Problem 1 (Required, 25 marks) (a) (10 marks) We consider a 5-year annuity-immediate that pays $250 + 20k at the end of kth month for k = 1,2,3,...,60. Suppose that the money grows at an annual effective interest rate of 6.55% and compound interest is assumed, Question: Find the present value of this annuity. (b) (15 marks) Peter owns a 5-year bond at time 0 and the bond pays a series of payments as follows: The bond pays $50 (known as coupon) at the end of every 6 months for 5 years. The next payment is made 6 months after today. In addition, the bond pays a final payment of $2000 (known as redemption value) at the end of 5th year. Suppose that Peter deposits the payment received immediately to an investment fund which earns interest at an annual nominal interest rate of 8% convertible continuously. Question: Find the amount value of the investment fund at the end of 10th year. Problem 1 (Required, 25 marks) (a) (10 marks) We consider a 5-year annuity-immediate that pays $250 + 20k at the end of kth month for k = 1,2,3,...,60. Suppose that the money grows at an annual effective interest rate of 6.55% and compound interest is assumed, Question: Find the present value of this annuity. (b) (15 marks) Peter owns a 5-year bond at time 0 and the bond pays a series of payments as follows: The bond pays $50 (known as coupon) at the end of every 6 months for 5 years. The next payment is made 6 months after today. In addition, the bond pays a final payment of $2000 (known as redemption value) at the end of 5th year. Suppose that Peter deposits the payment received immediately to an investment fund which earns interest at an annual nominal interest rate of 8% convertible continuously. Question: Find the amount value of the investment fund at the end of 10th year