Consider a bond with 3 years to maturity and a coupon rate of 5%. The term structure is flat and the bond's yield to maturity is 3%. Assume the bond's face value is $1,000 and that it pays annual coupons.

a. Use modified duration to estimate the dollar change in bond value if yields increase by 1%.

b. If you wanted to immunize this bond's interest rate risk with 5-year zero coupon bonds, what dollar weight in zeroes would you need to short?

c. Suppose at the end of the first year that interest rates increase to 4%, calculate the price of the bond at the end of the first year.