Bilbo plans to save for his retirement in 30 years (t=30) from today, with constant annual  saving of $50,000 starting from year 1 (t=1) through year 30 (t=30). Bilbo aims to maintain constant annual expense in the retirement from year 31 (t=31) to year 50 (t=50). The annual  discount rate for Bilbo's entire life is 10%.

a) What is the Bilbo's maximum expense per year in his retirement?

 
b) If Bilbo also wants to leave $10,000,000 to his son Frodo in year 50 (t=50). What is his  maximum annual expense in the retirement?