You find a bond with $27$ years until maturity that has a coupon rate of $9\mathrm{.}0$ percent and a yield to maturity of $8\mathrm{.}1$ percent. Suppose the

yield to maturity on the bond increases by $0\mathrm{.}25$ percent.

a$.$ What is the new price of the bond using duration and using the bond pricing formula?

Note: Do not round intermediate calculations. Round your answers to $2$ decimal places.

b$.$ Now suppose the original yield to maturity is increased by $1$ percent. What is the new price of the bond?

Note: Do not round intermediate calculations. Round your answers to $2$ decimal places.