Consider an insurance company that issues a guaranteed investment contract, called ABC, for $100,000. ABC has a five-year maturity and a guaranteed interest rate of 5%. The market interest rate is 5% for all maturities. Assume the payment is compounded annually.

a) Calculate the amount the insurance company promises to pay in five years.

b) Suppose that the insurance company funds this obligation with a two-year zero coupon bond and a seven-year zero coupon bond using $100,000. Show how to use these two bonds to construct a portfolio with a duration of five years.

c) Following b), assume all market interest rates increase to 6% and stay unchanged for the next five years. Calculate the portfolio value in five years.

d) Following b), assume all market interest rates decrease to 4% and stay unchanged for the next five years. Calculate the portfolio value in five years.

e) Explain why this portfolio could immunize the interest rate risk of ABC.