The yield on a one$-$year Treasury security is $5\mathrm{.}3800\%,$ and the two$-$year Treasury security has a $7\mathrm{.}2630\%$ 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.$)$

$9\mathrm{.}1796\%$

$10\mathrm{.}4647\%$

$11\mathrm{.}6581\%$

$7\mathrm{.}8027\%$

Recall that on a one$-$year Treasury security the yield is $5\mathrm{.}3800\%$ and $7\mathrm{.}2630\%$ 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 $0\mathrm{.}4\%.$ What is the market$$s estimate of the one$-$year Treasury rate one year from now? $($Note: Do not round your intermediate calculations.$)$

$8\mathrm{.}3669\%$

$9\mathrm{.}5383\%$

$10\mathrm{.}626\%$

$7\mathrm{.}1119\%$

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.$)$

$7\mathrm{.}10\%$

$6\mathrm{.}61\%$

$6\mathrm{.}69\%$

$6\mathrm{.}45\%$