1. Jason got a job at age of 25 with a salary of 50k per year. He expects the salary to go up at a rate of 3% per year, and he expects to retire in 40 years at the age of 65.

   (a) What will be Jasons salary in 40 years? (b) Jason wants to save for his retirement. He decides to invest 5% of his earnings at the end of each year into a pension fund. The pension fund is expected to grow at a rate of 7% a year. We can model this using the following dynamical system: x₁=50, y₁=0, x_n+1 = 1.03x_n , y_n+1 = 1.07y_n + 0.05x_n . Here x_n denotes the salary at the end of year n and y_n is the amount in the pension fund at the end of year n. Write a Python program to compute x_n and y_n, n = 1, . . . , 40. Print out the salary and pension plan amounts each year. (c) Suppose Jason wants to retire with 1 million dollars in his account. What percentage of his earnings should he invest each year? (d) The pension fund is designed pay out for 20 years, on average (as Jason is expected, on average, to live to 85 years old). Jason wants to be paid out a yearly pension equivalent to 60% of his salary at the end of his career. What percentage of his earnings should he invest each year? (e) Redo question (d), but with the starting salary of 100K instead of 50K. Python program