Bond Valuation and Changes in Maturity and Required Returns

Suppose Hillard Manufactoring 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?

The answer is $1,251.22--show all work/formula

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

The answer is $898.94. Show all work/formula.

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.

Provide a summary-logical answer.