The compound interest formula is given by:

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

Where:

• $A$ is the amount of money accumulated after $t$ years, including interest.
• $P$ is the principal amount (the initial investment).
• $r$ is the annual interest rate (in decimal form).
• $n$ is the number of times the interest is compounded per year.
• $t$ is the time the money is invested or borrowed for, in years.

For this problem:

• $P = 8000$ (initial investment)
• $r = 0.003$ (APR of 0.3%, converted to decimal)
• $n = 1$ (interest is compounded annually)
• $t = 12$ years

Now we can calculate the balance:

$A = 8000 \left( 1 + \frac{0.003}{1} \right)^{1 \times 12}$

$A = 8000 \left( 1.003 \right)^{12}$

Let me calculate that for you.The balance in the account after 12 years will be approximately $8292.80.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How would the balance change if the interest were compounded monthly instead of annually?
2. What is the total interest earned over the 12 years?
3. How would the final amount change if the APR was increased to 1%?
4. What would the balance be after 12 years with a different initial investment, say $10,000?
5. How does compound interest differ from simple interest over long periods?

Tip: The more frequently interest is compounded, the greater the final balance will be.