Suppose that for calculation purpose we only have the three tables of values obtained above, calculate the following by making use of at least one of these three tables: (i) A loan of $700,000 is to be fully repaid by 25 level annual repayments made in arrears at an effective annual rate of 4% per annum. Calculate the amount of the level annual repayment. (2 marks) (j) A loan of $450,000 is to be fully repaid by level semi-annual repayments made in arrears for the next 8 years. The equivalent constant force of interest for this loan is 7.8441426% 2 per annum. Calculate the amount of the capital repayment between the 3rd and the 6th year. (5 marks) (k) Calculate the present value at time 0 of a 10-year continuous annuity with a payment rate of $300 per annum under an effective annual rate of 1.9804%. (4 marks) (1) Given an effective annual rate of 4%, calculate the present value at time 0 of a 20-year arithmetically increasing annuity immediate whereby the first annual payment is $6,000 and subsequent annual increment is $500. (3 marks) (m) Consider a 25-year annuity immediate with a payment amount of (26 t)2 at the end of year t. For instance, the payment amount at the end of year 6 is $400. Calculate its present value at time given an effective annual rate of 4%. (6 marks) Suppose that for calculation purpose we only have the three tables of values obtained above, calculate the following by making use of at least one of these three tables: (i) A loan of $700,000 is to be fully repaid by 25 level annual repayments made in arrears at an effective annual rate of 4% per annum. Calculate the amount of the level annual repayment. (2 marks) (j) A loan of $450,000 is to be fully repaid by level semi-annual repayments made in arrears for the next 8 years. The equivalent constant force of interest for this loan is 7.8441426% 2 per annum. Calculate the amount of the capital repayment between the 3rd and the 6th year. (5 marks) (k) Calculate the present value at time 0 of a 10-year continuous annuity with a payment rate of $300 per annum under an effective annual rate of 1.9804%. (4 marks) (1) Given an effective annual rate of 4%, calculate the present value at time 0 of a 20-year arithmetically increasing annuity immediate whereby the first annual payment is $6,000 and subsequent annual increment is $500. (3 marks) (m) Consider a 25-year annuity immediate with a payment amount of (26 t)2 at the end of year t. For instance, the payment amount at the end of year 6 is $400. Calculate its present value at time given an effective annual rate of 4%. (6 marks)
