Consider a life insurance company has a liability of a series of payments of 100,000 per annum in arrear for 20 years. Gov Bonds with annual coupons of 6% and 5 and 15 years to maturity can be purchased at par; Calculate the Present value, duration and convexity of this liability at 6% per annum effective and the mix of 5 and 15 year bonds required to match the duration of liabilities; Estimate the convexity of the liabilities and assets by calculating present values at 5.90% and 6.10% per annum. Comment on whether the conditions for immunisation were met or not with this asset mix and whether the sign of the change in npv of assets less liabilities corresponds.