Suppose that a $1-$year zero$-$coupon bond with face value $$100$ currently sells at $$90\mathrm{.}44,$ while a $2-$year zero sells at $$81\mathrm{.}59.$ You are considering the purchase of a $2-$year$-$maturity bond making annual coupon payments. The face value of the bond is $$100,$ and the coupon rate is $9\%$ per year.

Required:

a$.$ What is the yield to maturity of the $2-$year zero?

b$.$ What is the yield to maturity of the $2-$year coupon bond?

c$.$ What is the forward rate for the second year?

d$.$ If the expectations hypothesis is accepted, what are $(1)$ the expected price of the coupon bond at the end of the first year and $(2)$ the expected holding$-$period return on the coupon bond over the first year?

e$.$ Will the expected rate of return be higher or lower if you accept the liquidity preference hypothesis?