a. An insurance company must make payments to a customer of $10 million in 3 year and $4 million in 5 years. The interest rate is 10%. If it wants to fully fund and immunize its obligation to this customer with a single issue of a zero-coupon bond, what maturity bond must it purchase? What must be the face value and market value of that zero-coupon bond?

b. With the information in a) If the market interest rate increases by 0.3%, what is the impact on the market value of obligation for the insurance company?

c. You are managing a portfolio of $3 million. Your target duration is 10 years, and you can allocate your investment of $3 million in two bonds: a zero-coupon bond with maturity of 5 years and a perpetuity, each currently yielding 5%. How much will you invest in each bond this year? How much will you invest in each bond next year if target duration is 9 years then?