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March 24th, 2013, 02:27 AM  #1 
Newbie Joined: Mar 2013 Posts: 1 Thanks: 0  RealLife NPV question (When to collect Social Security)
Hi Finance math majors. I'm hoping you can help me make a reallife decision concerning the best time for me to begin collecting social security. Here's a condensed version of the math involved. The numbers are just hypothetical but should be representative of reality. I have the choice of collecting social security benefits at the age of 66 or waiting four years until I'm 70. If I begin collecting at 66 I will receive (theoretically) 1200 per month. If I wait until I'm 70, that benefit amount would go up by 1/3 to 1600 per month. I'm trying to decide which is the more practical choice. Here's the math as I see it... but perhaps I'm missing some NPV (net present value) calculation and my thinking may be flawed. If I begin collecting at the beginning of 2014 at 66, over the next for years, I will collect a total ($1200 per month at a time) of $57,6000. If, however, I wait until I'm 70 to begin collecting, I will get no money over then next four years, but will start collecting $1600 per month at that time. By my calculations, once I start collecting at age 70, it will take me 12 years to make up that $57,6000 I "lost" by not collecting from age 66. Further, if I add those "lost" 4 years to the 12 years it will take me to break even, it will be a total of 16 years from the beginning of 2014 (2030) before I will start to benefit from having waited for the larger monthly amount. So that's my dilemma... Breaking even 16 years from now (when I will be 84) does not seem to make a lot of sense unless I plan to live well over 100. (And who could plan such a thing anyway.) Certainly, if we all lived to be 150 or 200, waiting to collect the higher amount would make sense. But since the reality of life is that most of us don't live that long, there's no assurance of a big payoff over time by waiting. In the final analysis (from a practical standpoint) it seems that starting collecting at age 66 makes much more sense. But as I said, my "NPV" calculations might be flawed. If so, I'd appreciate your enlightening me. By the way... Yes my health is great... but one never knows what the future might hold. What are your mathematical opinions? Thanks! 
March 24th, 2013, 10:48 AM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: RealLife NPV question (When to collect Social Security) Quote:
If you break even at 66 + 4 + 12 = 82 that means that you would be better off if you expect to live to 83 retiring later, but worse off if you only live to 81. Since you describe yourself as being in good health I imagine living longer is the more likely option. The SSA computes the odds of you living to 82 as 52.3%, reinforcing what I said in the paragraph above.  
March 24th, 2013, 01:47 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039  Re: RealLife NPV question (When to collect Social Security)
Doing a Present Value comparison also shows they're about same... Using 6% annual cpd monthly: 16 years @ 1200 monthly: pv = ~147,886 12 years (4 year delay) @ 1600 monthly: pv = ~129,052 Using 7% annual cpd monthly: 16 years @ 1200 monthly: pv = ~138,375 12 years (4 year delay) @ 1600 monthly: pv = ~117,683 

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