Michael plans to retire in 40 years.He is now trying to decide how much to save for his retirement. He plans to deposit equal amount at the beginning of each month in a retirement account for 40 years, with his first saving made today. Assume the retirement account pays him an interest rate of 6.6% p.a., compounded monthly and Michael would like to have $2,000,000 in his retirement account 40 years later

a)How much will he have to deposit per month to accumulate $2,000,000 in 40 years?

b)If he hopes to live for 25 years in retirement, how much can he withdraw every month (starting one month after retirement) so that he will just exhaust his savings of $2,000,000 with the last withdrawal (assume his savings will continue to earn him 6.6% p.a. compounded monthly)?

c)If, instead he decides to withdraw $12,000 per month (again with the first withdrawal one month after retiring) for 25 years and leave the remaining account balance to his children, how much money will Michael be able to leave to his children?

d) Assuming Michael can now only afford to deposit $600 per month, but he still wants to retire with $2,000,000 in 40 years, what is the effective annual rate of return that he needs to earn on his retirement account?