$7.$ An investor purchased a bond when it was originally issued with a maturity of five years. The bond pays semiannual coupons of $$50.$ It is now $150$ days into the life of the bond. The investor wants to sell the bond the day after its fourth coupon. The first coupon occurs $181$ days after issue, the second $365$ days, the third, $547$ days, and the fourth $730$ days. At this point $(150$ days into the life of the bond$),$ the price of the bond is $$1,010.$ Note that the bond$$s price includes accrued interest.

a$.$ At what price could the owner enter into a forward contract to sell the bond on the day after its fourth coupon? $($Note that the owner would receive the fourth coupon$).$ The continuously$-$compounded risk$-$free rate is $8\%.$

b$.$ Now move forward another $365$ days. The new risk$-$free rate is $7\%$ and the new price of the bond is $$1,025.$ Determine the value of the bond forward to the bond owner and to the counterparty at this time.