Exercise 4: (Adapted from textbook problem 1.3: #7.) I am considering a $100,000 mortgage that charges 0.5% interest each month, compounded monthly. Suppose I decide to pay a monthly payment in the amount of p each month. Let an represent the amount owed after n months. (1) Formulate a difference equation model to calculate an. (2) Then analytically solve this difference equation to obtain a formula for an. (The formula should contain p as a parameter). (3) If the mortgage needs to be paid off after 30 years (exactly 360 months after the initiation of the loan), what should the monthly payment p be equal to? Exercise 4: (Adapted from textbook problem 1.3: #7.) I am considering a $100,000 mortgage that charges 0.5% interest each month, compounded monthly. Suppose I decide to pay a monthly payment in the amount of p each month. Let an represent the amount owed after n months. (1) Formulate a difference equation model to calculate an. (2) Then analytically solve this difference equation to obtain a formula for an. (The formula should contain p as a parameter). (3) If the mortgage needs to be paid off after 30 years (exactly 360 months after the initiation of the loan), what should the monthly payment p be equal to