ (or 0.04)

You are asked to find the accumulated value using different compounding periods:

1. Compounded semiannually (this is already calculated as $19,023.63).
2. Compounded quarterly (this is the part you need to complete).

To solve part b (compounded quarterly), we use the compound interest formula:

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

Where:
- $ A $ is the accumulated amount.
- $ P = 15,000 $ is the principal.
- $ r = 0.04 $ is the annual interest rate.
- $ n = 4 $ because the interest is compounded quarterly.
- $ t = 6 $ years.

Let me calculate this for you.The accumulated value when the money is compounded quarterly is approximately **$19,046.02** (rounded to the nearest cent).

Would you like more details on the calculation or have any other questions?

Here are some related questions you might find useful:
1. How is monthly compounding calculated in this formula?
2. What happens if we compound continuously instead of quarterly?
3. How does changing the interest rate affect the accumulated value?
4. What is the difference between simple and compound interest for the same scenario?
5. How does the number of compounding periods (n) impact the final amount?

**Tip:** The more frequently interest is compounded, the higher the accumulated value will be.

Find the accumulated value of an investment of $15,000 for 6 years at an interest rate of 4% if the money is compounded quarterly.

Learn how to calculate the accumulated value of an investment of $15,000 compounded quarterly at an interest rate of 4% over 6 years using the compound interest formula. This step-by-step guide is suitable for high school students studying finance or algebra.

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