A $9\%($semi$-$annual$)$ coupon $20-$year option$-$free bond currently trades at a YTM of $6\%.$ Compute its approximate modified duration for a $10$ basis points $($bps$)$ change in interest rates.

Group of answer choices

duration $10\mathrm{.}0$

$10\mathrm{.}0<$ duration $11\mathrm{.}0$

$11\mathrm{.}0<$ duration $12\mathrm{.}0$

$12\mathrm{.}0<$ duration