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.$)$

$6\mathrm{.}53\%$

$5\mathrm{.}46\%$

$6\mathrm{.}45\%$

$6\mathrm{.}61\%$