4. (20 marks) (1) You are in the second year at UIC and then go on to attend Graduate School. You will need $10,000 per year for four year, starting next year (that is, you will need to withdraw the first $10,000 one year from today). Your grandparents offer to put through your study at UIC and graduate program, and they will deposit a sum of money that is sufficient to provide four payments of $10,000 each in bank paying 7- per cent interest. The deposit will be made today. Required: a. How much money your parents have to deposit today? (3 marks) b. How much will it be in the account after you make the first withdrawal and the last withdrawal? (4 marks) 7 (2) As soon as you graduate from university, you begin to plan for your retirement. Your plan is to deposit $500 semiannually into a saving retirement account beginning at six months after graduation and continue to make the deposit until the day you retire, which you expect to be 30 years later. The fund will take 10 per cent interest rate compounded semiannually since it is established. a. How much money will you have when you retire (you just make the last $500 deposit into your saving retirement account)? Assume all the payments were made on time. (3 marks) b. Although you are able to make all the $500 deposits you plan, 10 years later you have to withdraw $10,000 from the fund to pay some medical expense. Compute the balance in the saving retirement account (when you retire) based on this situation. (5 marks) Tom just purchased a new apartment and took out a $100,000 fifteen-year mortgage at an interest rate of 2 percent per month from the bank. a). What will be the monthly payment of this mortgage? (2 marks) b). How much is the first interest payment and the first principle payment? (2 marks) c). Without calculation, describe how interest payments and principle payments will change during the whole mortgage period. (1 marks)