Consider an insurance company that issues a guaranteed investment contract, called XYZ, for $10,000.XYZ 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)Suppose that the insurance company funds this obligation with a two-year zero coupon bond and a seven-year zero coupon bond using $10,000. Show how to use these two bonds to construct a portfolio with a duration of five years.

b) Following a), assume all market interest rates increase to 6% and stay unchanged for the next five years.The payment received in two years will be reinvestedat the new market interest rate.Calculate the portfolio value in five years.