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To solve this problem, we will use the formula for compound interest to calculate the present value (the amount you need to deposit now).

The compound interest formula is:

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

Where:
- $ A $ is the future value of the investment/loan, which is $3000 in this case.
- $ P $ is the present value (the amount you need to deposit now).
- $ r $ is the annual interest rate (expressed as a decimal), so 4% becomes 0.04.
- $ n $ is the number of times the interest is compounded per year (monthly means $ n = 12 $).
- $ t $ is the number of years the money is invested, which is 15 years.

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

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

Substituting the given values:
- $ A = 3000 $
- $ r = 0.04 $
- $ n = 12 $
- $ t = 15 $

\[
P = \frac{3000}{\left(1 + \frac{0.04}{12}\right)^{12 \times 15}}
\]

Now, let's compute this:

\[
P = \frac{3000}{\left(1 + 0.00333\right)^{180}}
= \frac{3000}{\left(1.00333\right)^{180}}
\]

Using a calculator, $ \left(1.00333\right)^{180} \approx 1.81402 $.

Thus,

\[
P = \frac{3000}{1.81402} \approx 1653.11
\]

So, you would need to deposit approximately **$1653.11** now to have $3000 in 15 years at 4% interest compounded monthly.

Would you like further details or have any questions?

Here are some related questions you may find interesting:
1. What happens if the interest is compounded quarterly instead of monthly?
2. How would the answer change if the interest rate was 5% instead of 4%?
3. What is the total interest earned after 15 years on this deposit?
4. How does the formula for compound interest compare to simple interest?
5. What would the required deposit be if the goal was $5000 instead of $3000?

**Tip:** Compounding frequency has a significant impact on the growth of an investment. The more frequently interest is compounded, the more interest is earned.

How much would you need to deposit in an account now in order to have $3000 in the account in 15 years? Assume the account earns 4% interest compounded monthly.

Find out how much you need to deposit now to have $3000 in 15 years with a 4% annual interest rate compounded monthly. This problem explains the compound interest formula and demonstrates step-by-step calculations suitable for high school students in Grades 10-12.

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