You estimate that you will need about $80,000 to send you child to college in eight years. You have about $35,000. At what rate will you just reach your goal?

To find the rate of return that will allow you to grow your $35,000 to $80,000 in eight years, we can use the formula for compound interest:

\[
A = P(1 + r)^t
\]

Where:
- $A$ is the final amount ($80,000),
- $P$ is the initial amount ($35,000),
- $r$ is the annual interest rate (expressed as a decimal),
- $t$ is the time in years (8 years).

We want to solve for $r$. Let's plug in the known values:

\[
80,000 = 35,000(1 + r)^8
\]

First, divide both sides by 35,000:

\[
\frac{80,000}{35,000} = (1 + r)^8
\]

Simplifying:

\[
2.2857 \approx (1 + r)^8
\]

Now, take the 8th root of both sides to solve for $r$:

\[
1 + r = \sqrt[8]{2.2857}
\]

\[
r = \sqrt[8]{2.2857} - 1
\]

Let's calculate the value of $r$.The required annual interest rate to grow your $35,000 to $80,000 in eight years is approximately **10.89%**.

Would you like more details on how the calculation was done, or do you have any questions?

Here are five related questions you might find interesting:
1. What happens if the rate of return is lower than 10.89%?
2. How does the interest rate affect the time needed to reach $80,000?
3. What if you start with a different amount, say $40,000?
4. How does compounding frequency (monthly vs. yearly) impact the growth?
5. What strategies can help achieve a higher return on investment?

**Tip:** It's important to account for inflation when planning for future expenses like college tuition.

You estimate that you will need about $80,000 to send your child to college in eight years. You have about $35,000. At what rate will you just reach your goal?

Learn how to calculate the interest rate required to grow $35,000 to $80,000 over 8 years using the compound interest formula. This step-by-step solution covers key concepts in exponential growth and is suitable for students in Grades 10-12.

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