Suppose that Ally Financial Inc. issued a bond with $10$ years until$$ maturity, a face value of $$$$1,000,$ and a coupon rate of $12\%($annual payments$).$ The yield to maturity on this bond when it was issued was $8\%.$

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?