Question 2: 25 marks a) A client planning for retirement has two options of saving: ? A 20 year annuity at N$50 000 per year starting after one year or ? A lump sum of N$500 000 today. If the clients required rate of return on retirement fund investment is 6% per year, which plan has the higher present value and by how much? (5 marks) b) Suppose you are the eldest in your family and after this degree you will get a very nice paying job that allows you to send your brother to university in three years. You expect he will get a scholarship that will pay two thirds of the tuition fees so you estimate that your one third will be N$10 000 a year for four years. To estimate whether you have set aside enough money, you ignore possible inflation in tuition payments and assume that you earn 8 % annually on your investments. How much should you set aside now to cover these payments? (10 marks) c) A client is confused about two terms on some certificate of deposit rates quoted at his bank in Namibia. You explain that the stated annual interest rate is an annual rate that does not take into account compounding within a year. The rate his bank calls annual percentage yield (APY) is the effective annual interest rate taking into account compounding. The banks customer service representative mentioned monthly compounding, with a N$1 000 becoming N$1 061.68 at the end of a year. To prepare to explain the terms to your client, calculate the stated annual interest rate that the bank must be quoting. (5 marks) d) A perpetual preference share pays quarterly dividends of N$1 000 indefinitely, (forever). If an investor has a required rate of return of 12% per year compounded quarterly on this type of investment, how much should he/she be willing to pay for this dividend stream? (5 marks)