You determine that you would like to save $50,000 for your child’s college education in 18 years. If your
account earns 2.75% compounded quarterly, how much would you need to deposit today in order to reach
your 18-year goal?

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.

You determine that you would like to save $50,000 for your child’s college education in 18 years. If your account earns 2.75% compounded quarterly, how much would you need to deposit today in order to reach your 18-year goal?

Find out how much you need to deposit today to save $50,000 for college in 18 years, earning 2.75% interest compounded quarterly. Learn about compound interest formulas and exponential growth with this step-by-step solution. Suitable for students in Grades 10-12.

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