Suppose that the spot rate curve (continuously compounded) is 1% for t less than or equal to 6 years, and the forward rate f_6,tis 8% (continuously compounded) for t > 6 years. Suppose you have an obligation to pay $1,000,000 per year in perpetuity starting 14 years from now. Suppose further that you may invest in a LIBOR floating rate bond (on issue date, with first coupon rate still unfixed) and also in a 50 year zero coupon bond.

After calculating the spot rate curve to t > 6 years, the price of the zero coupon bond, the durations of the zero coupon bond and the floating rate bond, the present value of the obligation, and the Fisher-Weil duration of the obligation, finally calculate the face values of the floating rate bond and the zero coupon bond necessary to immunize your obligation.

What face value must you purchase of the zero coupon bond? (nearest $1)

Hint: For the obligation, Dfw = -d/dlambda[ln(P(lambda))] evaluated at lambda=0