Retirement planning in two stages (Learning Objective 3)}

You are planning for an early retirement. You would like to retire at age 50 and have enough money saved to be able to draw \(\$ 225,000\) per year for the next 30 years (based on family history, you think you'll live to age 80 ). You plan to save for retirement by making 25 equal annual installments (from age 25 to age 50 ) into a fairly risky investment fund that you expect will earn \(12 \%\) 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:

1. How much money must you accumulate by retirement? (Hint: Find the present value of the \(\$ 225,000\) withdrawals. You may want to draw a time line showing the savings period and the retirement period.)

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 25 years? (Hint: Your answer from Question 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 25 -year savings period and the withdrawals you will make during retirement?