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You plan to You are 25 years old and have just finished your degree at the work for 50 years and each month save a constant amount towards your retirement. . You estimate that by the time you retire the life expectancy will be 100 years, but since you eat healthy, run half a marathon each month and have never touched alcohol or drugs you assume that you will live to be 105. The interest rate is 0.5% per month. Your calculations show that you will need $50,000 per annum in each of your 30 years of retirement. a) How much do you need to save each month to finance your retirement? (5 marks) b) Suppose that just as you are about to start working you find out that there is a medical breakthrough that can cure all viruses. You now assume that you are likely to live until 110. How much do you need to save each month? (2 marks) c) Now assume that you decided to spend the first two years following university backpacking, another two years volunteering in Africa and a year lounging around in Amsterdam. That is, you will start working only at the age of 30. Also assume that your plans for the next five years will not affect your life expectancy (that will still be 105) or the age of retirement (75). Recalculate how much money you need to save each month. (2 marks) d) Now assume that your savings will increase each month at a constant rate of 0.1% (you still work for 50 years and live to be a 105). How much money will you need to save in the first month? Note, that for full marks you will need to solve it analytically and more marks will be given to simple solutions. (11 marks)