$($Bond valuation$)$ You are examining three bonds with a par value of $$1,000($you receive $$1,000$ at maturity$)$ and are concerned with what would happen to their market value if interest rates $($or the

market discount rate$)$ changed. The three bonds are

Bond A$-$a bond with $5$ years left to maturity that has an annual coupon interest rate of $9$ percent, but the interest is paid semiannually.

Bond B$-$a bond with $9$ years left to maturity that has an annual coupon interest rate of $9$ percent, but the interest is paid semiannually.

Bond $C-$a bond with $18$ years left to maturity that has an annual coupon interest rate of $9$ percent, but the interest is paid semiannually.

What would be the value of these bonds if the market discount rate were

a$.9$ percent per year compounded semiannually?

b$.4$ percent per year compounded semiannually?

c$.15$ percent per year compounded semiannually?

d$.$ What observations can you make about these results?