To find the effective annual rate of return on Juan's investment, we can use the formula for compound interest:

$A = P(1 + r)^t$

Where:

• $A$ is the future value of the investment ($35,393),
• $P$ is the initial principal ($25,000),
• $r$ is the annual rate of return (which we need to find),
• $t$ is the number of years (5 years).

Rearranging the formula to solve for $r$:

$r = \left(\frac{A}{P}\right)^{\frac{1}{t}} - 1$

Now let's plug in the values and calculate the effective annual rate of return.

$r = \left(\frac{35,393}{25,000}\right)^{\frac{1}{5}} - 1$

Let me calculate that.The effective annual rate of return on Juan's investment over the 5-year period is 7.20%.

Do you want any more details or have any questions?

Here are 5 related questions for further practice:

1. What would the final value be if Juan had invested $30,000 instead?
2. How would the rate of return change if the investment grew to $40,000 in 5 years?
3. What is the future value of an investment of $50,000 at a 7.20% annual return over 10 years?
4. How would the formula change if the investment was compounded quarterly?
5. How can you calculate the nominal rate if you only know the effective annual rate?

Tip: When solving for rates of return, always check whether the interest is compounded annually or more frequently to apply the correct formula.