An institution has the following liabilities due in the upcoming 12 years. . A lump sum payment of $15,000 due in 7 years' time Another $12,000 due in 12 years' time . The institution wishes to utilise immunisation techniques to protect their surpluses from small changes in interest rates. The current level of interest rate is 6% p.a. effective. The institution has the option to invest in the combination of the following 2 bonds: . A 12-year zero coupon bond redeemable at par A 5-year 8% coupon paying bond which pays annual coupons which is redeemed at par. a. Find the face-value of the two bonds such that the first two conditions of immunisation are met. b. Evaluate the convexity of assets and liabilities and hence comment on whether the portfolio of assets and liabilities are immunised. c. Approximate the change in surplus for a 1% increase in the effective annual rate of interest. An institution has the following liabilities due in the upcoming 12 years. . A lump sum payment of $15,000 due in 7 years' time Another $12,000 due in 12 years' time . The institution wishes to utilise immunisation techniques to protect their surpluses from small changes in interest rates. The current level of interest rate is 6% p.a. effective. The institution has the option to invest in the combination of the following 2 bonds: . A 12-year zero coupon bond redeemable at par A 5-year 8% coupon paying bond which pays annual coupons which is redeemed at par. a. Find the face-value of the two bonds such that the first two conditions of immunisation are met. b. Evaluate the convexity of assets and liabilities and hence comment on whether the portfolio of assets and liabilities are immunised. c. Approximate the change in surplus for a 1% increase in the effective annual rate of interest