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).

a) (4 points) Find the current value of this perpetuity, its DV01, Duration, and Convexity. Round your answer to the nearest cent. By how much the value of your perpetuity will change if interest rates increase to y=5.1% (round your answer to the nearest dollar)?

b) (5 points) You have decided to hedge your perpetuity using 20-year zero-coupon bonds. How many bonds you should sell (remember that the bond's face value is $100). Round your answer to the nearest integer number of bonds.