Question 4 (This question has three parts (a), (b) and (c))

(a) Ms Alice Basset is 65 years of age, and she expects that she will live until 85. She has $1,000,000 in her account and she wishes to invest in an annuity stream that will pay her an income every month to live until she is 85. If the interest on the annuity stream at the ANZ is 4.5% p.a., what income can Ms Basset expect to receive every month?

(b) What is the effective annual interest rate that she is earning on her investment?

(c) Ms Basset realises that she should check out the interest rates on offer at some other banks to see if she can get a better deal. She is disappointed to discover that they all have the same rate of 4.5%. However, Nab offers her the same deal with the payment made every week. Should she choose the annuity stream offered by ANZ or NAB and why? What is her weekly payment? What is the effective annual rate offered by NAB?

(3 + 2 + 5 = 10 marks)