Problem $11-11($Algo$)$

Required:

A pension plan is obligated to make disbursements of $$1\mathrm{.}8$ million, $$2\mathrm{.}8$ million, and $$1\mathrm{.}8$ million at the end of each of the next three years, respectively. The annual interest rate is $9\%.$ If the plan wants to fully fund and immunize its position, how much of its portfolio should it allocate to one$-$year zero$-$coupon bonds and perpetuities, respectively, if these are the only two assets funding the plan? $($Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$

What is the Investment in one$-$year zero$-$coupon bonds

What is the Investment in perpetuity