A thirty-year treasury bond has a coupon of 6%, and the current market discount rate for it is 5%. The dollar duration (i.e. dp/dr) is 17,214.8. (Remember that by convention the negative sign on dp/dr is omitted.) The bond has exactly thirty years until maturity and the face amount is $1,000,000.
a. What is the price of this bond?
b. What is the Modified Duration of this bond?
c. What is the Macaulay duration of this bond?
d. If the market discount rate for this bond changed from 5% to 5.5%, based on the various durations above, what you estimate the price change of the bond would be? How much is it if you actually change the discount rate and then re-price it?