Interest rates on $8-$ year Treasury securities are currently $2\mathrm{.}1\%,$while $10-$ year Treasury securities yield $2\mathrm{.}34\%.$If the pure expectations theory is correct, what does the market believe that $2-$ year Treasury securities will be yielding $8$years from now? $($Please explain all steps and list and explain all formulas$).$

$3\mathrm{.}12$Percent

$3\mathrm{.}30$ Percent

$3\mathrm{.}41$Percent

$2\mathrm{.}46$Percent

$2\mathrm{.}62$percent