East Empire Company must pay a liability of $100, 000 due in 4 years. The current interest rate is 6% effective per year. The company attempts to immunize itself from small changes in interests. It does so by constructing a portfolio consisting of:

(i) A 1-year $20, 000 par value zero coupon bond maturing at par

(ii) A 2-year zero coupon bond with the redemption value of X

(iii) A 6-year zero coupon bond with the redemption value of Y The amounts X and Y are chosen to satisfy the asset-liability matching (1st condition) and duration matching (2nd condition).

(a) Calculate X and Y.

(b) Show that the company's liability is Redington immunized by this portfolio at valuation rate of 6%.

(c) Prove that this portfolio fully immunizes the company's liability.