You are twenty years old and you would like to have at the time of your retirement, planned in forty-five years, a savings account whose balance would allow you to start making annual withdrawals for fifteen years. The first withdrawal would be $10,000 at the end of the first year of retirement and would increase by 2% per year thereafter. You then decide to begin today to make contributions to this account at the end of each month until the day of retirement. 

Assuming an average effective annual interest rate of 7% over the entire period:

 a) How much do you need to have in your account in 45 years to be able to make the desired annual withdrawals (account balance in 45 years)?

b) How much do you then have to contribute to this account each month to reach this balance?