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: