Avatar4321 said:
You know, your math doesnt even make sense. How do you get 1200 from 120,000 at 12% apr? Im dying to know.
Besides, interest compounds over a lifetime. Ben Franklin put 3 dollars in the back and a few decades ago that three dollars had enough money to build a bridge that now bears his name. And that wasnt nearly at 12% interest.
He has absolutely no clue how to compute such an annuity.
Fortunately, I am a Fellow in the Society of Actuaries. :read:
Actuaries are specifically the same people employed by the government to determine the future cost of Social Security. My last job was at the largest private actuarial consulting firm in the world, Milliman Global.
Our mathematical poser ArchAngel spits out a solution to a formula for determining the present value of a life contingent annuity at 12% without using life expectancy tables.
The fact that he failed to mention a period of time for such payments, or moreover even an age of reference to begin payments at retirement from, demonstrates he doesn't even understand which necessary inputs are required to work out such a simple formula using interest accumulation only, let alone the more complex math behind the fact that Social Security annuitization does not operate on the simple principle of interest alone.
With interest as the only factor in computing the present value of an annuity
without any life contingencies, the formula for solving this equation is already complicated enough. The unitized formula for the present value of an interest bearing annuity payment, of say, N number of monthly payments of $1, or conversely, the amount of each interest bearing monthly payment from a set present value of $1, is going to make ArchAngels eyes google out and his head explode.
The P.V. of a monthly annuity of $1, at 'i' interest and over 'n' periods, without life contingencies, is:
(1-V^n)/d
Where i = .12 (average annual rate of return)
i(adjformonthlypayments) = [(1+i)^(1/12)] - 1
d = i(adjformonthlypayments)/[1+i(adjformonthlypayments)]
V = 1/[1+i(adjformonthlypayments)]
n = # of months of certain annuity payment
So you would then take the unitized result and multiply it by the the actual amount in question, in this case a present value of 120,000.
Does it equal $1,200 @ 12% annual interest (or more appropriately (1.12^(1/12)) -1 % = .948879% monthly interest?
The problem is ArchAngel doesn't specify 'n', the number of expected payment before the person recieving social security payments dies and no longer will require them. In fact, he discards this essential input into the formula for life expectancy, as if paying out 1,200 monthly is the same regardless of whether its for 10 years or 20 years!
You need an 'n'. In the business, a
certain immediate annuity is one which pays money out regardless of whether or not the orginal benefactor is still alive, and 'n' is known for certain.
But that's not the way personal social security benefits pay out. All of the above concerns a formula where 'n' is known for certain, and can be simplified greatly. You can compute this only if you disregard the fact that under social security, when a person dies, the payments stop.
But social security payments are what we call life annuities. And the present value of a life annuity requires that you not only discount for interest, but for mortality. That opens up an entirely new can of mathematical worms which took me a full 300 hours to study and pass one of the many,
intensely grueling exams to become a Fellow in the Society of Actuaries. (and a jolly good one!)
In the case of a large group like SS retirees, you have to also account for the various spreads of average life expectancy, depending upon multiple decrement factors like the distributions of sexes, smokers/non-smokers, retirement ages, etc... the math gets rapidly much more complex and requires multiple published life expectency tables and a formulated spreadsheet to calculate the true cost of a retirement annuity for any particular person (or more appropriately the average cost of an entire cohort of grouped retirees who share that persons retirement age, sex, smoking habits, etc...).
This is the kind of math FAR beyond his capabilities.
In other words, our math wizard wanna be, ArchAngel, is completely full of it.
P.S. All the mathematically credible information on the future balance of social security depends on actuaries, which are a very, very rare breed in this country. The scope and complexity behind the subject is far too complex for the average person to really get into, and therefore the math nerds
own this debate.
P.S.S. If you read this far, you are maybe as nerdy as I am. :hail:
P.S.S.S. Anybody who pisses me off, remember, I may just be in a situation someday to personally slash your benefits when you're old and crippled. :teeth: