Fixing Welfare

I seem to get my best thoughts while in my car. On the way to work this morning, I had another perfect solution. Once again, the White House refused my call. It could be because it was 4 a.m., but I really am beginning to see a pattern here.
anyway....
I have a proposal that would affect the way we handle welfare/unemployment/even social security.

My proposal is that the government gives every newborn a savings account, depositing $10,000 into it. With a half-way normal amount of interest, the 10K should turn into about 30K by the time the 'child' is 21, 100K by the time the 'child' is 40, and nearly a quarter of a million dollars by the time the child retires. At retirement, the governement gets their entire 10K investment back, and the citizen gets to use the rest of the money to supplement his/her retirement.
In between 21 and 65, this money is earmarked to be used to supplement income during times of unemployment. Think about it: a man is 40, making 60K a year, and loses his job. Currently, he would make 66% of his wages for about a year, until unemployment runs out. Then, he either has to take whatever job he can find, or lose everything. Under my program, he would be able to take another job at less money...say 50K a year, and be able to dip into his "fund" and draw an extra 10K/year out of his fund for a set number of years, while he adjusts his payments and lifestyle to the new income level.
The key is that once the fund is gone, it is gone. If someone chooses to use it all during times of unemplyment during their 20's (when the value of the fund is still pretty low), then that is all there is. No more welfare, no more public aid. If someone is vigilant and uses the money wisely, they retire in additional comfort.
Because the original investment is returned to the government upon retirement, the program actually costs the government next to NOTHING.
There. next problem?