Problem $11-22($Algo$)$

You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are going to closely resemble level perpetuities of $$1\mathrm{.}6$ million per year. The interest rate is $8\%.$ You plan to fully fund the obligation using $5-$year and $20-$year maturity zero$-$coupon bonds.

Required:

a$.$ How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position? $($Do not round intermediate calculations. Enter your answers in millions. Round your answers to $1$ decimal place.$)$

Five$-$year:$\_\_\_\_\_\_\_\_\_$million Twenty$-$year:$\_\_\_\_\_\_\_\_\_\_$million

b$.$ What must be the face value of each of the two zeros to fund the plan? $($Do not round intermediate calculations. Enter your answers in millions rounded to $2$ decimal places.$)$ Five$-$year:$\_\_\_\_\_$million Twenty$-$year:$\_\_\_\_\_\_\_\_\_\_\_$million