In the capital markets, we use duration as an approximate measure of a bond's price sensitivity to changes in interest rates. For simplicity, in this question, we define duration as the percentage change of the bond price if the market interest rate increases by $1\%.$ Now please calculate the duration $($the change in the bond's price if the YTM increases by $1\%)$ of a bond which has a $9\%$ coupon paid annually, maturing in $20$ years. The bond's current YTM is $10\%.$

the answer is $-8\mathrm{.}10\%$

the answer is $9\mathrm{.}31\%$

the answer is $-8\mathrm{.}19\%$

the answer is $-8\mathrm{.}82\%$