If you think your gonna earn 10.99% on your money yearly, your the one living in La-La Land (as Dave Ramsey likes to say). First of all, the government will shave about 3% off the top of 'your' money for interest it would have made had it just done what it usually does, and invest the money in T-bonds and securities. Initial costs to implement a 4% private contribution for those 55 and under is 2-4 trillion dollars in the first 10 years. Where do you think this money is coming from to pay for this? Can't borrow that type of money.
That's right, from part of the money you would have earned had you earned your average 7.99% in C funds. After all, you don't expect the rich to pay for this now do You? But we are the government, so we'll only take half your unearned income. That leaves you with a tidy 4.0% as opposed to the 3% you would have earned in the current system. So there.
Ok, except that now the government no longer has the extra $115 billion dollars it currently uses in 'extra' SS money yearly, and well, it now has to borrow the money to meet its obligations. This forces interest rates to go up as countries like China and Russia demand a higher return for their cash investment on a credit-addicted U.S. government. This forces federal funds rates to go up which gets passed on by the banks to the consumers, that's you and me, in higher credit card rates, home-loan and car-loan rates.
So for generous 1% increase in my investment money over what I make now, I get charged higher interest rates on my loans, I get a country more dependent on borrowing from China and Russia, countries with dubious nationalistic intentions, and I get to eat double loses on down years because the government is still gonna expect its cut.
Where do I sign up?

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