$($Bond valuation relationships$)$ Arizona Public Utilities issued a bond that pays $$80$ in interest, with a $$1,000$ par value. It matures in $30$ years. The market's required yield to maturity on a comparable$-$risk bond is $6$ percent.

a$.$ Calculate the value of the bond.

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 $5$ 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 $30$ 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.

a$.$ What is the value of the bond if the market's required yield to maturity on a comparable$-$risk bond is $6$ percent?

$$1275\mathrm{.}30($Round to the nearest cent.$)$

b$.($i$)$ What is the value of the bond if the market's required yield to maturity on a comparable$-$risk bond increases to $12$ percent?

$ $($Round to the nearest cent.$)$