You have just purchased $$1,000,000$ in face value of the February $15,20493\mathrm{.}00\%$ Treasury bond at an agreed upon price of $116\mathrm{.}086$ to settle on October $22,2019.$ The bond pays interest twice a year on February $15$ and August $15.$ What is the effective convexity of the bond?

A$)20\mathrm{.}15$

B$)20\mathrm{.}38$

C$)517\mathrm{.}24$

D$)29\mathrm{.}32$

CORRECT ANSWER$=517\mathrm{.}24$ BUT HOW?