Suppose $1-$year Treasury bonds yield $4\mathrm{.}00\%$ while $2-$year T$-$bonds yield $5\mathrm{.}10\%.$ Assuming the pure expectations theory is correct, and thus the maturity risk premium for T$-$bonds is zero, what is the yield on a $1-$year T$-$bond expected to be one year from now?$$Round the intermediate calculations to $4$ decimal places and final answer to $2$ decimal places.

$$ a$.6\mathrm{.}21\%$

$$ b$.6\mathrm{.}40\%$

$$ c$.5\mathrm{.}03\%$

$$ d$.7\mathrm{.}52\%$

$$ e$.7\mathrm{.}27\%$