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 $5\mathrm{.}22=2\mathrm{.}6\%).$

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

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

b$-2.$ If the yield to maturity changes to $8\%,$ what will be the present value?

b$-3.$ If the yield to maturity changes to $15\%,$ what will be the present value?

Note: For all requirements, do not round intermediate calculations. Round your answers to $2$ decimal places.

$\backslash$table$[[$a$.$ Present value,$],[$b$-1.$ Present value,$],[$b$-2.$ Present value,$],[$b$-3.$ Present value,$]]$