At 30, Maya, a dedicated soware developer with a passion for wildlife photography and environmental conservaon, is planning for early rerement from the workforce by age 50. With $150,000 already in her rerement savings and an ambious goal, she esmates needing $100,000 yearly to live her dream life postrerement unl she is 80. The first payment will be at the end of age 51. Aware of the financial intricacies this goal entails, Maya, who is inclined towards a balanced yet slightly aggressive investment strategy, expects an average annual return of 8% on her savings unl retirement. Postretirement, she plans to she to a conserve investment approach, ancipang a 4% return. 

a. Calculate the total amount Maya will need at the beginning of her retirement to ensure she can withdraw $100,000 annually for 30 years, considering a 4% annual return on investment during her retirement. (Withdraw at the beginning of the year) 

b. Determine how much Maya needs to save annually for the next 20 years to meet her required retirement fund by age 50, assuming a 8% annual return on her current savings and future annual contributions. (Maya saves at the end of the year)