https://file.aiquickdraw.com/mathbot/file/1730046295776lz9fc6q0.jpg

To solve this problem, we’ll use the compound interest formula:

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

where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (initial deposit), which is $4000.
- $ r $ is the annual interest rate (in decimal), so 4% becomes 0.04.
- $ n $ is the number of times the interest is compounded per year, which is monthly, so $ n = 12 $.
- $ t $ is the number of years, which is 5.

Let's plug in the values:

\[
A = 4000 \left(1 + \frac{0.04}{12}\right)^{12 \times 5}
\]

### Step-by-Step Calculation:

1. **Calculate the monthly interest rate**: $\frac{0.04}{12} = 0.003333$.
2. **Calculate the exponent**: $12 \times 5 = 60$.
3. **Calculate the base inside the parentheses**: $1 + 0.003333 = 1.003333$.
4. **Raise the base to the power of 60**: $1.003333^{60}$.
5. **Multiply the result by the initial deposit $ P $, which is $4000**.

I’ll calculate this for the exact answer.

#### Calculation:
\[
A \approx 4000 \times (1.003333)^{60}
\]
\[
A \approx 4000 \times 1.22139
\]
\[
A \approx 4885.56
\]

### Final Answer:
After 5 years, the amount in the account will be approximately **$4885.56**.

Would you like additional details on this calculation or have any questions?

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Here are some related questions to explore:

1. What would the amount be if the interest was compounded quarterly instead of monthly?
2. How would the result change if the interest rate were increased to 5%?
3. What is the impact of compounding frequency on the final amount in general?
4. How much interest would you earn if it were compounded annually at the same rate?
5. How does the compounding effect compare over a longer period, like 10 years?

**Tip**: Compounding more frequently generally increases the total amount, as interest is calculated and added to the principal more often.

You deposit $4000 in an account earning 4% interest compounded monthly. How much will you have in the account in 5 years?

Learn how to calculate compound interest for an initial deposit of $4000 at an interest rate of 4% compounded monthly over 5 years. This solution uses the compound interest formula to determine the final amount, covering essential financial math concepts suitable for high school students.

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