A risk $-$ free, zero $-$ coupon bond with a face value of $$5,000$ has $20$ years to maturity. If the YTM is $4\mathrm{.}5\%,$ which of the following would be closest to the price this bond will trade at$?$

A$.$ $$2,902$

B$.$ $$3,317$

C$.$ $$2,488$

D$.$ $$2,073$