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This problem involves calculating compound interest. The formula for compound interest is:

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

Where:
- $A$ is the amount of money accumulated after $t$ years, including interest.
- $P$ is the principal amount (initial investment).
- $r$ is the annual interest rate (decimal).
- $n$ is the number of times the interest is compounded per year.
- $t$ is the time in years.

### Given values:
- $P = 4035$ (initial investment)
- $r = 1.5\% = 0.015$ (annual interest rate)
- $n = 12$ (monthly compounding)
- $t = 4$ years

### Part (a): The overall amount $A$
Now, substituting the given values into the formula:

\[
A = 4035 \left(1 + \frac{0.015}{12}\right)^{12 \times 4}
\]

Let me calculate that.The overall amount $A$ after 4 years is approximately **$4284.35**.

### Part (b): The compound interest

To find the compound interest, we subtract the principal $P$ from the overall amount $A$:

\[
\text{Compound Interest} = A - P
\]

Let me calculate that next.The compound interest earned after 4 years is approximately **$249.35**.

### Summary:
- **The overall amount** after 4 years is **$4284.35**.
- **The compound interest** is **$249.35**.

Would you like further details or have any questions?

Here are five related questions you might find helpful:
1. How does increasing the interest rate affect the overall amount?
2. What happens if the compounding is done quarterly instead of monthly?
3. How would the results change if the investment period were 5 years instead of 4?
4. How does the formula change for continuous compounding?
5. What is the impact of doubling the principal investment?

**Tip:** The more frequent the compounding, the greater the accumulated amount due to interest being applied more often.

Solve the compound interest problem. $4035 is invested at 1.5% compounded monthly for 4 years. a. Find the overall amount. b. Find the compound interest.

Learn how to calculate the overall amount and compound interest for an investment of $4035 at a 1.5% interest rate, compounded monthly for 4 years. This guide uses the compound interest formula, showing step-by-step calculations and results.

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