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To solve this compound interest problem, we need to determine how much Collin and Mei should invest now to reach $52,000 in 18 years, with an annual interest rate of 7.9%, compounded annually.

The compound interest formula is:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- $A$ is the amount of money accumulated after $n$ years, including interest ($52,000),
- $P$ is the principal amount (initial investment, which we need to find),
- $r$ is the annual interest rate (7.9% or 0.079),
- $t$ is the time the money is invested for (18 years),
- $n$ is the number of times the interest is compounded per year (1 for annually).

Rearranging to solve for $P$:
\[
P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}
\]

Now, plug in the values:
\[
P = \frac{52000}{\left(1 + \frac{0.079}{1}\right)^{1 \times 18}}
\]

Let me calculate this for you.

\[
P = \frac{52000}{(1.079)^{18}}
\]

\[
P \approx \frac{52000}{3.987}
\]

\[
P \approx 13043.74
\]

So, Collin and Mei should invest approximately **$13,043.74** now to have $52,000 in 18 years.

Would you like more details on the steps, or do you have any further questions?

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Here are 5 related questions to deepen your understanding:
1. How would the investment amount change if the interest were compounded quarterly instead of annually?
2. What would happen to the future value if they invested more than $13,043.74?
3. How does increasing the interest rate to 10% affect the required investment?
4. If they wanted to reach the goal in 15 years instead of 18, how much should they invest?
5. What if the interest rate was compounded continuously? How would that change the formula?

**Tip**: Remember, the more frequently interest is compounded, the more you earn over time, even with the same interest rate.

Collin and Mei have a new grandson. How much money should they invest now so that he will have $52,000 for his college education in 18 years? The money is invested at 7.9% compounded annually.

Learn how to calculate the initial investment required for a $52,000 college fund in 18 years, using a 7.9% compound interest rate compounded annually. The step-by-step solution involves applying the compound interest formula and solving for the principal. Ideal for students in Grades 10-12.

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