So we often hear how taking Social Security early results in a loss of $$. If all you did was collect the money and not invest it, that is probably true.
If I take SS @ 62, I will get $25,368/yr and they claim life expectancy is 22.2 years. For simplicity I made it 22.
If I take SS @ 67, I will get $36,600/yr and they claim life expectancy is 18.6 years. For simplicity I made it 19.
If you stop there and do the math, I am selling myself $117K short. But ...
What we are trying to do is estimate the value of having an additional $25,368 for five years and then a $11,232 deficit for 19 years until I am 85.
I calculate a break-even rate of return at about 4.635%. IN other words if you invest it (or everything else) with a fair amount of consevatism and manage only that with your assets, it comes out the same.
The first year I get $25,368 but I only have half of it on average, so 25,368 turns into 25,368 x 1.023 = 25,956.
The next year I assume that $25,956 compounds and I just add in the next year's 25,368.
That gets up to $139,861 I have amassed by collecting early, and at age 67 I start penalizing myself $11,232/yr but still compounding the balance.
As I said, at a 4.635% rate of return the difference is zero. I will have lots of assets to support me (over $1.1M excluding the house, goal is $2.0M but might settle for less) but I had never given this question serious thought and wondered if anyone else had or wanted to poke holes in this. I do work as an actuary - but not a life actuary :)