A $10-$year U$.$S$.$ Treasury bond with a face value of $$1,000$ pays a coupon of $5\mathrm{.}5\%(2\mathrm{.}75\%$ of face value every six months$).$ The reported yield to maturity is $5\mathrm{.}2\%($a six$-$month discount rate of $5\mathrm{.}2/2=2\mathrm{.}6\%).$

a$.$ What is the present value of the bond?

b$.$ Generate a graph or table showing how the bond$$s present value changes for semiannually compounded interest rates between $1\%$ and $15\%.$