3. A financial institution issues a guaranteed investment contract for $10,000 to its customers, which has a 6-year maturity and a guaranteed interest rate of 5% per year. The institution wants to fund the obligation using two debt instruments, which include 4-year zero-coupon bonds selling at a yield-to-maturity (YTM) of 5%, and also 5% annual coupon-paying perpetuities selling at par. Answer the following questions with steps of calculation shown: (i) Describe 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) (ii) Next year, assume that YTM will remain at 5%. Describe the rebalancing strategy for the immunized portfolio.