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The problem asks for the final amount of money in an account where $2,000 is deposited at 5% interest, compounded semi-annually, for 7 years.

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

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

Where:
- $A$ is the final amount
- $P$ is the principal amount (initial deposit), which is $2,000
- $r$ is the annual interest rate (5% or 0.05)
- $n$ is the number of times the interest is compounded per year (semi-annually means $n = 2$)
- $t$ is the number of years (7 years)

### Step-by-step solution:
1. $P = 2000$
2. $r = 0.05$
3. $n = 2$
4. $t = 7$

Now, substituting these values into the formula:

\[
A = 2000 \left(1 + \frac{0.05}{2}\right)^{2 \times 7}
\]

\[
A = 2000 \left(1 + 0.025\right)^{14}
\]

\[
A = 2000 \times (1.025)^{14}
\]

\[
A = 2000 \times 1.423297
\]

\[
A \approx 2846.59
\]

### Final Answer:
The final amount is **$2,846.59**.

Would you like further details or have any questions?

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Here are 5 related questions for further exploration:
1. What would the final amount be if the interest was compounded quarterly?
2. How does the final amount change if the interest rate was increased to 6%?
3. What is the formula for simple interest, and how does it compare to compound interest?
4. What is the impact of increasing the number of compounding periods per year?
5. How long would it take to double the investment at the same interest rate and compounding period?

**Tip:** The more frequently interest is compounded, the greater the final amount due to the power of compound growth.

Find the final amount of money in an account if $2,000 is deposited at 5% interest compounded semi-annually and the money is left for 7 years. Round the answer to 2 decimal places.

Learn how to calculate the final amount when $2,000 is deposited at 5% interest compounded semi-annually for 7 years. This problem covers key concepts in compound interest and provides a detailed step-by-step solution. Suitable for students in Grades 9-12.

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