On the first day of your new job, your employer presents you with the following two plans regarding retirement contributions: Plan A: The company will make an annual contribution of $20,000 into your retirement account for the next 30 years. The first payment starts 1 year from now. Plan B: If you stay with the company for 3 years, then the company makes annual contributions starting from $20,000 and grow at 5% per year. The first payment starts 3 years from now, and there will be 28 payments in total, from year 3 to year 30. If you leave within 3 years, then the company makes no payment. Assume that the annual interest rate is 3%. For simplicity, also assume that you will either quit within 3 years or stay with the company for the rest of your career.

c) If the probability of quitting in 3 years is p. How high does p need to be so that you'd prefer plan A to plan B?

d) Suppose you need to pay a 20% tax on those contributions, how does that change your analysis in c)?