Answer: 719.2

## Explanation Effective convexity measures the sensitivity of the duration measure to changes in interest rates. It is given by the formula: \[ C = \frac{1}{P} \left[ \frac{P^+ + P^- - 2P}{(\Delta r)^2} \right] \] Where: - \(P^+\) is the value of the bond when all rates increase by \(\Delta r\) - \(P^-\) is the value of the bond when all rates decrease by \(\Delta r\) - \(P\) is the current bond price - \(\Delta r\) is the change in interest rates From the table: - Current interest rate: 4.00% - Current bond price \(P = 97.8910\) - When rates decrease to 3.95% (\(\Delta r = -0.05\%\)): \(P^- = 97.9430\) - When rates increase to 4.05% (\(\Delta r = +0.05\%\)): \(P^+ = 97.8566\) - \(\Delta r = 0.0005\) (0.05% in decimal form) Calculating: \[ C = \frac{1}{97.8910} \cdot \left[ \frac{97.8566 + 97.9430 - 2 \cdot 97.8910}{(0.0005)^2} \right] \] \[ C = \frac{1}{97.8910} \cdot \left[ \frac{195.7996 - 195.7820}{0.00000025} \right] \] \[ C = \frac{1}{97.8910} \cdot \left[ \frac{0.0176}{0.00000025} \right] \] \[ C = \frac{1}{97.8910} \cdot 70,400 \] \[ C = 719.1672 \] Therefore, the estimated effective convexity is approximately 719.2, which corresponds to option D.

Author: LeetQuiz .