A $$1,000$ maturity value bond currently has $9$ years left to maturity. The

bond has a $6\%$ coupon rate and pays interest annually.

a$.$ If you want to earn a $7\%$ rate of return, how much would you be willing to pay today for this bond?

b$.$ Suppose you buy the bond for the value you calculated in part a$.$ After

holding the bond for $5$ years and receiving $5$ interest payments, you sell the bond for $$1,100.$ What annual, compound rate of return have you earned over this $5$ year period? $***$Prove your answer by showing that PV get equals PV give up$.***$

C$.$ Suppose you buy the bond for the value you calculated in part a$.$ After holding the bond for $4$ years and receiving $4$ interest payments, you sell the bond. What price must you receive $($at time $4)$ if you now want to receive an $8\%$ rate of return?

d$.$ Suppose you buy the bond for the value calculated in part a$.$ After holding the bond for $2$ years and receiving $2$ interest payments, the bond defaults with no chance of paying you anything more. What annual, compound rate of return have you earned over this $2$ year period?