Consider a bond with a coupon of $5\mathrm{.}2$ percent, eight years to maturity, and a current price of $$1,055\mathrm{.}30.$ Suppose the yield on the bond suddenly increases by $2$ percent.

Use duration to estimate the new price of the bond.

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

Calculate the new bond price using the usual bond pricing formula.

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