What’s the typical income of a U.S. retiree? $40,000? $50,000? Higher, lower?

It’s $31,157 as of 2008.

That’s the median income of households age 65 and older as reported by Pat Purcell of the Congressional Research Service. The median means that half of older households had a higher income, half lower. Technically, it’s not the income of “retirees,” because it includes the income of older households whether they are fully retired or still working. Still, it’s a good metric of the income of retired Americans.

Switching to a slightly different set of statistics, from the Social Security Administration, about 8% of age 65+ households have incomes above $100,000, and about 12% below $10,000.

Most working people I know typically regard $31,000 as a surprisingly low figure for retirement income. Partly that’s because they’re generally well educated and well paid, and are thus hoping for a higher income in retirement. Yet the figure reminds me of a psychological element of retirement income: Even if you are substantially well prepared for retirement, with significant savings, the income you can derive from a given pool of savings may seem modest.

Call it the millionaire’s dilemma. Consider a hypothetical couple who have accumulated $1 million in retirement savings—on top of raising a family, buying a house, and sending some or all of their kids to college. Arguably this couple is one of the best prepared retirement households in the U.S. Assume “he” worked and “she” stayed home. To work with even numbers, assume he’ll be receiving Social Security of $20,000 a year, and she’ll receive a 50% spousal benefit of $10,000 a year. That’s a total of $30,000 of baseline income in retirement from Social Security.

Now, what about the million dollars? If our couple tilts their portfolio toward higher-yielding stocks and bonds, they might be able to generate an income yield of 3%, producing $30,000 a year in dividend income. They could also invest in a balanced strategy and use the 4% withdrawal rule, which helps minimize the risk of running out of money. That would yield $40,000 in the first year of retirement. In either of these two cases, their gross income in retirement is $60,000 to $70,000. This income puts them comfortably in the top quartile of retired U.S. households.

But many millionaires (and the nonmillionaires reading about them) might be surprised at the math. In order to accumulate $1 million, this couple probably was earning a regular six-figure income. They were probably not envisioning retiring on $60,000 to $70,000 a year.

So how does our millionaire couple get to a six-figure income in retirement? One option would be to convert the entire million dollars into a fixed annuity. It might pay $60,000 to $70,000 a year to a surviving couple, depending on their ages, interest rates, and other factors. That, plus $30,000 in Social Security, would put the couple at or near the six-figure level. It would also require the couple to lose permanent control of their assets, something they’d be unwilling to do. At most, they might annuitize a portion of the million dollars to boost guaranteed income. That would keep them shy of their six-figure income lifestyle.

Another alternative is for one of the spouses to have earned a generous public-sector DB pension plan (or generous private-sector pension, though these are growing less common). Let’s suppose the stay-at-home spouse had a better-paying government job with a pension paying $50,000 a year. (By the way, that’s nearly triple the typical public pension of $18,000 a year.) With both of them working, their total Social Security payments would now be, say, $40,000. Add to that the $50,000 pension, plus the $30,000 to $40,000 in income from the million dollars. They’re now in six-figure territory.

What’s the lesson here? It’s not about being a millionaire in retirement. I used $1 million just to keep the math even. You can convert the numbers to your own situation by dividing (or multiplying) by the appropriate factor.

The lesson is that, regardless of the size of your assets, each dollar of retirement savings in a portfolio could generate 3 to 4 cents in retirement income. In other words, you could expect 3% to 4% from a portfolio. You could double that rate to 6% to 7% for assets in an annuity contract, where you’ll need to give up control of your assets.

This is the new retirement math that most Americans, as they approach retirement, are coming to understand. Like the millionaire couple, many will be surprised by the income levels that a pool of assets can generate.

“Asset rich,” in other words, does not necessarily feel like “income rich.”

Note: Annuity product guarantees are subject to the claims-paying ability of the issuing insurance company.