Some Numbers

Quite a while back, I wrote a post on Social Security Reform. I mentioned President Bush's now seemingly defunct plan to reform the current system through Private Accounts and the fact that I liked the idea. What I gave was a purely Lincoln-Douglas type argument based off of responsibility and ownership. But below I've posted some cold hard numbers that are difficult to dispute.

I decided to do this little exercise while sitting at my desk this afternoon (took about 5 minutes). The funny thing about it is how elementary the economics are. I am only an engineer, not an economists, so much of my training is in what most would call "micro-economics", ie annuities, pay out, present/future value calculations--the type of calculations that are needed for decisions regarding operational facilities. That politicians and their advisors can do these same calculations seems quite obvious.

The way I developed the data was with two different calculations. First, I calculated the Future Value of Social Security contributions. I used the following equation for compounding interest with additional contributions:

FV = P(1+i)n + C((1+i)n+1-(1+i))/i

Where
P = the original principal
C = the annual social security tax payment
i = the annual rate-of-return
n = the total number of years of contributions

This will give the Future Value of all your Social Security contributions.

For the calculation I used:

P = 0
C = $50,000/yr*10.6% = $5,300
(Yes, 10.6%, don’t' be fooled into thinking it's only 5.3%)
n = 62 - 21 = 41 years

I then used various rates of return from 0.5% to 15% to calculate a range of Future Values. These are the actual amount of money YOU would have at the respective rate of return IF ALL of your Social Security tax went into an investment account.

I then used the Social Security Administrations website to approximate a Social Security distribution upon retirement at age 62. Again, I used an income of $50,000 with no salary increases. The monthly distribution for this wage earner would be:

SS Distribution = $1,181/month

Using the following Present Value equation (or annuity equation) I assessed the total value of these distributions at retirement age.

PV = C/i*(1-1/(1+i)n)

(by the way, you must divide each i by 12 and multiply each n by 12 for monthly distributions)

As you can see, this value is dependent not only on the amount of the distribution, but also the length of time (life expectancy less retirement age) and rate-of-return. For arguments sake, I took a life expectancy of 90 years, so:

n = 90 - 62 = 28

I then used various rates of return, again from 0.5% to 15%, to calculate a range of Present Values at Retirement Age for the Social Security distribution. These data, along with the Future Value calculations, are presented in the table below. Where the two lines intersect is the actual Rate of Return-on-Investment for the sample wage earner.

That's right! 1.5% !! If you take an inflationary rate of 2-2.5%, that means that the Actual Return on Investment for social security is…

NEGATIVE! (-0.5-1.0%) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

For comparison sake, if we calculate the future value of our Social Security payments using a conservative 7% interest rates, and then purchase an annuity of the same distribution length as above (28 years, monthly distribution), the monthly amount would be $7,694!!! That's almost quadruple what Social Security is going to do with this money! Even if you were more conservative, say 5% ROI, you still would have a monthly distribution of $3,721 or more than triple the Social Security distribution.

All other things aside, I cannot see how anyone can want to perpetuate this system!