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From the image you uploaded, the problem involves calculating the future value of a savings account with compound interest.

The formula provided is:

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

Where:
- $ A $ is the amount of money in the account after $ t $ years.
- $ P $ is the principal (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 number of years the money is invested.

### Given dataFrom the image you uploaded, the problem involves calculating the future value of a savings account with compound interest.

The formula provided is:

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

Where:
- $ A $ is the amount of money in the account after $ t $ years.
- $ P $ is the principal (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 number of years the money is invested.

### Given 
- Principal $ P = 9000 $
- Rate $ r = 4.5\% = 0.045 $ (in decimal form)
- Compounded monthly, so $ n = 12 $
- Time $ t = 5 $ years.

Let's plug the values into the formula:

\[
A = 9000 \left( 1 + \frac{0.045}{12} \right)^{12 \times 5}
\]

\[
A = 9000 \left( 1 + 0.00375 \right)^{60}
\]

\[
A = 9000 \left( 1.00375 \right)^{60}
\]

Now let's calculate that:

\[
A = 9000 \times 1.233004
\]

\[
A \approx 11097.04
\]

So, after 5 years, the amount of money in the account will be approximately **\$11,097.04**.

Would you like to ask anything else or need a more detailed explanation?

Here are 5 related questions to expand your understanding:
1. How does the frequency of compounding affect the total amount?
2. What would the amount be if the interest were compounded annually instead of monthly?
3. Can you explain the difference between simple interest and compound interest?
4. How would the total change if the time was 10 years instead of 5 years?
5. How can you compute the interest earned instead of the final amount?

**Tip**: Always convert percentage rates into decimal form when using them in formulas!

Find how much money there will be in the account after 5 years, with a principal of $9000, a 4.5% annual interest rate compounded monthly.

Learn how to calculate the future value of a savings account with a principal of $9000, compounded monthly at a 4.5% annual interest rate over 5 years. This detailed guide covers the compound interest formula and exponential growth principles, suitable for high school students in Grades 10-12.

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