"I'm ignoring the interest income but also ignoring the effects of inflation."
That's the error in the calculation right there. They simply aren't a wash. Yes, if your investment strategy is sticking the money in a savings account, saving 10% of your income is just not going to do you any good. But average investment returns exceed inflation by a few percent... and those few percent over a long enough time make a HUGE difference.
If you start saving in your early working years (in a tax-deferred plan) and set aside 10% of your income, you will actually find that your 401(k) will
more than "take the place" of Social Security and a pension. This assumes your investments average the market return of the last 50 years and inflation is around what it has been over the same period. ADD Social Security and a pension to that mix and you retire quite comfortably, likely quite a bit more comfortably than when you were working.
The key to the math is
time.
If you are currently in your mid 40's and haven't saved up anything substantial for retirement, you're right. There's almost nothing you can do to replace a lost pension or to match Social Security.
Now, when you talk about the cost of nursing homes? You are completely correct. No combination of SS,pension, and personal savings seems to make them look "affordable". There needs to be a better plan there.
Try playing around with the following calculator:
http://www.smartmoney.com/retirement/401k/index.cfm?story=plannerIf you start at age twenty with an income of $25,000 and your only raises equal inflation (so you basically earn this salary for your whole working life). Then you set aside 10% of your salary into a 401(k) until you retire at age 65 and assume an average return of 8% and average inflation of 3%. Take into account
no additional savings and no pension fund... and you have about $1.5Million - and can retire on your full (inflation adjusted $25,000) salary and it will last until you are in your mid 90's.
Add
either social security (which at that salary level replaces about 45% of your income) OR a pension if your company still has one (would probably equal less than 30% of final salary) and you can retire at
well above your life-long standard of living. Add them both and you're sitting pretty.
The critical factor is "time". Start the identical savings plan at age 45 and you will save a "whopping" 150K and your retirement savings will last from the day you retire until about age 72 even WITH social security.