You are managing a portfolio of $$1$ million. Your target duration is $10$ years, and you can invest in two bonds, a zero$-$coupon bond with

maturity of five years and a perpetuity, each currently yielding $5\%.$

a$.$ What weight of each bond will you hold to immunize your portfolio? $($Round your answers to $2$ decimal places.$)$

b$.$ How will these weights change next year if target duration is now nine years? $($Round your answers to $2$ decimal places.$)$