Answer: -0.1178.

This is given by the natural logarithm of the new price divided by the old price; ln(80 / 90) = −0.1178. **Explanation in markdown format:** The continuously compounded rate of return is calculated using the formula: \[ r = \ln\left(\frac{P_t}{P_{t-1}}\right) \] Where: - \( P_t \) = ending price = $80 - \( P_{t-1} \) = beginning price = $90 Substituting the values: \[ r = \ln\left(\frac{80}{90}\right) = \ln(0.888888...) \] \[ r = \ln(0.888888...) ≈ -0.1178 \] **Why other options are incorrect:** - **Option B (-0.1000)**: This is the simple rate of return: (80-90)/90 = -10/90 = -0.1111, not the continuously compounded return. - **Option C (-0.1250)**: This would be (80-90)/80 = -10/80 = -0.1250, which is incorrect for either simple or continuously compounded returns. **Key Concept:** Continuously compounded returns use natural logarithms, which provide the instantaneous rate of return and have useful mathematical properties for financial modeling, particularly in options pricing and time series analysis.

Author: LeetQuiz Editorial Team