Recall that on a one$-$year Treasury security the yield is $5\mathrm{.}3800\%$ and $6\mathrm{.}4560\%$ 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 $0\mathrm{.}5\%.$ What is the market's estimate of the one$-$year Treasury rate one year from now? $($Note: Do not round your intermediate calculations.$)$

$6\mathrm{.}5351\%$

$8\mathrm{.}2996\%$

$7\mathrm{.}45\%$

$5\mathrm{.}5548\%$

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.$)$

$6\mathrm{.}61\%$

$5\mathrm{.}46\%$

$6\mathrm{.}45\%$

$7\mathrm{.}10\%$