A company has assumed liabilities of 1,000; 3,000 and 5,000 due in 4, 5 and6 years respectively. It can match the liabilities with 2 zero-coupon bonds: a 2-year and an 8 year The market interest rate is 10%

a. Find the amounts of each bond that the company should purchase to match the liabilities;

b. Demonstrate whether the conditions for Redington immunization are met by testing the effect of an increase in interest rate from 10% to 10.1%