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."