a) Mark wants to invest the amount of 40,000 on a saving account and keep it for 8 years. He can choose among two possibilities. Bank A offers a nominal annual interest rate of 4.5%, with quarterly compounding, for the first 3 years, and then a nominal annual interest rate of 4%, with annual compounding, thereafter. Bank B offers a nominal annual interest rate of 3.5%, with quarterly compounding, for the first 5 years, and then a nominal interest rate of 4%, with annual compounding, thereafter. Suppose that banks A and B have the same probability of default. Which option should Mark choose? [10 marks] b) Calculate the present value of an investment offering 20,000 at the end of each year in perpetuity, assuming a relevant interest rate of 6%. [5 marks]