The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Your data is... principal: $4500, rate: 3.5%, compounded: monthly, time: 4 years. Find how much money will be in the account after 4 years in $, rounding to the nearest cent if needed.

To calculate the amount of money in the account after 4 years with compound interest, we can 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 the specified time.
- $P$ is the principal (initial amount of money deposited).
- $r$ 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 for, in years.

Given:
- $P = 4500$ (the principal)
- $r = 3.5\% = 0.035$ (the annual interest rate in decimal form)
- $n = 12$ (since the interest is compounded monthly)
- $t = 4$ years

Let's plug these values into the formula:

\[
A = 4500 \left(1 + \frac{0.035}{12}\right)^{12 \times 4}
\]

Now, calculate it step by step:

1. Calculate $\frac{r}{n}$:

\[
\frac{0.035}{12} \approx 0.00291667
\]

2. Add 1 to this value:

\[
1 + 0.00291667 \approx 1.00291667
\]

3. Calculate the exponent $nt$:

\[
12 \times 4 = 48
\]

4. Raise the base to the exponent:

\[
(1.00291667)^{48}
\]

5. Multiply by the principal $P$:

\[
A = 4500 \times (1.00291667)^{48}
\]

Let's compute this.The amount of money in the account after 4 years, with the given conditions, will be **$5,175.18**.

Would you like more details or have any questions about this calculation?

Here are 5 related questions you might consider:
1. What would the amount be if the interest was compounded quarterly instead of monthly?
2. How much interest is earned after 4 years?
3. What is the formula for simple interest, and how does it differ from compound interest?
4. How would the amount change if the interest rate increased to 5%?
5. What would the amount be if the principal was $6,000 instead of $4,500?

**Tip:** Understanding the difference between simple and compound interest can help you make better financial decisions for saving and investing.

Learn how to calculate compound interest with a principal of $4500, an annual interest rate of 3.5% compounded monthly over a period of 4 years. Understand the exponential growth formula used in finance calculations. Suitable for advanced high school students and anyone interested in financial mathematics.

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