Consider a bond with a coupon of $7\mathrm{.}8$ percent, eight years to maturity, and a current price of $$1,035\mathrm{.}30.$ 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.

Answer is complete but not entirely correct.

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.