To determine how much you would need to deposit now to have $3,000 in 10 years, given an interest rate of 7% compounded monthly, we can use the Present Value (PV) formula for compound interest:

$PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}$

Where:

• $PV$ is the present value (the amount to deposit now),
• $FV$ is the future value (the amount you want in the future, which is $3,000),
• $r$ is the annual interest rate (7% or 0.07),
• $n$ is the number of times the interest is compounded per year (monthly means $n = 12$),
• $t$ is the number of years (10 years).

Plugging in the values:

$PV = \frac{3000}{(1 + \frac{0.07}{12})^{12 \times 10}}$

Let's calculate this.

You would need to deposit approximately $1,492.79 now in order to have $3,000 in the account in 10 years, assuming an interest rate of 7% compounded monthly.

Would you like more details or have any questions?

Here are some related questions:

1. How does the compounding frequency affect the required deposit?
2. What if the interest were compounded quarterly instead of monthly?
3. How much would the deposit change if the interest rate were 5% instead of 7%?
4. How would the result change if the time period were 20 years instead of 10?
5. What if the account was earning simple interest instead of compound interest?

Tip: The more frequently interest is compounded, the faster the account balance grows, since interest is applied to previously earned interest as well.