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.

a) Compute the present value of Plan A.

b) Compute the present value of Plan B.

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)?