1. Jack Ziebell is planning for his impending retirement from the AF and has $1,000,000 to invest as a lump sum into a retirement investment account. Although retiring as a player Jack plans to work for another 25 years in the AFL industry before retiring from the workforce at the age of 55. On top of the $1,000,000 lump sum, Jack plans to deposit $1,000 into his retirement fund at the end of each month of his remaining working life. Jack conservatively estimates that his retirement account will earn an annual return of 5%. Jack plans to retire at 55 and then draw a pension from his savings for a further thirty years. During this retirement phase, Jack expects to be investing conservatively and estimates a 4% per annum return. At the age of 85, at the completion of the pension, Jack would like to have $500,000 remaining in the account for contingencies.

(i) Calculate the Future Value of Jacks retirement account on the day he retires based on monthly compounding and an expected earning rate of 5% per annum (4 marks).

(ii) Jack plans to receive his pension monthly with his first retirement pension payment occurring one month after he retires. Calculate the monthly pension that Jack will receive after retirement, taking into account the requirement to have $500,000 remaining at the end of the pension period (6 marks).