Please show ALL work! Thank you!

1. End-of-Chapter Problem 19 in Chapter 11 (as follows) You are managing a portfolio of $1 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity five years, and a perpetuity, each currently yielding 5% a. (Immunization) How much of each bond will you hold in your portfolio (in percentage)? b. (Rebalance) How will these fractions change next year if target duration is now nine years