$1)$One$-$year Treasury securities yield $3\mathrm{.}15\%.$ The market anticipates that $1$ year from now, $1-$year Treasury securities will yield $3\mathrm{.}5\%.$ If the pure expectations theory is correct, what is the yield today for $2-$year Treasury securities$?$ Calculate the yield using a geometric average. Do not round intermediate calculations. Round your answer to two decimal places.

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$2)$Interest rates on $4-$year Treasury securities are currently $5\mathrm{.}6\%,$ while $6-$year Treasury securities yield $7\mathrm{.}75\%.$ If the pure expectations theory is correct, what does the market believe that $2-$year securities will be yielding $4$ years from now? Calculate the yield using a geometric average. Do not round intermediate calculations. Round your answer to two decimal places.

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$3)$Due to a recession, expected inflation this year is only $3\mathrm{.}75\%.$ However, the inflation rate in Year $2$ and thereafter is expected to be constant at some level above $3\mathrm{.}75\%.$ Assume that the expectations theory holds and the real risk$-$free rate $($r$*)$ is $2\mathrm{.}5\%.$ If the yield on $3-$year Treasury bonds equals the $1-$year yield plus $2\mathrm{.}0\%,$ what inflation rate is expected after Year $1?$ Round your answer to two decimal places.

$4)$Due to a recession, expected inflation this year is only $3\mathrm{.}75\%.$ However, the inflation rate in Year $2$ and thereafter is expected to be constant at some level above $3\mathrm{.}75\%.$ Assume that the expectations theory holds and the real risk$-$free rate $($r$*)$ is $2\mathrm{.}5\%.$ If the yield on $3-$year Treasury bonds equals the $1-$year yield plus $2\mathrm{.}0\%,$ what inflation rate is expected after Year $1?$ Round your answer to two decimal places.

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