Course: Retirement Planning
Lesson 1: Using IRAs to Build and Distribute More Retirement Income

Student Question:

I am confused about this calculation (question below). If I use 20 years instead of 15 years,  my need is now $90,305 from my own savings. The math makes sense but  the answer does not. If I have an additional 5 years to save, shouldn’t the required out-of-pocket cash be less than the original $77,898?

Example
After sitting down with Bob and looking at his future income needs, you have determined that he will need $75,000 per year at retirement in 15 years. Further, you anticipate that Bob will receive $25,000 per year in today’s dollars from Social Security beginning in 15 years and thereafter increasing by the CPI each year. This leaves a retirement income need of $50,000 per year for Bob and his family in terms of today’s dollars. But what will Bob really need if he retires in 15 years if we assume 3% annual inflation? Enter the following variables into your HP-12C or HP-10bII calculator to find out (set your calculator to four decimal places)
Inflation = 3%
Present Value = $50,000
Time to Retirement = 15 years
Now solve for Future Value. After entering these values into an HP-10bII or a HP-12C, we find Bob will need $77,898 from his own savings in the first year of retirement.

Michael


Instructor Response:

Hi Michael-

Thank you for the question.  In the time-honored American tradition of answering a question with a question, is this a savings question or future income need question?

Onward and Upward,
Bruce


Student Question:

Bruce,
 
I think it’s both.  I may be mistaken, however.  I used the data given in the example: inflation 3%, PV $50k, SS $25k, time to retirement 15 years, end state of $75k each year of retirement for 30 years.  Calculating the first year of retirement results in $77,898 needed from Bob’s own savings, Year One of retirement.
 
Bob will need to accumulate $1,589,704 for his 30-year retirement plan.  Assets will earn 6% after taxes.
 
Same data as in paragraph 1, but 20 years instead of 15 yields the first year of retirement of $90,305 needed from Bob’s own savings.  Bob now needs to accumulate $1,842,900 in order to achieve $75k a year in retirement.
 
I understand the math and it makes sense to me that Bob will accumulate more over 20 years, but wouldn’t he still need to only accumulate $1.6mm in order to achieve $75k/year?  I would think that by starting five years earlier, Bob would have to provide less than $78k/year from his retirement accumulation, not $90k.  I am missing something.
 
Thanks.

Michael


Instructor Response:

Hi Michael,
 
Here’s the dynamic at work here.  If his year of retirement is 20 years from now, inflation will drive his first year need higher.
 
With a higher first year need and continuing to assume 30 years in retirement, the capital needed to retire increases.
 
If, however, we reduce his time in retirement from 30 years to 25 years, the capital required will adjust accordingly.  His waiting 20 years to retire should not impact his life expectancy.  If his life expectancy in 15 years is 30 years, his life expectancy in 20 years should be 25 years.
  
Onward and Upward,

Bruce