$6.$ a$.$ XYZ Co Inc. issued a bond with $10$ years to maturity, It has an annual coupon interest rate of $$80.$ Similar bond have a YTM of $8\%.$ The face value of the bond is $$1000.$ How much will this bond be sold for? $(3$ marks$)$

a$.$ Assume the YTM has increased to $12\%,$ what will the bond be sold for? $(3$ marks$)$

b$.$ Assume the YTM has decreased to $6\%,$ what will the bond be sold for? $(3$ marks$)$

c$.$ Explain the movement with the price of the bond $(3$ marks$)$