Problem $5.$ A six$-$month zero$-$coupon bond with face value $$1,00$ sells for $$99\mathrm{.}46,$ a one$-$year zero$-$coupon bond sells for $$97\mathrm{.}23,$ and an $18-$month zerocoupon bond sells for $$90\mathrm{.}50.$ Suppose a new coupon bond, making semiannual coupon payments, is issued today with face value $$100,$ maturity of $18$ months, and a semi$-$annual coupon payment of $9\%($the $9\%$ is expressed as an annual rate$).$

Calculate the no$-$arbitrage price of the coupon bond today.

Calculate the implied forward rates in this economy.

If the liquidity preference theory is correct and there exists a liquidity premium of $0\mathrm{.}5\%$ per period, what is the market's expectation of the price the bond will sell for in one year? $1$ year $=2$ periods here.