Your corporation has a $3,000,000 liability due in precisely 4.381896 years  (Yes, you may assume that is the Macaulay Duration). You have decided to dedicate an investment in one bond to satisfy the  liability; characteristics of bond: Precisely 5 years until maturity, Coupon  rate = 6%, paid semi-annually, current bond price = 97.000, coupon  payments reinvested at YTM. a significant change in market interest rates will occur precisely 18 months  after you purchase the bond; interest rates will decrease by 150 bps  (annually). 
Prove that your liability is very close to being immunized against one change  in interest rates?