$1.$ Bond valuation: A tax$-$exempt bond was recently issued at an annual $7$ percent coupon rate and matures $20$ years from today. The par value of the bond is $$5,000.$

a$.$ If required market rates are $7$ percent, what is the market price of the bond?

b$.$ If required market rates fall to $3$ percent and maturity is $20$ years, what is the market price of the bond?

c$.$ If required market rates rise to $14$ percent and maturity is $20$ years, what is the market price of the bond?

d$.$ At what required market rate $(7$ percent, $3$ percent, or $14$ percent$)$ does the above bond sell at a discount? At a premium?