Question 2 [18 marks] A retiree deposits $500,000 in a bank account which pay interest j12 = 5.4% p.a. Starting in a month's time, they intend to withdraw $4000 to cover their living expenses until run out of money. [NB It is likely that their final withdrawal will be a partial withdrawal].

a) Illustrate this scenario as a fully labelled time line diagram. [2 marks]

b) Determine how many full sized withdrawals they can mark. Enter this value as an answer to "Assignment 1 - Milestones" question 2b. You can have as many attempts of this as you wish without penalty, but this question will close at 4:00pm on Friday 7 August. There will be no marks available for this question part after then. [2 marks]

c) Determine the size of the final partial withdrawal made one month after the last full sized withdrawal. [4 marks]

d) Construct an amortization schedule showing the last three withdrawals (two full and one partial withdrawals. Ensure that you show how you found the outstanding principal. Ensure that you have shown example calculations for one line of the table. {NB this scenario is essentially the same as a fully amortized loan repayment, except the person and the institution have swapped roles.) [4 marks]

e) After exactly one year, they had to have hip replacement surgery, and had to withdraw an extra $15000 from the account to cover the cost. That is, their 12th withdrawal was $19000 rather than the usual $4000. Determine how many more full sized withdrawals they can make after this.