A portfolio of assets consists of the following as of January $1,1997$:

$1)$ an annuity$-$immediate with $20$ annual payments of $2,000$ each, with the first payment on December $31,2007$

$2)$ a $10,000$ zero$-$coupon bond maturing on December $31,2001$ at an annual effective interest rate of $8\%$

Calculate the modified duration of the portfolio as of January $1,1997.$

A$)10\mathrm{.}67$

B$)11\mathrm{.}11$

C$)11\mathrm{.}53$

D$)11\mathrm{.}98$

E$)12\mathrm{.}41$