A $21-$year U$.$S$.$ Treasury bond with a face value of $$1,000$ pays a coupon of $5\mathrm{.}75\%(2\mathrm{.}875\%$ of face value every six months$).$ The reported

yield to maturity is $5\mathrm{.}4\%($a six$-$month discount rate of $\frac{5\mathrm{.}4}{2}=2\mathrm{.}7\%).$

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

b$.$ If the yield to maturity changes to $1\%,$ what will be the present value?

c$.$ If the yield to maturity changes to $8\%,$ what will be the present value?

d$.$ If the yield to maturity changes to $15\%,$ what will be the present value?

$($For all requirements, do not round Intermediate calculations. Round your answers to $2$ decimal places.$)$