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This is a compound interest problem where the interest is compounded semi-annually. We can use the compound interest formula to solve it:

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

Where:
- $A$ is the final amount.
- $P = 7,900$ is the principal (initial deposit).
- $r = 0.05$ (5% annual interest rate).
- $n = 2$ because the interest is compounded semi-annually (twice a year).
- $t = 5$ years is the time the money is left in the account.

Substituting these values into the formula:

\[
A = 7,900 \left(1 + \frac{0.05}{2}\right)^{2 \times 5}
\]

Let's calculate:

\[
A = 7,900 \left(1 + 0.025\right)^{10}
\]
\[
A = 7,900 \times (1.025)^{10}
\]
\[
A = 7,900 \times 1.280084
\]
\[
A \approx 10,112.66
\]

So, the final amount after 5 years, rounded to two decimal places, is **$10,112.66**.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What if the interest was compounded quarterly instead of semi-annually?
2. How does the final amount change if the interest rate increases to 6%?
3. What if the investment period was only 3 years?
4. How would the final amount change if the initial deposit was $10,000 instead of $7,900?
5. What is the difference between simple interest and compound interest in terms of growth over time?

**Tip:** The more frequently interest is compounded, the higher the final amount will be due to the "compounding effect."

Find the final amount of money in an account if $7,900 is deposited at 5% interest compounded semi-annually and the money is left for 5 years.

Learn how to calculate the final amount for $7,900 deposited at 5% interest compounded semi-annually for 5 years. This problem covers compound interest, a key concept in financial mathematics, and uses the compound interest formula A = P(1 + r/n)^(nt). Suitable for students in Grades 10-12.

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