https://file.aiquickdraw.com/mathbot/file/1728425504159b5mhcpoh.jpg

We can solve this problem using the compound interest formula provided in the image:

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

Where:
- $F$ is the future value (the balance after 6 years),
- $P = 500$ is the principal (initial deposit),
- $r = 4.5\%$ or 0.045 is the annual interest rate,
- $n = 1$ is the number of times the interest is compounded per year (since it's compounded annually),
- $t = 6$ is the number of years.

Now, plug in the values:

\[
F = 500 \left(1 + \frac{0.045}{1}\right)^{1 \times 6}
\]

\[
F = 500 \left(1 + 0.045\right)^6
\]

\[
F = 500 (1.045)^6
\]

Next, calculate $ (1.045)^6 $:

\[
(1.045)^6 \approx 1.3006
\]

Now multiply by the principal:

\[
F = 500 \times 1.3006 = 650.30
\]

So, the balance after 6 years is approximately **$650.30**, rounded to the nearest cent.

Do you want more details on any step or have any questions? 

Here are 5 related questions:
1. What would the balance be if the interest were compounded monthly instead of annually?
2. How does the balance change if the interest rate increases to 5%?
3. What would the total interest earned be after 6 years?
4. How would the formula change if you wanted to calculate continuous compounding?
5. What is the balance if the time period were extended to 10 years instead?

**Tip:** Compound interest grows faster the more frequently it's compounded (monthly, daily, etc.).

If $500 are deposited into an account with a 4.5% interest rate, compounded annually, what is the balance after 6 years? Round to the nearest cent.

Find out how to calculate the future balance of $500 deposited with a 4.5% annual interest rate, compounded annually over 6 years. Learn the compound interest formula and its application, with the balance rounded to the nearest cent. Suitable for Grades 9-11 students.

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