Assume that the Pure Expectations Theory of the term structure is correct. Also assume that the interest rate today on a $9-$year security is $6\mathrm{.}40\%,$ while the interest rate today on a $15-$year security is $8\mathrm{.}00\%.$ Finally assume that the interest rate on a $3-$year security to be bought at Year $9$ and held over Years $10,11,$ and $12$ is $6\mathrm{.}80\%.$ Given this information, determine the average annual return that investors today must expect that they will receive from investing in a $3-$year security in $12$ Years $($that is$,$ buying the security at Year $12$ and holding it over Years $13,14,$ and $15).$

$13\mathrm{.}00\%$

$12\mathrm{.}50\%$

$13\mathrm{.}50\%$

$12\mathrm{.}00\%$

$14\mathrm{.}00\%$