Cathy Kung, 25, plans to retire at the age of 65. She estimates that she will need $50,000 in the first year of her retirement, and this post-retirement expenditure will increase at the rate of inflation of 2% per year. Based on her family history, she does not expect to live beyond the age of 90. After retirement, she will invest her money in bank deposits with an expected rate of return of 4% per year. Her post-retirement marginal tax rate is 30%.

Required:

(a)How much money will she need at age 65 to finance her post-retirement life style? Assume that all annual expenditure occurs at the beginning of the year. (5 marks)

(b)She plans to achieve the goal in (a) by saving annually, starting at the end of the first year. She will increase her annual savings at the rate of 5% per year. If she can earn 6% before tax and her appropriate tax rate is 30%, how much must she invest this coming year? (5 marks)