The yield to maturity on a $10-$year Treasury note $($with face value $=$$$100$ and annual coupon rate $=2\mathrm{.}625\%)$ is $3\mathrm{.}37\%.$ If the price of this Treasury note goes up$,$ its:

I. coupon rate drops below $2\mathrm{.}625\%.$

II$.$ coupon rate rises above $2\mathrm{.}625\%.$

III. yield to maturity drops below $3\mathrm{.}37\%.$

IV$.$ yield to maturity rises above $3\mathrm{.}37\%.$

A$.$ III.

B$.$ IV$.$

C$.$ I and III.

D$.$ II and IV$.$

E$.$ I.