In this problem, we consider the effects of starting early or late to save for retirement. Assume that each account considered has an APR of 6% compounded monthly.

(a) At age 20, you realize that even a modest start on saving for retirement is important. You begin depositing $50 each month into an account. What will be the value of your nest egg when you retire at age 65?

(b) Against expert advice, you begin your retirement program at age 40. You plan to retire at age 65. What monthly contributions do you need to make to match the nest egg from part a?

(c) Compare your answer to part b with the monthly deposit of $50 from part a. Also compare the total amount deposited in each case.

(d) Lets return to the situation in part a: At age 20, you begin depositing $50 each month into an account. Now suppose that at age 40, you finally get a job where your employer puts $400 per month into an account. You continue your $50 deposits, so from age 40 on, you have two separate accounts working for you. What will be the total value of your nest egg when you retire at age 65?