You are managing a portfolio of $$1$ million. Your target dur$$tion 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 $5\mathrm{.}6\%.$

Required:

a$.$ What weight of each bond will you hold to immunize your portfolio?

b$.$ How will these weights change next year if target duration is now nine years?