4. An insurance company has a saving plan on which the customers deposit $10,000 into the insurance company, which has a 7-year maturity with a fixed market interest rate of 6% per year and get back the money when the plan matures. The insurance company buys two debt instruments for the repayment of the future obligation, which include 5-year zero-coupon bonds selling at a yield-to-maturity (YTM) of 6%, and also 6% annual coupon-paying perpetuities selling at par. (a) Construct an immunized portfolio for the first year such that the duration of asset portfolio is equal to the duration of the single-payment liability. (5 marks)

(b) Assume that YTM will remain at 6%. Use a rebalancing strategy for immunization next year.