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The crossover age, simplistically, is 82.5 years. Assume that the full retirement benefit at age 66 is $1,000 per month, while the deferred benefit at age 70 is $1,320. At 82.5 years the 66 y.o. claimant shall have received (82.5-66)*12*$1,000=$198,000 in the aggregate, and the 70 y.o. claimant shall likewise have received (82.5-70)*12*$1,320 =$198,000.
The chart prepared by Charles Schwab (below) shows the breakeven longevity to be 76 (early retirement claimant at 62 vs full retirement at 66), 79 (early retirement at 62 vs deferred retirement at 70), and 82 (full retirement at 66 vs deferred retirement at 70).
Focusing on the crossover ages is, however, too narrow a perspective. The longer a Social Security recipient lives, the bigger the gap between the curves and the more incorrect would be the decision to take benefits earlier.
On the other hand the inclusion of a discount rate shrinks the advantage of deferral. (The previous analyses assumed no discount rate, i.e., a dollar today was worth the same as a dollar in the future.)
There are several ways of looking at discount rates, but one simple approach is to view it as the rate one earns on savings. For example, if the rate is 3%, a dollar received today would grow to $1.127 after 48 months, assuming monthly compounding. Including interest, the full retiree would have amassed $51.06 by age 70, not the $48 in the simplistic no-interest analysis. Because the deferral cash flow has a bigger gap to make up, the crossover age at 3% interest becomes 87.
If the earnings rate is 6% the crossover age is 101. (Your humble blogger has--cough--outperformed this rate over the long term, though truthfully there have been some down years when I could least afford it). Extrapolating past performance into the future, as financial institutions always disclaim, is not guaranteed, but doing so argues for taking the money now. Getting to 101 is pollyannish, even for me. (And, yes, a number of friends' deaths by the age of 72 have influenced my deliberations.)
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