You are managing a portfolio of $$1\mathrm{.}0$ million. Your target duration is $16$ 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? $($Do not round intermediate

calculations. Round your answers to $2$ decimal places.$)$

Answer is complete and correct.

b$.$ How will these fractions change next year if target duration is now fifteen years? $($Do not round intermediate calculations. Round

your answers to $2$ decimal places.$)$

Answer is complete but not entirely correct.