1. You got a car loan for $20,000. It has an annual interest rate of 4% compounded monthly. Your monthly payments are $400 per month, to be paid at the beginning of each month. You can model this using the following dynamical system:

   x₀ = 20000, x_n+1 = r(x_n 400) ,

   where r = (1.04)^1/12 1.003273.

   1. (a) Write a Python program that prints out a table x₁, . . . , x₆₀

   2. (b) How many months does it take until the car is paid off? That is, compute N such that X_N1 > 0, but x_N 0.

   3. (c) What should the monthly payment be to pay of the car loan in 3 years?