Note: Correct answer to calculations-based questions will only be awarded full mark if clearly stated numerical formula (including the left-hand side of the equation) is provided. Correct answer without calculations support will only receive a tiny fraction of mark assigned for the question. Question 2 (20 marks) a) Carter expects to live for 30 years more after his retirement. He would like to withdraw $120,000 every year from his investment account (Account A) to pay for his living expenses. Carter's investment account (Account A) pays 5% interest per year. How much money (a lump-sum) will Carter required to deposit in Account A at the beginning of his retirement (at age 60) to pay for his living expenses if (i) Account A start to pay interest one year after his retirement? ( 5 marks) (ii) Account A start to pay interest on the day of his retirement? ( 5 marks) [Hint: The total deposit that Carter made at the beginning of his retirement in Account A should be the same as the amount required to provide for the monthly living expenses during his retirement years.] b) Continued with part (aii). Suppose Carter has just had his 35th birthday today and decided to begin his retirement (exactly) 25 years from now, at his age of 60 . To ensure having sufficient funds to meet his goal, Carter plans to start depositing a fixed amount at the end of every month to a retirement savings account (Account B) that pays an interest of 12%, compounded monthly. The first deposit will be made today (on his 35th birthday) and the last on his 58th birthday. (i) Compute the size of the monthly deposit into Account B that will allow Carter to meet the financial goal of his retirement. (8 marks) (ii) If Carter is going to make one single (lump-sum) deposit into Account B on his 40th