Note: Please professor don't use ChatGpt or any kind of AI tool for the answer and also don't use internet sources. Requesting you to please answer in your own way.

Managing a Pension Fund Analysis - CLO 3, CLO 4

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 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.

1. What is Zero Coupon Bond and which bond have no coupon payments?
2. How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position?
3. What must be the face value of each of the two zeros to fund the plan?

Explain your work in detail with examples.