6.(18 POINTS). To ensure that she would have enough resources to go to university, Sarah's parents have opened an education saving account on the day that she was born (that is, today). They will be making annual deposits into this account. Currently, (i.e., when Sarah is born) tuition, books and other costs average $20,000 per year and are expected to grow at a rate of 2% per year until the end of her studies. (Draw the timeline carefully for each part of the question.) (a) Find the cost of one year of university education 18 years from now. (6) Find the amount of money Sarah will need by age 18 to pay for all four years of her undergraduate education if the yearly cost is invested in an account paying 4% interest (EAR) during those four years of university education. (Recall that the yearly cost also keeps increasing during those years.) Assume she enters first year of university at age 18. (In your time-line keep track of Sarah's age as well as the number of years). (c) What is the amount of money that the parents should deposit each year (starting today) in an education savings account that offers 4% interest (EAR)? (Assume the amount deposited each year is constant.)