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This is a compound interest problem where we need to find the present value (the amount of money Esteban and Sunny should invest now). The formula for compound interest is:

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

Where:
- $A$ is the future value, or the amount needed ($78,000).
- $P$ is the present value, or the initial investment (which we are solving for).
- $r$ is the annual interest rate (6.15% or 0.0615).
- $n$ is the number of times interest is compounded per year (quarterly compounding means $n = 4$).
- $t$ is the number of years (18 years).

We need to solve for $P$:

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

Plugging in the given values:

\[
P = \frac{78,000}{\left(1 + \frac{0.0615}{4}\right)^{4 \times 18}}
\]

Let me calculate this for you.

\[
P = \frac{78,000}{\left(1 + 0.015375\right)^{72}} = \frac{78,000}{1.015375^{72}}
\]

\[
P \approx \frac{78,000}{3.014} \approx 25,872.79
\]

So, Esteban and Sunny should invest approximately **$25,872.79** now to have $78,000 in 18 years.

Would you like a detailed explanation or have any other questions?

Here are 5 related questions:
1. How does the frequency of compounding affect the final amount?
2. What if the interest was compounded monthly instead of quarterly?
3. What would happen if they wanted the money sooner, say in 10 years?
4. How would inflation impact the future value in terms of real purchasing power?
5. How can you calculate the future value for varying interest rates?

**Tip:** The higher the frequency of compounding, the more interest is accrued over time!

Esteban and Sunny have a new grandson. How much money should they invest now so that he will have $78,000 for his college education in 18 years? The money is invested at 6.15% compounded quarterly.

Find out how much Esteban and Sunny should invest now to reach $78,000 in 18 years for their grandson's college education, with a 6.15% interest rate compounded quarterly. This problem involves compound interest calculations suitable for Grades 9-12.

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