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 amount of money after $t$ years (future value),
• $P$ is the initial investment (present value),
• $r$ is the annual rate of return (which we need to find),
• $t$ is the time period in years.

Given:

• $A = 40,807$
• $P = 24,000$
• $t = 5$ years

We can rearrange the formula to solve for $r$:

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

Substituting the given values:

$r = \left( \frac{40,807}{24,000} \right)^{\frac{1}{5}} - 1$

Now, let's calculate the result.The effective annual rate of return on Juan's investment over the 5-year period is 11.20%.

Would you like more details on the calculation or have any other questions?

Here are 5 related questions to expand on this topic:

1. How does the compound interest formula change if the interest is compounded monthly?
2. What is the difference between the nominal interest rate and the effective annual rate?
3. How can we calculate the future value if the investment earns simple interest instead of compound interest?
4. How does the investment's growth compare with inflation over the same period?
5. How would the effective annual rate change if the investment duration was extended to 10 years?

Tip: The effective annual rate is always higher than the nominal rate when interest compounds more than once a year.