You are twenty years old and you would like to have at the time of your retirement, foreseen in forty-five years of 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 retirement year and would increase by 2% per year thereafter. You then decide to start today to make contributions at the end of each month to this account until the day of retirement. Assuming an average effective annual interest rate of 7% over the entire period: a) How much must you have in your account in 45 years to be able to make the annual withdrawals desired (account balance in 45 years)? b) How much do you have to contribute to this account each month to reach this balance?