To solve this problem, we need to apply the compound interest formula:

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

Where:

• $A$ is the final balance.
• $P$ is the principal (initial deposit) = $400.
• $r$ is the annual interest rate as a decimal = 13% = 0.13.
• $n$ is the number of times interest is compounded per year = 1 (since it's compounded annually).
• $t$ is the time in years = 8.

Now, we can plug these values into the formula:

$A = 400 \left( 1 + \frac{0.13}{1} \right)^{1 \times 8}$

Simplify:

$A = 400 \left( 1 + 0.13 \right)^8$ $A = 400 \times (1.13)^8$ $A = 400 \times 2.848107$ $A = 1139.24$

So, the balance after 8 years is $1139.24.

Would you like more details or further clarification? Here are 5 related questions:

1. How does the number of times interest is compounded affect the final balance?
2. What would the balance be if the interest rate were 10% instead of 13%?
3. How would the balance change if Tammy left the money for 10 years instead of 8?
4. What is the difference between simple interest and compound interest?
5. How can you calculate the principal if you know the final amount, interest rate, and time?

Tip: The more frequently interest is compounded (quarterly, monthly, etc.), the more you earn in the long run.