From discussions with your broker, you have determined that the expected inflation premium is $1\mathrm{.}35$ percent next year, $1\mathrm{.}50$ percent in year $2,1\mathrm{.}75$ percent in year $3,$ and $2\mathrm{.}00$ percent in year $4$ and beyond. Further, you expect that real risk$-$free rates will be $3\mathrm{.}20$ percent next year, $3\mathrm{.}30$ percent in year $2,3\mathrm{.}75$ percent in year $3,$ and $3\mathrm{.}80$ percent in year $4$ and beyond. You are considering an investment in either $5-$year Treasury securities or $5-$year bonds issued by PeeWee Corporation. The bonds have no special covenants. Your broker has determined the following information about economic activity and PeeWee Corporation $5-$year bonds:

Default risk premium $=2\mathrm{.}10\%$

Liquidity risk premium $=1\mathrm{.}75\%$

Maturity risk premium $=0\mathrm{.}75\%$

Further, the maturity risk premium on PeeWee bonds is $0\mathrm{.}1875$ percent per year starting in year $2.$ PeeWee$$s default risk premium and liquidity risk premium do not change with bond maturity.

a$.$ What is the fair interest rate on $5-$year Treasury securities$?$

b$.$ What is the fair interest rate on PeeWee Corporation $5-$year bonds?

c$.$ Plot the $5-$year yield curve for the Treasury securities$.$

d$.$ Plot the $5-$year yield curve for the PeeWee Corporation bonds.

Please provide step by step on how the answers were done.