Question 3: Time Value of Money and application (25 marks) a) Your 35-year old uncle is considering his retirement needs. He expects to retire at age 65 in 30 years) and plans to live to age 99. He wants to buy a house costing $300,000 on his 65th birthday and his living expenses will be $30,000 a year after that (starting at the end of year 65 and continuing through the end of year 99, i.e. for 35 years). Assume an annual interest rate of 8%, annual compounding: i) How much will he need to have saved by his retirement date to be able to afford this plan? ii) Suppose he already has $50,000 in savings today. If he can invest money at 8% a year, how much would he need to save at the end of each year for the next 30 years to be able to afford this retirement plan? (5+10=15 marks) b) You have been hired to run a pension fund for Mackay Inc, a small manufacturing firm. The firm currently has $5 million in the fund and expects to have cash inflows (receipts) of $2 million a year for the first 5 years followed by cash outflows (payments) of $3 million a year for the next 5 years. Assume that interest rates are at 8%. (1) How much money will be left in the fund at the end of the tenth year? (ii) If you were required to pay a perpetuity after the tenth year (starting in year 11 and going through infinity) out of the balance left in the pension fund, how much could you afford to pay every year? (10 marks)