To determine how much you need to deposit today to reach your $50,000 goal, given the account earns 2.75% compounded quarterly over 18 years, we can use the formula for compound interest:

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

Where:

• $A$ is the future value (the amount you want, $50,000).
• $P$ is the present value or the amount you need to deposit today.
• $r$ is the annual interest rate (2.75% or 0.0275).
• $n$ is the number of times the interest is compounded per year (quarterly = 4 times a year).
• $t$ is the time in years (18 years).

We need to rearrange this formula to solve for $P$:

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

Let's plug in the values and calculate.

$P = \frac{50,000}{\left(1 + \frac{0.0275}{4}\right)^{4 \times 18}}$You would need to deposit approximately $30,530.21 today in order to reach your $50,000 goal in 18 years, with an interest rate of 2.75% compounded quarterly.

Would you like more details or have any questions about the calculation?

Here are five related questions to consider:

1. How does the compound frequency affect the amount to be deposited?
2. What would happen if the interest rate was higher, such as 5%?
3. How would the required deposit change if you had only 10 years to save?
4. What if you wanted to reach a goal of $100,000 instead of $50,000?
5. How would the deposit change if interest was compounded annually instead of quarterly?

Tip: The more frequently interest is compounded, the less you need to deposit initially to reach a future goal, since the interest builds more often.