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?

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.