Based on the pure expectations theory, is the following statement true or false?

The pure expectations theory assumes that a one$-$year bond purchased today will have the same return as a one$-$year bond purchased five years from now.

False

True

The yield on a one$-$year Treasury security is $5\mathrm{.}6100\%,$ and the two$-$year Treasury security has a $7\mathrm{.}5735\%$ 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.$)$

$12\mathrm{.}1583\%$

$9\mathrm{.}5735\%$

$8\mathrm{.}1375\%$

$10\mathrm{.}9138\%$

Recall that on a one$-$year Treasury security the yield is $5\mathrm{.}6100\%$ and $7\mathrm{.}5735\%$ 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.$)$

$8\mathrm{.}5572\%$

$9\mathrm{.}7552\%$

$7\mathrm{.}2736\%$

$10\mathrm{.}8676\%$

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.$)$

$5\mathrm{.}46\%$

$6\mathrm{.}45\%$

$7\mathrm{.}10\%$

$6\mathrm{.}69\%$