That's intriguing! I'd love to see the math you used.
So many variables, so it's best to work with averages as well as standard deviations (10th and 90th percentiles) to consider reasonable best and worst cases. The plan is to put the funds into an index fund total market style investment vehicle. All numbers below factor inflation out as well as reinvestment of dividends. So we don't need to worry about how inflation (COLA) factors into anything. Every dollar figure below is in 2018 dollars.
Looking at the Shiller data and using the average as 6.615% above inflation for the market; I'm also going to use the 10,20,30 and 40 year 90th and 10th percentiles for returns to give best and worst cases for each type at age 72, 82, 92 and 102. Reality is, when you're looking at 30 or 40 year average real returns you'll kind of know going in if you're prime for a really bad time or good time ahead based on the current state of the market. For example... only once in a rolling 30 year period did the market return as low as just 1.9% above inflation and it just happened to occur right after a few decades of amazing returns (you caught the regression back to more normal numbers. Same can be seen in reverse. The best 30 year rolling return period of 11.15% above inflation happened after the market was in one of it's worst periods in history the decades prior. Anyway... here are the numbers:
SSA says my monthly collection at age 62 is $2,121 a month and at age 70 it is $3,752 a month
(
avg: is always 6.615%,
low is 10, 20, 30, or 40 year 10th percentile rolling annual return average,
high is 10, 20, 30, or 40 year 90th percentile rolling annual return average) - obviously on the 10 and 20 year returns the 10th and 90th percentiles vary wildly. The gap closes when you narrow out to 30 and 40 year average returns in those percentiles further down. Example... at age 82 I'm using the high and low for 10 year rolling periods for the overall market when looking at the late start (age 70) and I'm using the 20 year rolling percentiles for the early start (62) because each had about that long to invest at the given age.
Assuming all funds are invested in the market, here is what we get based on age:
At Age 72
early (age 62): (avg: $405,043) (low: $270,098) (high: $615,188) <--- 10 year 10th and 90th percentiles
late (age 70): (avg: $148,973) (low: about $90K) (high: about $200K)
At Age 82
early (age 62): (avg: $1,125,319) (low: $708,205) (high: $1,898,566) <--- 20 year 10th and 90th percentiles
late (age 70): (avg: $913,756) (low: $499,068) (high: $2,770,981) <--- 10 year 10th and 90th percentiles
At Age 92
early (age 62): (avg: $2,492,047) (low: $1,666,683) (high: $3,741,166) <--- 30 year 10th and 90th percentiles
late (age 70): (avg: $2,364,937) (low: $1,412,362) (high: $4,252,385) <--- 20 year 10th and 90th percentiles
At Age 102
early (age 62): (avg: $5,085,422) (low: $3,243,276) (high: $7,852,725) <--- 40 year 10th and 90th percentiles
late (age 70): (avg: $5,118,560) (low: $2,893,874) (high: $9,021,038) <--- 30 year 10th and 90th percentiles
The take away from this... the benefit of those first 8 years of collection left to compound at the long term average 6.615% of the market won't be overtaken by the later higher figure (collecting at age 70) until age 101. That's "on average"
Another interesting note, is that the worst case scenario (bad market years ahead) always points to the collecting early as being more beneficial, even at the age of 102 it comes out ahead.
(if you're confused by this post... please read my previous message about 15 prior to this one in the thread that shows my situation/plan for SS before replying. My situation is a bit unusual for plans with SS money. Point being, this probably doesn't apply to many others.)