Consider the attached spreadsheet with U$.$S$.$ Treasury zero$-$coupon bond prices. The face values are equal to $$1,000.$

a$.$ What is the annual four$-$year risk$-$free spot rate?

b$.$ What is the current fair price of a U$.$S$.$ Treasury coupon bond with face value $$1,000,4$ years to maturity, annual coupon rate of $4\%,$ and paying semi$-$annual coupons?

c$.$ What is the current fair yield$-$to$-$maturity of the coupon bond in the previous question $($U$.$S$.$ Treasury coupon bond with face value $$1,000,4$ years to maturity, annual coupon rate of $4\%,$ and paying semi$-$annual coupons$)?$

d$.$ Consider a bond like that of two questions ago $($U$.$S$.$ Treasury coupon bond with face value $$1,000,4$ years to maturity, annual coupon rate of $4\%,$ and paying semi$-$annual coupons$).$ Assume you are a bond dealer facing negligible transaction costs. What would you do if the market price of the bond was equal to $$980?$