Olivia & Hugo are a couple of engineers and have just celebrated their 35th birthday each. Even if they are young, they are already beginning to discuss their retirement. They both want to retire on their 65th birthday, in exactly 30 years. Obviously, they wisely made an appointment with a financial planner to define how much to set aside for the next 30 years, from their 36th to 65th birthday inclusively. However, loving to prepare well for this kind of meeting, the couple would like to get an idea of the order of magnitude of this annual amount of savings. They identified that if they had access to an amount of $80,000 per year in today's dollars from their 65th birthday until their 84th birthday inclusively (so for 20 years), their retirement would be great! If they expect to make a monthly compounded nominal average return of (6%; 12) per year from now until their 84th birthday, a) How much should they set aside annually in exactly one year? (16 points) Note 1: For this question, assume a tax-free world. In a real case, several possibilities of registered investments are to be considered (TFSA, RRSP, etc.). Note 2: For this question, assume that inflation does not exist. b) Without doing any calculations, if you anticipate an inflation rate of 2% per year, all other things being equal, what will be the impact on your amount calculated in a)? (4 points)