Sue wants a yearly income of $80,000 starting at her age 66 and continuing each year of her retirement, no matter how long she lives. She therefore needs a large sum of money (which she plans to save up) which will be the source of her $80,000/year retirement income. Assume she can earn 4% on her money. [This is a perpetuity question. See Chapter 6.] The amount of money Sue needs at her age 65 is:
The answer to question 1 is known as Sue’s (retirement) “number”, as mentioned on various TV advertisements. Sue would like to know how much money she needs to put away TODAY (she is 25 years old), which will grow to her retirement number in 40 years. Again, assume that she can earn 4% on her money. [This is a Single Cash flow problem of Chapter 5. Given the FV, r and number of periods, find PV.]
Unfortunately Sue doesn’t have the answer to number 2 available to put away today. She therefore wants to know how much she must save on a yearly basis (one payment per year for 40 years), which will produce the same result as putting away the single cash flow of question number 2 above. Sue knows to use the Chapter 6 formula for finding the yearly value, given the present value of an annuity. The present value of the annuity is, of course, the answer to question 2. The number of periods is (again) her planning horizon of 65-25=40 years. Again, assume a saving rate of 4%. Her yearly contribution to her retirement is therefore:
Aggressive Al, also age 25, is planning his retirement too. Al prefers to believe that his investments will average 8% throughout his lifetime, including his retirement years. For Al, re-calculate the above three problems, replacing the assumed rate of 4% with Al’s choice of 8%. Using Aggressive Al’s approach, how much money must be saved each year to accomplish the same retirement income of $80,000 per year?