Suppose an Insurance Company 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 immunize this payment against any interest rate risk, the company 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 passes, and there is a mismatch in the duration between the payment and the bond portfolio. The Insurance Company needs to replace some of the coupon bonds with zero-coupon bonds to remain immunized. 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?

a. 14.38%

b. 0%

c. 9.36%

d. 19.72%

e. 7.19%