The correct answer is A (93.7). The percentage change in the bond's price is calculated using the formula:
%ΔP=−Modified Duration×ΔY+21×Convexity×(ΔY)2
Substituting the given values:
%ΔP=−6.9×0.0075+21×(−212)×(0.0075)2
%ΔP=−0.05175−0.0059625=−0.0577125
This results in a price decline of approximately 5.77%. The new bond price is:
99.4×(1−0.0577125)=93.6634
Rounded to 93.7, which matches option A.
Option B (94.3) is incorrect because it uses par value (100) instead of the given bond price (99.4).
Option C (94.9) is incorrect because it incorrectly treats convexity as a positive value, leading to an inaccurate price adjustment.