Suppose an Insurer has to make a guaranteed payment $1,000 to a policyholder in a few years (I am not telling you how many years). In order to immunize against any interest rate risk, the insurer used 8% coupon bond with 6 year maturity when the yield is also 8%. The bond successfully immunizes against the interest rate risk on the payment for now. A year later, if there is a mismatch in the duration, the bank needs to replace some of the coupon bonds with zero-coupon bonds. Suppose there are zero coupon bonds available for which the payment is due in 1 year, what fraction of the old portfolio of coupon bonds need to be replaced with zero coupon bonds for full immunization?