EDITED: Ha, I made the changes to reflect the SS being taxed. I used provisional income of $30,000 for the SS tax calculation.
I Exceled a scenario of taking SS at 62 vs 70 with a goal of which pays the most. I got a surprising answer and would love to have a double-check.
Actuals from SS form:
SS est at 62 = $1568 or $18,816
SS est at 70 = $2745 or $32,940
Assumptions:
1. SS checks taken at 62 would be saved and privately annuitized at 70.
2. The income after age 70 from the private annuity would not be COLA'd.
3. SS checks taken at 62 would be COLA'd at 3% and also be invested and earn 3%.
4. SS taxed from 62 to 70.
Calculations:
Future Value of SS paid from 62 to 70 = $18,816*((((1+0.03)^8)-1)/0.03) = $167,318
Private $167,318 annuity payouts beginning at 70 for single male (immediateannuities.com) = $1,114 or $13,368
Future Value of SS check begun at 62 when age 70 is reached = $18,816*(1.03^8)=$23,836
Conclusion:
At age 70, the combination of the private annuity of $13,368 and the SS(begun at 62) of $23,836 = $37,204
At age 70, the SS (begun at 70) would be $32,940.
Amazingly, running the number out from 70 till 95 shows both plans are equal in cumulative amount and the yearly checks are higher than the SSat70 checks up until age 84.