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The question asks you to find the amount of money that will be in a savings account after 3 years with a principal of $4500, an interest rate of 2.5% compounded monthly.

The formula to use is the compound interest formula:

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

Where:
- $ A $ is the amount of money in the account after $ t $ years,
- $ P $ is the principal ($4500),
- $ r $ is the annual interest rate (2.5% or 0.025 as a decimal),
- $ n $ is the number of times the interest is compounded per year (monthly means $ n = 12 $),
- $ t $ is the time the money is invested for (3 years).

Let's plug in the values:

\[
A = 4500 \left( 1 + \frac{0.025}{12} \right)^{12 \times 3}
\]

Now let's compute step by step:

1. First, calculate $ \frac{0.025}{12} = 0.0020833 $,
2. Then, add 1: $ 1 + 0.0020833 = 1.0020833 $,
3. Now, raise this to the power $ 12 \times 3 = 36 $:
   \[
   1.0020833^{36} \approx 1.077925
   \]
4. Finally, multiply by the principal $ P = 4500 $:
   \[
   A \approx 4500 \times 1.077925 \approx 4850.66
   \]

So, the amount of money in the account after 3 years is approximately **$4850.66**.

Let me know if you'd like a detailed breakdown or have any further questions!

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**Relative questions:**

1. What happens if the interest is compounded daily instead of monthly?
2. How would the result change if the interest rate increased to 3%?
3. Can you calculate the effective annual yield $ Y $ based on this compound interest?
4. How does the time $ t $ affect the total interest earned in the account?
5. What is the impact of increasing the principal to $5000?

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**Tip:** Always convert interest rates into decimals when applying them in formulas.

The principal represents an amount of money deposited in a savings account subject to compound interest at a given rate. Answer parts (a) and (b). For part (a), find how much money there will be in the account after 3 years. The principal is $4500, the rate is 2.5% compounded monthly.

Learn how to calculate the future value of a $4500 savings account with 2.5% interest compounded monthly over 3 years. This problem uses the compound interest formula A = P(1 + r/n)^(nt) to find the balance after 3 years.

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