Problem 3 (Required, 25 marks) We consider the on-year annuity-immediate which pays some amount at the end of every year. The first payment is made one year after today. It is given that the amount of each payment is X during the first 2n years, 2X during next 2n years and 3X thereafter. The present value of this annuity-immediate is A. The payments of this annuity are shared by 3 people (Mr. A, Mr. B and Mr. C). Mr. A gets the first 2n payments, Mr. B gets the next n payments and Mr. C gets the remaining payments. You are given that The total present value (at current time) of payments received by Mr. B and Mr. C is 0.789A. The present value of payments received by Mr. C is cA. Question Find the value of c. Problem 3 (Required, 25 marks) We consider the on-year annuity-immediate which pays some amount at the end of every year. The first payment is made one year after today. It is given that the amount of each payment is X during the first 2n years, 2X during next 2n years and 3X thereafter. The present value of this annuity-immediate is A. The payments of this annuity are shared by 3 people (Mr. A, Mr. B and Mr. C). Mr. A gets the first 2n payments, Mr. B gets the next n payments and Mr. C gets the remaining payments. You are given that The total present value (at current time) of payments received by Mr. B and Mr. C is 0.789A. The present value of payments received by Mr. C is cA. Question Find the value of c