Question 1 (20 marks)

You are considering taking out an $800,000 30-year loan with equal monthly payments with a bank, which quotes annual rates on its deposits and loans of 1.2% and 3.6%, respectively.

(a) Without constructing a loan amortization schedule,

(i) calculate the amount of interest that will be paid in the first month of the 25th year into the loan. (5 marks)

(ii) calculate the total amount of interest that will be paid over the life of the loan. (3 marks)

(b) Interpret your answer for (a)(ii) and discuss the limitation(s), if any, of such an interpretation. (3 marks)

(c) Calculate the present value of the loan payments using a discount rate of 1.2%. (2 marks)

(d) Interpret your answer for (c) as well as the difference between that answer and the actual loan principal. What can explain this difference? (7 marks)