You are planning for a very early retirement. You would like to retire at age 40 and have enough money saved to be able to draw $255,000 per year for the next 40 years (based on family history, you think you'll live to age 80). You plan to save for retirement by making 20 equal annual installments (from age 20 to age 40) into a fairly risky investment fund that you expect will earn 10% per year. You will leave the money in this fund until it is completely depleted when you are 80 years old.

To make your plan work answer the following questions:

1. How much money must you accumulate by retirement? (Hint: Find the present value of the $255,000 withdrawals.) 2. How does this amount compare to the total amount you will draw out of the investment during retirement? How can these numbers be so different? 3. How much must you pay into the investment each year for the first twenty years? (Hint: Your answer from Requirement 1 becomes the future value of this annuity.) 4. How does the total out-of-pocket savings compare to the investment's value at the end of the twenty-year savings period and the withdrawals you will make during retirement