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

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

Where:
- $A$ is the amount of money accumulated after $n$ years, including interest.
- $P$ is the principal amount (the initial sum of money) = $54,000.
- $r$ is the annual interest rate (decimal) = 12% = 0.12.
- $n$ is the number of times that interest is compounded per year = 12 (since it's compounded monthly).
- $t$ is the time the money is invested for in years = 7.

Let's substitute these values into the formula:

\[
A = 54000 \left(1 + \frac{0.12}{12}\right)^{12 \times 7}
\]

\[
A = 54000 \left(1 + 0.01\right)^{84}
\]

\[
A = 54000 \left(1.01\right)^{84}
\]

Now, I will calculate the final amount.The balance after 7 years, if $54,000 is invested at 12% p.a. compounded monthly, will be **$124,563** (rounded to the nearest dollar).

Would you like more details or have any other questions?

Here are 8 related questions to expand your understanding:
1. How would the balance change if the interest rate were 10% instead of 12%?
2. What would the balance be if the interest were compounded quarterly instead of monthly?
3. How does the compounding frequency affect the final balance?
4. What would the balance be after 10 years instead of 7 years?
5. How much interest is earned in total over the 7 years?
6. How would the balance change if $100,000 were invested instead of $54,000?
7. What is the formula for continuously compounded interest, and how does it differ?
8. How can this calculation be done using a financial calculator?

**Tip:** When solving compound interest problems, always ensure you convert the interest rate to a decimal and match the compounding period with the time duration (e.g., monthly, quarterly).

Learn how to calculate compound interest with $54,000 invested at 12% per annum compounded monthly over 7 years. Understand the impact of different interest rates and compounding frequencies on final balances.

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