The yield on a one$-$year Treasury security is $4\mathrm{.}9200\%,$ and the two$-$year Treasury security has a $7\mathrm{.}3800\%$ yield. Assuming that the pure expectations theory is correct, what is the market's estimate of the one$-$year Treasury rate one year from now? $($Note: Do not round your intermediate calculations.$)$

$9\mathrm{.}8976\%$

$12\mathrm{.}57\%$

$8\mathrm{.}413\%$

$11\mathrm{.}2833\%$

Recall that on a one$-$year Treasury security the yield is $4\mathrm{.}9200\%$ and $7\mathrm{.}3800\%$ on a two$-$year Treasury security. Suppose the one$-$year security does not have a maturity risk premium, but the two$-$year security does and it is $0\mathrm{.}2\%.$ What is the market's estimate of the one$-$year Treasury rate one year from now? $($Note: Do not round your intermediate calculations.$)$

$8\mathrm{.}0654\%$

$9\mathrm{.}4887\%$

$12\mathrm{.}0506\%$

$10\mathrm{.}8171\%$

Suppose the yield on a two$-$year Treasury security is $5\mathrm{.}83\%,$ and the yield on a five$-$year Treasury security is $6\mathrm{.}20\%.$ Assuming that the pure expectations theory is correct, what is the market's estimate of the three$-$year Treasury rate two years from now? $($Note: Do not round your intermediate calculations.$)$

$6\mathrm{.}53\%$

$7\mathrm{.}10\%$

$6\mathrm{.}45\%$

$6\mathrm{.}69\%$