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 a maturity of five years and a perpetuity, each currently yielding $5\%.$ The duration of the perpetuity is $21$ years. Answer in decimal form to $4$ decimal places.

How much of the zero coupon bond will you hold in your portfolio?

How much of the perpetuity will you hold in your portfolio?

What will the weight of the zero coupon bond be next year if the target duration is now nine years?

What will the weight of the perpetuity be next year if the target duration is now nine years?