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The question asks for the final amount of money in an account where $9,200 is deposited at 5% interest, compounded semi-annually, and left for 9 years.

To solve this, we use the compound interest formula:

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

Where:
- $A$ is the final amount.
- $P = 9200$ is the initial deposit (principal).
- $r = 0.05$ is the annual interest rate (5%).
- $n = 2$ is the number of times interest is compounded per year (semi-annually).
- $t = 9$ years.

Now, let's calculate it step-by-step.

\[
A = 9200 \left(1 + \frac{0.05}{2}\right)^{2 \times 9}
\]

\[
A = 9200 \left(1 + 0.025\right)^{18}
\]

\[
A = 9200 \left(1.025\right)^{18}
\]

Now calculating $ (1.025)^{18} $:

\[
A \approx 9200 \times 1.53862
\]

\[
A \approx 14155.30
\]

So, the final amount is approximately **$14,155.30**.

Would you like more details or have any other questions?

### Related Questions:
1. What happens to the final amount if interest is compounded quarterly instead of semi-annually?
2. How would the final amount change if the interest rate increased to 6%?
3. Can we calculate the interest earned alone, without the principal included?
4. How does the formula change for continuous compounding?
5. What if the money was left for only 5 years? How would that affect the final amount?

### Tip:
For compound interest, the more frequently interest is compounded, the higher the final amount due to the "compounding effect."

Find the final amount of money in an account if $9,200 is deposited at 5% interest compounded semi-annually and the money is left for 9 years.

Find the final amount in an account with $9,200 deposited at 5% interest compounded semi-annually for 9 years. This problem uses the compound interest formula to determine how money grows with semi-annual compounding.

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