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.