Please answer and show steps, thank you.

Problem 3 (14 points): Assume the term structure of forward rates is flat and they are equal to 5%. The factor y is the forward rate (such one-factor model is called "parallel yield shift" model and in class we called the duration D in this special case by Dmod, i.e., D=Dmod). Assume you own a perpetuity with $1M annual payments paid semi-annually (i.e., it pays $500,000 every six months).

d) (2 points) If, in addition to the 20-year zero-coupon bonds, you would be able to use 5-year zero-coupon bonds, would you be able to construct a better hedge? Explain why (no calculations are necessary).