Consider a bond with a coupon of 4.6 percent, five years to maturity, and a current price of $1,046.10. Suppose the yield on the bond suddenly increases by 2 percent.

a. Use duration to estimate the new price of the bond. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. Calculate the new bond price using the usual bond pricing formula. (Do not round intermediate calculations. Round your answer to 2 decimal places.)