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 An represent the balance on the loan after n months.

(a) Explain why the following equations are true:
A1 = 1.005(10000) −100
A2 = 1.005²(10000) −1.005(100) −100
A3 = 1.005³(10000) −1.005²(100) −1.005(100) −100
A4 = 1.005⁴(10000) −1.005³(100) −1.005²(100) −1.005(100) −100

(b) Find a formula for An.

(c) How long does it take to pay off the loan?