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{.}1$ million per year. The interest rate is $10\%.$ 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.$)$

$\backslash$table$[[,$Market Value$],[$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.$)$

$\backslash$table$[[,$Face Value$],[$Five$-$year,,million$],[$Twenty$-$year,,million$]]$