Consider an insurance company that issues a guaranteed investment contract, called ABC, for $1,000. ABC has a four-year maturity and a guaranteed interest rate of 4%. The market interest rate is 4% for all maturities. Assume the payment is compounded annually and all rates are quoted with annual compounding.

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

b) Suppose that the insurance company funds this obligation with a two-year zero coupon bond and a six-year zero coupon bond using $1,000. Show how to use these two bonds to construct a portfolio with a duration of four years.

c) Following b), assume all market interest rates increase to 5% and stay unchanged for the next four years. The cashflows received within four years are reinvested at the market interest rates. Calculate the portfolio value in four years.

d) Following b), assume all market interest rates decrease to 3% and stay unchanged for the next four years. The cashflows received within four years are reinvested at the market interest rates. Calculate the portfolio value in four years. e) Explain why this portfolio could immunize the interest rate risk of ABC.