$$ 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 $$2\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?

Note: Do not round intermediate calculations. Enter your answers in

millions. Round your answers to $1$ decimal place.

b$.$ What must be the face value of each of the two zeros to fund the plan?

Note: Do not round intermediate calculations. Enter your answers in

millions rounded to $2$ decimal places.