Consider a bond with a coupon of $4\mathrm{.}6$ percent, five years to maturity, and a current price of $$1,047\mathrm{.}80.$ Suppose the yield on the bond

suddenly increases by $2$ percent.

a$.$ Use duration to estimate the new price of the bond.

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

Price

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

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

Price