$($Bond valuation relationships$)$ A bond of Telink Corporation pays $$120$ in annual interest, with a $$1,000$ par value. The bonds mature in $20$ years. The market's required yield to maturity on a comparable$-$risk bond is $10$ 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$.$ Interpret your findings in parts a and $b.$

a$.$ What is the value of the bond if the market's required yield to maturity on a comparable$-$risk bond is $10$ percent? $($Round to the nearest $5$ sent.$)$

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.$)$