You want to save for your retirement, but you have zero savings now. To live comfortably, you decide you will need to have $2M saved by your 62nd birthday. Suppose that today (December 16th) is your 30th birthday.

a. (3 points) Suppose you decide that, beginning on your 31st birthday and continuing on every birthday up to and including your 62nd birthday, you will put the same amount into a savings account. If you can earn 3% on your savings (with interest compounded annually), how much must you save each year starting on your 31st birthday to have $2M in your account on your 62nd birthday?

b. (4 points) Suppose instead that you decide to save the same amount every month on the 16th of the month (starting one month from now) to accumulate $2M by age 62. How much must you save each month if you can earn 3% (assuming now that the 3% rate is stated as an APR with monthly compounding)?

c. (4 points) Now suppose that, because your income will increase over your lifetime, you decide instead to save a smaller amount one month from today and then let your monthly savings deposit grow by 0.2% each month, still hoping to accumulate $2M by your 62nd birthday. How much must you put into your account one month from today? Continue to assume your savings earn 3% stated as an APR with monthly compounding.

d. (4 points) Suppose that you have successfully accumulated $2M in your savings account at age 62. What constant monthly amount can you withdraw, starting one month after your 62nd birthday and continuing every month until your 98th birthday (after which you plan to have nothing left in the account)? Continue to assume your savings earn 3% stated as an APR with monthly compounding.