$"$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$-1.$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?