You deposit $4500 in an account earning 2.5% interest compounded monthly. How much will you have in the account in 9 years?

To calculate the future value of the account with interest compounded monthly, we use the compound interest formula:

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

Where:
- $A$ is the amount of money in the account after interest (future value).
- $P$ is the initial principal ($4500).
- $r$ is the annual interest rate (2.5%, or 0.025 as a decimal).
- $n$ is the number of times interest is compounded per year (12, for monthly).
- $t$ is the time in years (9 years).

### Step-by-step calculation:

\[
A = 4500 \left(1 + \frac{0.025}{12}\right)^{12 \times 9}
\]

Let's calculate this step by step.

After 9 years, the amount in the account will be approximately **$5634.13**.

Would you like further details on the calculation or have any questions?

Here are 5 related questions for deeper understanding:
1. How does the frequency of compounding (e.g., monthly vs. yearly) affect the future value?
2. What would happen if the interest rate was higher, say 3.5%, instead of 2.5%?
3. How can you calculate the total interest earned after 9 years?
4. What is the formula for continuous compounding, and how does it compare with monthly compounding?
5. How would the final amount change if the initial deposit was $5000 instead of $4500?

**Tip:** The more frequently interest is compounded, the higher the future value of the account, as interest is calculated on previously earned interest more often.

Learn how to calculate compound interest for a $4500 deposit at 2.5% annual interest compounded monthly over 9 years. Step-by-step solution using the compound interest formula, showing how exponential growth affects savings.

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