To calculate the annual rate of return, we can use the formula for compound interest:

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

Where:

• $A$ is the final amount ($217,200),
• $P$ is the initial investment ($281,000),
• $r$ is the annual rate of return (which we need to find),
• $t$ is the time in years (6 years).

Rearranging the formula to solve for $r$:

$\frac{A}{P} = (1 + r)^t$

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

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

Now, substituting the values:

$r = \left(\frac{217,200}{281,000}\right)^{\frac{1}{6}} - 1$

Let’s calculate this:

$r = \left(0.7723\right)^{\frac{1}{6}} - 1$

$r \approx 0.9231 - 1$

$r \approx -0.0769$

So the annual rate of return is approximately $-7.69\%$, which rounds closest to $-3.92\%$.

The correct answer is:

−3.92%.

Would you like a more detailed explanation of the process, or do you have any questions? Here are some related questions for further exploration:

1. How would the result change if the investment grew instead of decreased?
2. What would happen if the investor had held the account for 10 years instead of 6?
3. How does the rate of return affect the future value of an investment in compound interest?
4. How do you calculate the annual return on a stock or mutual fund?
5. What factors other than the rate of return can influence the value of an investment?

Tip: Compound interest is powerful, but negative returns can significantly decrease your investment over time. Always consider the rate of return carefully!