Question 1 (25 marks) Lily, now aged 40, would like to save money for her retirement at the age of 65. The following three investment plans have been offered to her by different financial institutions in Hong Kong: Plan 1: Plan II: Deposit an equal amount of $150,000 in a fund account at the end of each year for 25 years to accumulate $10,965,900 at the end of the 25th year. Invest a lump sum of $2,000,000 in a saving plan today with an annual interest rate of 7% for 25 years. Invest various amounts in a plan which offers an annual rate of interest of 9% based on the following investment schedule: Plan III: At the end of year 1 - 6 7 - 11 12-16 17 - 20 21 - 23 24 - 25 Amounts Invested $135,000 $130,000 $125,000 $120,000 $115,000 $110,000 Required: (All answers should be rounded to 2 decimal places, if applicable.) (a) Determine the annual rate of interest of Plan I. (4 marks) (b) Based on the above information, determine the returns of these three investment plans at the end of the 25th year. Which of the investment plan provides the largest return at maturity? (18 marks) (c) Daisy, five years younger than Lily, plans to have $12,500,000 for her retirement at the age of 65, determine how much money she should invest today if the annual rate of interest is 8%