Consider a $10-$year $8\%($Semi$-$annually paid$)$ bond that is traded at $7\%.$ Approximate its duration and convexity when we expect yield to change by $50$ bps$.$ Assume a FV of $100.$

Group of answer choices

Approximate Duration$=48,9374$ and Approximate Convexity $=8\mathrm{.}7653$

Approximate Duration$=56\mathrm{.}0172$ and Approximate Convexity $=6\mathrm{.}9368$

Approximate Duration$=8\mathrm{.}7653$ and Approximate Convexity $=48,9374$

Approximate Duration$=6\mathrm{.}9368$ and Approximate Convexity $=56\mathrm{.}0172$