2) (34 points) Jack and Marys lovely daughter, Betsy, is 10 years old today. As a birthday gift, her maternal and paternal grandparents give her a check of $10,000 each. When they are giving the checks they tell her that these checks are for her college education. At that moment Jack and Mary realize that they need to start saving for Betsys college education. At that night they make a small research and learn that an average tuition fee for a year in college is $40,000 today. Betsy will start the college when she is 18. The tuition fees will be paid at the beginning of each year for four years (initial payment will be made when she is 18, the last payment will be done when she is 21). Jack also realizes that the cost of the education will increase every year with the inflation rate which is 0.5%. Both Jack and Mary decide to prepare the total amount they need for the four year education when Betsy is 18. They also plan to use the money given by her grandparents for this aim. They talk to a bank manager and learn that if they deposit the money in the bank account they can earn 10% compounding semiannually.

1. a) (6 points) Calculate the amount they should have in their bank account for the four year college education when Betsy is 18 years old (the interest rate will still be 10% compounding semiannually).

2. b) (3 points) Calculate the amount they need to save for the education when you take into account the checks given by the grandparents.