Arizona Public Utilities issued a bond that pays $$$$60$ in$$ interest, with a $$$$1,000$ par value. It matures in $25$ years. The$$ market's required yield to maturity on a$$ comparable$-$risk bond is $8$ percent.

a$.$Calculate the value of the bond at $8$ percent

b$.$How does the value change if the$$ market's required yield to maturity on a$$ comparable$-$risk bond$($i$)$ increases to $12$ 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 $15$ years instead of $25$ years. Recompute 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.