Suppose you deposit $10,000 in an account that pays 7% annual interest. What is the balance after three years if the interest is compounded quarterly? 

To calculate the balance of an account with compound interest, we use the compound interest formula:

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

Where:
- $A$ is the amount of money in the account after interest (the final balance),
- $P$ is the initial principal (the amount initially deposited),
- $r$ is the annual interest rate (as a decimal),
- $n$ is the number of times the interest is compounded per year,
- $t$ is the number of years the money is invested or borrowed for.

### Given:
- $P = 10,000$
- $r = 7\% = 0.07$
- $n = 4$ (since the interest is compounded quarterly),
- $t = 3$ years.

Now, plugging the values into the formula:

\[
A = 10,000 \left(1 + \frac{0.07}{4}\right)^{4 \times 3}
\]

Let’s calculate this step by step.

1. $\frac{0.07}{4} = 0.0175$
2. $1 + 0.0175 = 1.0175$
3. $4 \times 3 = 12$
4. $1.0175^{12} \approx 1.23144$
5. $A = 10,000 \times 1.23144 \approx 12,314.40$

Thus, the balance after three years is approximately **$12,314.40**.

Would you like further details or have any questions?

Here are five related questions for deeper exploration:
1. How does the balance change if the interest rate is compounded monthly instead of quarterly?
2. What would the balance be after five years instead of three?
3. How does increasing the interest rate to 8% affect the balance?
4. How much interest is earned in total after the three years?
5. How would the formula differ if the interest were compounded continuously?

**Tip:** The more frequently interest is compounded, the higher the balance will be, due to more frequent interest calculations.

Suppose you deposit $10,000 in an account that pays 7% annual interest. What is the balance after three years if the interest is compounded quarterly?

Learn how to calculate compound interest on a $10,000 deposit with 7% annual interest, compounded quarterly over 3 years. This problem involves key concepts such as exponential growth and the compound interest formula, suitable for students in Grades 9-12.

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