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To solve this problem, we can use the formula for compound interest:

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

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

**Given values:**
- $ P = 4000 $
- $ r = 4\% = 0.04 $
- $ n = 12 $ (since interest is compounded monthly)
- $ t = 5 $ years

**Substitute the values into the formula:**

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

1. Calculate $ \frac{0.04}{12} \approx 0.003333 $.
2. Add 1 to get the monthly growth factor: $ 1 + 0.003333 \approx 1.003333 $.
3. Compute the exponent $ 12 \times 5 = 60 $.
4. Finally, calculate $ A $.

Let's proceed with these calculations:

\[
A = 4000 \times (1.003333)^{60}
\]

Using this formula, the approximate amount in the account after 5 years will be:

\[
A \approx 4000 \times 1.22139 = 4885.56
\]

So, you would have approximately **$4885.56** in the account after 5 years.

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

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Here are 5 related questions to deepen understanding:
1. What would the amount be if interest were compounded quarterly instead of monthly?
2. How would the final amount change if the interest rate was 5% instead of 4%?
3. What is the difference in final amount if the initial deposit was $5000 instead of $4000?
4. How much interest would be earned if the account had no compounding (simple interest only)?
5. How long would it take to double the initial deposit with monthly compounding?

**Tip:** Remember, the frequency of compounding (monthly, quarterly, etc.) can significantly affect the final amount due to compound interest's exponential growth effect.

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 a $4000 deposit at a 4% annual interest rate, compounded monthly over 5 years. This example uses the compound interest formula to demonstrate exponential growth in financial savings.

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