Suppose that Ally Financial Inc. issued a bond with $10$ years until maturity, a face value of $$1000,$and a coupon rate of $6\%($annual payments$).$ The yield to maturity on this bond when it was issued was $10\%.$

a$.$ What was the price of this bond when it was issued?

b$.$ Assuming the yield to maturity remains constant, what is the price of the bond immediately before it makes its first coupon payment?

c$.$ Assuming the yield to maturity remains constant, what is the price of the bond immediately after it makes its first coupon payment?