A man has a credit card with a $1000 balance, 18.9% annual interest, and no grace period and decides not to use the card again. He makes no payments for a year and is surprised when his statement shows a balance of more than $1,189.

a. Build a dynamical system model and find the balance after one year and five years. Use your results to help him out. Note: Solve the model both analytically and numerically.

b. Introduce payment to the above model. Assume a minimum monthly payment of 3% of the balance, determine what the balance will be after five years. How long will it take to get the balance down to under $10?

c. Suppose he pays $10 more than the minimum payment each month. What effect does this have on the total payments and the time to pay off the card?