In a casino, or making a bet, you cannot simply looking at your chances of winning. You will also need to look at the payouts for winning vs the bet size. Even if the odds of winning a particular bet is only 30%, it is still better to take that bet if your payout is more than 7/3x the bet size. Similarly if the odds of winning the bet is 70%, it is not a good idea to take the bet if the payout is less than 3/7x your bet.
The cost of paying out annuities to someone grows exponentially with their life expectancy, so it's perfectly correct that there are less than half of these people.
I beg to differ
Math cannot lie because logic is always there. let use a simpler example for you. I had invested $50K from my SA account many years back and now it is worth 100K. Excluded that, I now have 120K in my SA, of which I am taking $80K to invested for a short period
SA-invested $181,000.00. Now next year I am 55, I dump all my OA and balance SA into new newly created RA to form FRS of $181,000.00. Then I refund all my investment back to SA. So now,
SA = $181,000.00, RA = $181,000.00
Age 65, now my SA = $278,000.00, RA = $278,000 (For calculation sake, let assume it is possible)
Now for the draw down using CPF life estimator, I will use the lower end of Standard withdrawal of $1400.00 pr month for the rest of my life. Using
https://www.bankrate.com/calculators/investing/annuity-calculator.aspx
I calculate at $1400.00 p/mth, my SA account will last me till 93 years old based on interest at 4.3 percent.
Now let assume I live to 100 years old with additional 84 mth of payout
$1400x84 mths = $117,600.00 (additional payout till age 100)
$1400x108 mth = $151,200.00 (additional payout till age 102)
Your argument of exponential payout failed
Your risk of losing $159,000.00 at 81 ( Based on the remainder I had in my SA) against additional $117,600 at age 100 or $151,000.00 at age 102
The losing bargain
1)You need to risk from 65 to 93 which is 28 years without dying against additional 8 years of additional payout after the 28 years
2)You need to risk $159,000.00 against winning $117,600
3) You know the odds that 70 over more percent will be dead at 93 against 20 over percent alive
4) There is no exponential is the calculation, the amount you put in to bet is more than the amount you can gain
5) The male life expectancy is at 81 years of age today. This made your risk increase exponentially in dying younger
6) the rate of death of male and female is 66:34, this again increase your risk exponentially
7)At any point of dead before 91, I always have an bequest as compare to Std withdrawal plan which will be zero at 81
8)BTW, the percentage of alive at 100 in 2 % or 0.007% for males
Now that I calculated, I still find the MBS odds better