Question 2 a) You are 35 years old today and are considering your retirement needs. You expect to retire at age 65 (in 30 years) and you plan to live to 99. You want to buy a house costing $300,000 on your 65th birthday and your 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, 35 years), assume an annual interest rate of 8%, annual compounding: How much will you need to have saved by your retirement date to be able to afford this course of action? Alternatively, suppose you already have $50,000 in savings today. If you can invest money at 8% a year, how much would you need to save at the end of each year for the next 30 years to be able to afford this retirement plan? b) In 30 years, you plan to set up a fellowship fund for Carleton university that pays out $100,000 per year in perpetuity with an annually compounded discount rate of 5%. In order to set up the fund in 30 years, how much do you need to save each year (starting this year) assuming you can get a semi-annually compounded return of 10% on your savings for the next 30 years?