A person takes out a loan of $10,000 at an annual interest rate of 6%, compounded monthly, and makes payments at $100 per month. Let Anrepresent the balance on the loan after n months. (a) Explain why the following equations are true: A1 = 1.005(10000) 100 A2 = 1.005(10000) 1.005(100) 100 A3 = 1.005(10000) 1.005(100) 1.005(100) 100 A4 = 1.005(10000) 1.005(100) 1.005(100) 1.005(100) 100 (b) Find a formula for An. (c) How long does it take to pay off the loan?