Suppose Hillard Manufacturing sold an issue of bonds with a 10-year maturity, a $1,000 par value, a 10% coupon rate, and semiannual interest payments.

a. Two years after the bonds were issued, the going rate of interest on bonds such as these fell to 6%. At what price would the bonds sell?

b. Suppose that 2 years after the initial offering, the going interest rate had risen to 12%. At what price would the bonds sell?

c. Suppose that 2 years after the issue date (as in Part a) interest rates fell to 6%. Suppose further that the interest rate remained at 6% for the next 8 years. What would happen to the price of the bonds over time

Please show all work including formulas. I do not not need calculator inputs nor excel functions. Excel formuls are fine too.