You are managing a portfolio of $$1\mathrm{.}0$ million. Your target duration is $12$ years, and you can choose from two bonds: a zero$-$coupon bond with maturity five years and a perpetuity, each currently yielding $5\%.$ Required: a$.$ How much of $($i$)$ the zero$-$coupon bond and $($ii$)$ the perpetuity will you hold in your portfolio?