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

$A = P \left(1 + \frac{r}{n}\right)^{n \times t}$

where:

• $A$ is the amount of money accumulated after $t$ years, including interest.
• $P$ is the principal amount (initial deposit), which is $2000 in this case.
• $r$ is the annual interest rate (decimal), which is 2%, or 0.02.
• $n$ is the number of times the interest is compounded per year, which is monthly (12 times per year).
• $t$ is the time the money is invested for, which is 5 years.

Plugging in the values:

$A = 2000 \left(1 + \frac{0.02}{12}\right)^{12 \times 5}$

Calculating step-by-step:

1. Calculate the monthly interest rate: $\frac{0.02}{12} = 0.0016667$.
2. Add 1 to the monthly rate: $1 + 0.0016667 = 1.0016667$.
3. Multiply $n$ and $t$: $12 \times 5 = 60$.
4. Raise the result to the power of 60: $(1.0016667)^{60} \approx 1.1047$.
5. Multiply by the principal: $2000 \times 1.1047 \approx 2209.40$.

So, the amount in the account after 5 years will be approximately $2209.40.

Would you like more details or have any questions?

Here are five related questions to explore further:

1. What is the difference between simple and compound interest in terms of calculations?
2. How does increasing the compounding frequency (e.g., daily vs. monthly) affect the final amount?
3. What would be the final amount if the interest rate were increased to 5% instead of 2%?
4. How does the formula change if interest is compounded continuously?
5. What if you make additional deposits every year? How does that affect the total amount?

Tip: When dealing with compound interest, increasing the frequency of compounding (like switching from annually to monthly) results in a higher final amount due to interest compounding on accumulated interest more frequently.