The yield on a one$-$year Treasury security is $5\mathrm{.}1500\%,$ and the two$-$year Treasury security has a $6\mathrm{.}1800\%$ 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.$)$

$6\mathrm{.}1371\%$

$7\mathrm{.}2201\%$

$8\mathrm{.}2309\%$

$9\mathrm{.}1695\%$

Recall that on a one$-$year Treasury security the yield is $5\mathrm{.}1500\%$ and $6\mathrm{.}1800\%$ 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.$)$

$5\mathrm{.}794\%$

$8\mathrm{.}657\%$

$7\mathrm{.}7708\%$

$6\mathrm{.}8165\%$

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.$)$

$6\mathrm{.}45\%$

$7\mathrm{.}10\%$

$6\mathrm{.}69\%$

$6\mathrm{.}61\%$