Please answer the question below and show working out.

Nicole is currently 40 years old and is planning to retire at age 65 . She has $100,000 invested in a superannuation fund that currently yields 5% per annum, on average. It is expected that the long term inflation rate will be 3% per annum during Nicole's retirement. a) A well-established strategy for funding a retirement is spending 4% of the retirement savings in the first year of retirement over a 30-year period and adjusting that amount annually to keep pace with the expected inflation rate. Applying this strategy to Nicole's retirement and assume that she will continue to earn 5% annual return throughout her retirement, what is the actual proportion of the retirement savings at the beginning of the first year she can have access to according to the strategy? If Nicole would like to start with a $100,000 for her retirement, how much does she need to save by the time she retires? Briefly explain your working steps and show your formulas and calculations