A $13-$year U$.$S$.$ Treasury bond with a face value of $$1,000$ pays a coupon of $5\mathrm{.}25\%(2\mathrm{.}625\%$ of face value every six months$).$ The reported yield to maturity is $5\mathrm{.}0\%($a six$-$month discount rate of $5\mathrm{.}02=2\mathrm{.}5\%).$