​Use the appropriate compound interest formula to compute the balance in the account after the stated period of time
$14000 is invested for 6 years with an APR of 6​% and quarterly compounding. The balance in the account after 6 years is __?

To compute the balance of the account using compound interest, we use the compound interest formula:

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

Where:
- $A$ is the final amount (balance) in the account,
- $P$ is the initial principal (amount invested),
- $r$ is the annual percentage rate (APR) in decimal form,
- $n$ is the number of times interest is compounded per year,
- $t$ is the time the money is invested for, in years.

### Given:
- $P = 14000$,
- $r = 6\%$ or $0.06$ in decimal form,
- $n = 4$ (since the interest is compounded quarterly),
- $t = 6$ years.

Now, plug these values into the formula:

\[
A = 14000 \left(1 + \frac{0.06}{4}\right)^{4 \times 6}
\]

Simplifying step by step:

1. Calculate $ \frac{0.06}{4} = 0.015 $,
2. Calculate $1 + 0.015 = 1.015$,
3. Calculate $4 \times 6 = 24$,
4. Now, raise $1.015$ to the power of 24:

\[
1.015^{24} \approx 1.423297
\]

5. Finally, multiply by the principal:

\[
A = 14000 \times 1.423297 \approx 19926.16
\]

### Answer:
The balance in the account after 6 years is approximately **$19,926.16**.

Do you have any questions or need more details?

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Here are 5 related questions for further practice:
1. What would the balance be if the APR was 5% instead of 6%?
2. How would the balance change if the investment period was 10 years?
3. What is the effect of monthly compounding instead of quarterly compounding on the final amount?
4. How would you calculate the balance if the investment was compounded continuously?
5. If $10,000 is invested for 4 years at an APR of 7% with annual compounding, what will the final balance be?

**Tip:** The more frequently interest is compounded, the greater the accumulated amount over time!

Use the appropriate compound interest formula to compute the balance in the account after the stated period of time. $14000 is invested for 6 years with an APR of 6​% and quarterly compounding. The balance in the account after 6 years is __?

Learn how to calculate compound interest for a $14,000 investment over 6 years with a 6% APR and quarterly compounding. This example uses the compound interest formula and demonstrates step-by-step how to determine the final balance of $19,926.16. Suitable for high school students (Grades 9-12).

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