Juan invested $25,000 in a mutual fund 3 yr ago. Today his investment is worth $31,318. Find the effective annual rate of return on his investment over the 3-yr period. (Round your answer to two decimal places.)

To calculate 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 final amount ($31,318),
- $ P $ is the initial investment ($25,000),
- $ r $ is the effective annual rate of return,
- $ t $ is the number of years (3 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:

\[
r = \left(\frac{31,318}{25,000}\right)^{\frac{1}{3}} - 1
\]

I'll calculate that for you.

The effective annual rate of return on Juan's investment over the 3-year period is **7.80%**.

Would you like more details or have any other questions?

Here are five related questions for further exploration:
1. How would the rate change if the investment had grown to $35,000 in 3 years?
2. What would be the final amount if Juan had earned an 8% effective annual return?
3. How would the calculation differ for continuous compounding?
4. What is the difference between effective annual rate and nominal interest rate?
5. How can inflation impact the real return on investments?

**Tip:** Always double-check the investment horizon and compounding method when evaluating returns to ensure accurate calculations.

Find out how to calculate the effective annual rate of return on Juan's $25,000 investment, which grew to $31,318 over 3 years. Using compound interest formulas, this problem covers exponential growth and rate calculations, ideal for students in Grades 10-12.

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