Answer: 0.35%

**Explanation:** To calculate the geometric mean annual return, we need to use the formula: \[ \text{Geometric Mean} = \left[ \prod_{i=1}^{n} (1 + R_i) \right]^{\frac{1}{n}} - 1 \] Where: - \( R_i \) are the annual returns - \( n \) is the number of periods (5 years) **Step-by-step calculation:** 1. Convert percentages to decimal form: - Year 1: -8.0% = -0.08 - Year 2: -5.5% = -0.055 - Year 3: -7.2% = -0.072 - Year 4: 20.8% = 0.208 - Year 5: 4.4% = 0.044 2. Calculate the product of (1 + return): \[ (1 - 0.08) \times (1 - 0.055) \times (1 - 0.072) \times (1 + 0.208) \times (1 + 0.044) \] \[ = 0.92 \times 0.945 \times 0.928 \times 1.208 \times 1.044 \] 3. Calculate step by step: - 0.92 × 0.945 = 0.8694 - 0.8694 × 0.928 = 0.8068 - 0.8068 × 1.208 = 0.9746 - 0.9746 × 1.044 = 1.0175 4. Take the 5th root: \[ (1.0175)^{\frac{1}{5}} = 1.0175^{0.2} \] \[ \approx 1.00347 \] 5. Subtract 1 and convert to percentage: \[ 1.00347 - 1 = 0.00347 = 0.347\% \] **Verification:** The geometric mean of approximately 0.347% is closest to option A (0.35%). **Why not the other options?** - Option B (0.90%) would be too high given the negative returns in three of the five years - Option C (1.75%) is significantly higher than what the calculation shows **Key Concept:** The geometric mean is the appropriate measure for average returns over multiple periods because it accounts for compounding effects, unlike the arithmetic mean which would overstate returns when there is volatility.

Author: LeetQuiz .