You just turned 30 years old, have received your MBA, and have accepted your first job. You are permitted to deposit $19,500 per year into your 401(k) plan. Assume that you plan to work for 40 years and make the deposits at the end of each year (the first one on your 31^st birthday, one year from today, and the last on your 70^th birthday, 40 years from today). You expect all money invested in the plan to earn 5% per year. You will not pay any taxes on the deposits or earnings in the account until it is withdrawn. During your retirement, you plan to withdraw funds from the account at the end of each year (assume your first withdrawal is on your 71^st birthday).

a. How much do you expect to have saved in your 401(k) at age 70 just after your last deposit?

b. What constant (pre-tax) amount will you be able to withdraw each year if you want the last withdrawal to be on your 100^th birthday? (30 total withdrawals)

c. Suppose instead that you want to make monthly withdrawals at the end of each month, starting at the end of the month after you turn 70. Hence, you will be making 360 withdrawals. Assuming the investments earn 5%, what constant (pre-tax) amount can you withdraw at the end of each month? (Note: for this part, assume the 5% is stated as an APR with monthly compounding)

d. Now assume that you will be able to increase your annual deposits by 2% per year while working (the first deposit will still be $19,500). Assuming the same 5% annual return as in part (a) above, how much will you have saved in your 401(k) at age 70 just after your last deposit?