Suppose you are exactly 25 years old and you are planning to save for your retirement which will happen in 40 years. You plan to deposit equal amount at the beginning of each month in your retirement account with the first saving made today. Assume the retirement account pays you 6% p.a. compounded monthly.

a. If you would like to have $1,000,000 in your retirement account 40 years later when you are retired, how much will you have to deposit monthly?

b. If you could only afford to deposit $400 per month, but you still want to retire with $1,000,000 in 40 years, what is the effective annual rate of return that you need to earn on your retirement account?

c. If you are expected to live for 30 years in retirement and you need to withdraw $4,000 per month (with the first withdrawal one month after retiring) for living expense. Assume your saving will continue to earn you 6% p.a. compounded monthly. Calculate how much remaining account balance will you be able to leave to your children 30 years later?