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To solve this problem, we will use the compound interest formula, which is:

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

Where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (the initial investment), which is $14,000.
- $ r $ is the annual interest rate (decimal form), which is 4% or 0.04.
- $ n $ is the number of times the interest is compounded per year. Since it's compounded quarterly, $ n = 4 $.
- $ t $ is the time the money is invested or borrowed for, in years. Here, $ t = 6 $.

### Step-by-Step Calculation:
1. The principal $ P = 14,000 $.
2. The annual interest rate $ r = 0.04 $.
3. The number of times compounded per year $ n = 4 $ (quarterly compounding).
4. The time period $ t = 6 $ years.

Substitute these values into the formula:

\[
A = 14000 \left(1 + \frac{0.04}{4}\right)^{4 \times 6}
\]

\[
A = 14000 \left(1 + 0.01\right)^{24}
\]

\[
A = 14000 \left(1.01\right)^{24}
\]

Using a calculator for $ (1.01)^{24} $:

\[
(1.01)^{24} \approx 1.26824
\]

Now, multiply by the principal:

\[
A = 14000 \times 1.26824 = 17,755.38
\]

### Final Answer:
The balance in the account after 6 years is approximately **$17,755.38**.

Would you like more details on this solution, or do you have any questions?

Here are 5 related questions:
1. How would the balance change if the compounding was done monthly instead of quarterly?
2. What would the balance be after 10 years with the same conditions?
3. How does changing the APR from 4% to 5% affect the final balance?
4. What would happen to the balance if it was compounded annually instead of quarterly?
5. What is the formula for continuous compounding, and how would it affect the outcome?

**Tip**: When solving compound interest problems, always double-check how often the interest is compounded to ensure you're using the correct value for $ n $.

Use the appropriate compound interest formula to compute the balance in the account after the stated period of time. $14,000 is invested for 6 years with an APR of 4% and quarterly compounding. What is the balance in the account after 6 years?

Learn how to calculate compound interest for an investment of $14,000 over 6 years at an APR of 4% with quarterly compounding. The solution uses the compound interest formula to compute the final balance of approximately $17,755.38.

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