You're purchasing a home with a price of $240,000. You have 20% in cash for the down payment, and the rest is being financed with a 30-year mortgage with an annual interest rate of 3.85%.

a. (10 points) What is the monthly payment?

b. (10 points) Formulate a dynamical system that models the change in the amount owed on the home.

C. (5 points) Generate a spreadsheet that gives the month and the balance of the mortgage at the end of each month.

d. (5 points) Include a scatterplot of the data generated in part c.