Final answer:
The average annual rate of return realized in the three-year period is approximately 14.60%. The average annual return realized over the three-year period is approximately 6.11%.
Step-by-step explanation:
The average annual rate of return for the three-year period can be calculated by finding the geometric mean of the individual rates of return.
To find the geometric mean, we multiply the rates of return and then take the square root of the result.
For the given rates of return: 100%, -50%, and 30%, the average annual rate of return is found as:
[(1 + 1) × (1 - 0.5) × (1 + 0.3)]^(1/3) - 1 ≈ 14.60%
Therefore, the average annual rate of return realized in the three-year period is approximately 14.60%.
If you invested $100 each at the beginning of year 1 and year 2 and withdrew $100 at the beginning of the third year, the total investment would be $300. The total return would be the sum of the individual returns:
Total Return = ($100 × 1) + ($100 × (-0.5)) + ($100 × 0.3) = $55
The average annual return can be calculated by dividing the total return by the total investment and dividing by the number of years:
Average Annual Return = ($55 / $300) × (1/3) = 6.11%
Therefore, the average annual return realized over the three-year period is approximately 6.11%.