The yield to maturity on $1-$year zero$-$coupon bonds is currently $7\%$; the YTM on $2-$year zeros is $8\%.$ The Treasury plans to issue a $2-$year maturity coupon bond, paying coupons once per year with a coupon rate of $10\%.$ The face value of the bond is $$100.$

a$.$ At what price will the bond sell? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

b$.$ What will the yield to maturity on the bond be$?($Do not round intermediate calculations. Round your answer to $3$ decimal places.$)$

c$.$ If the expectations theory of the yield curve is correct, what is the market expectation of the price that the bond will sell for next year? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

d$.$ Recalculate your answer to part $($c$)$ if you believe in the liquidity preference theory and you believe that the liquidity premium is $2\%.$

$($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

$\backslash$table$[[,,],[$a$.,$Price,,$],[$b$.,$Yield to maturity,,$],[$c$.,$Price,,$\%$