$-$year, $$default$-$free bond with annual coupons of $4\%$ and a face value of $ $1000.$

a$.$ Without doing any$$ calculations, determine whether this bond is trading at a premium or at a discount. Explain.

b$.$ What is the yield to maturity on this$$ bond?

c$.$ If the yield to maturity on this bond increased to $4\mathrm{.}30\%,$ what would the new price$$ be$?$