You own a bond that pays $$$$100$ in annual$$ interest, with a $$$$1$ comma $000$ par value. It matures in $20$ years. The$$ market's required yield to maturity on a$$ comparable$-$risk bond is $12$ percent.

a$.$Calculate the value of the bond.

b$.$How does the value change if the yield to maturity on a$$ comparable$-$risk bond$($i$)$ increases to $16$ percent or$($ii$)$ decreases to $7$percent$?$

c$.$Explain the implications of your answers in part b as they relate to$$ interest$-$rate risk, premium$$ bonds, and discount bonds.

d$.$Assume that the bond matures in $5$ years instead of $20$ years and recalculate your answers in parts a and b$.$

e$.$Explain the implications of your answers in part d as they relate to$$ interest$-$rate risk, premium$$ bonds, and discount bonds.