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...

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. How much of (i) the zero-coupon bond and (ii) the perpetuity will you hold in your portfolio?
b. How will these fractions change next year if target duration is now nine years?