The yield on a $2-$year security is $7\mathrm{.}8\%.$ If the yield of a security maturing in $1$ year is $7\mathrm{.}2\%,$ what is the expected yield on a $1-$year security maturing at the end of year $2?$

Multiple Choice

$7\mathrm{.}2\%$

$8\mathrm{.}4\%$

$8\mathrm{.}8\%$

$9\mathrm{.}6\%$