I am currently 25 years old. 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 saving account that gives me a return of 2.05% compounded daily (First payment will be one month from now and last payment will be the month I retire. You can assume I turned 25 today. Also, assume a year has 365 days).

As soon as I retire, I plan to move somewhere warm and buy a house for $60,000 and invest all my remaining money into risk free treasury bonds that will give me a return of 2% compounded quarterly. My expected monthly expense for the remainder of my life, after retirement, is $1000 a month that I will be needing at the beginning of each month. A fortune teller told me Ill live until I am 80 years old and I believe them.

a.) (10 points): 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.) (5 points): Recalculate the same above question but assume my saving account that gives me 2.05% compounds continuously instead of daily.