Question 1: Savings goals (20 marks). The Thanos family is planning to install an inground swimming pool in 5 years. The family is very excited about having a pool at home and have already saved $20,000. The swimming pool model they want is estimated to cost $55,000 in 5 years. The savings account earns 4% p.a. Ignore taxes. Required: a) What is the end of year annual savings amount needed so they will have $55,000 to purchase the inground swimming pool in 5 years? Note: They will move the $20,000 to the savings account at the same time they deposit their annual savings in year 1. (6 marks) b) During year 4, due to the increase in demand for inground swimming pools, the cost for the model they want to install has increased to $65,000 (cost at time of purchase in year 5). For years 1-3, the family saved only $4,000 at the end of each year. What is the amount of annual savings needed for each of the remaining 2 years to save $65,000? (10 marks)