Grace Crowne will retire today 31st December on her 60th birthday. Her family has a rare medical disease which causes them to die on their 75th birthday. She needs to choose between three retirement plans: i) She will receive $70,000 per annum for the rest of her life ii) She will receive 80% of the value in i) above in the first year with a growth rate of 4% per annum iii) She will receive a lump sum payment of $500,000. Grace lives in Utopia, where the economy is very stable the interest rate is 9% and is expected to remain unchanged for the remainder of her life. Her estimated annual expenses, which she anticipates will not change is as follows: - Property including utilities 35,000 - Medical 15,000 - Food 10,000 - Miscellaneous. 5,000 Based on her medical condition she received a tax exemption. Given her expenses and the information above which plan would you recommend to Grace? Show all your workings and provide justification for your answer.