To find out how much you need to deposit now in order to have $3,000 in 10 years, we can use the formula for compound interest:

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

Where:

• $A$ is the amount of money in the account after interest, which is $3,000.
• $P$ is the principal, or the amount you need to deposit now (this is what we are solving for).
• $r$ is the annual interest rate, which is 2% or 0.02.
• $n$ is the number of times the interest is compounded per year. Since it's compounded monthly, $n = 12$.
• $t$ is the number of years, which is 10 years.

We need to solve for $P$. Rearranging the formula:

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

Substitute the known values:

$P = \frac{3000}{\left( 1 + \frac{0.02}{12} \right)^{12 \times 10}}$

Let me calculate this for you.You would need to deposit approximately $2,456.60 now in order to have $3,000 in the account in 10 years, assuming the account earns 2% interest compounded monthly.

Would you like more details on how this calculation works or have any questions?

Here are 5 related questions to explore further:

1. What happens if the interest rate increases to 3%?
2. How does the frequency of compounding (e.g., quarterly vs. monthly) affect the required deposit?
3. How much interest would be earned after 10 years?
4. How would the required deposit change if the goal was $5,000 in 10 years?
5. What is the difference between simple interest and compound interest?

Tip: The more frequently interest is compounded, the more you benefit from "interest on interest," leading to faster growth of your investment.