Bond Valuation and Changes in Maturity and Required Returns

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.

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? Round your answer to the nearest cent.

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Suppose that $2$ years after the initial offering, the going interest rate had risen to $15\%.$ At what price would the bonds sell? Round your answer to the nearest cent.

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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?

I. The price of the bond will remain the same.

II$.$ The price of the bond will rise, approaching $$1,000$ at the maturity date.

III. The price of the bond will decline, approaching $$1,000$ at the maturity date.

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