I am currently 25 years old (so basically 35x12=420 months until I retire).

Additionally, I have $20,000 invested in a brokerage account that I expect to give me a return of 8% compounded semi-annually. I am planning to work until I am 60 and put some money away monthly in a investment account that gives me a return of 5% compounded monthly. (First payment will be one month from now and last payment will be the month I retire. You can assume I turned 25 today). As soon as I retire, I plan to move somewhere warm and buy a house for $600,000 and invest all my remaining money into risk free treasury bonds that will give me a return of 2% compounded monthly. My expected monthly expense for the remainder of my life is $5000 a month, that I will be needing at the beginning of each month. Hopefully, Ill live until I am 80 years old.

a) How much should I put away each month in my savings account until I retire, so I can meet all my retirement needs. (Try not to round any intermediate results)

b) Recalculate the same above question but assume my brokerage account that gives me 8% compounds continuously instead of semianually.

Thank you! I will upvote upon correct answer!