Would an immediate annuity work for you?

— -- You may remember word problems in high school, which asked you questions like this:

Ralph leaves Philadelphia on Amtrak averaging 23 miles an hour. What time does he hit the bar car?

But here's a real-life problem we all must solve:

You have $500,000. You could live three minutes after you retire or 45 years. Your returns could average 20% to -20% a year. How much can you safely withdraw from your retirement account each month?

Please be sure to check your answer.

The essential problem with planning for retirement is that you have too many utterly unknowable variables. For that reason, you might want an immediate annuity, which gives you predictable income over your lifetime. But don't buy one yet.

In its simplest form, an immediate annuity is a contract with your insurance company. You pay the insurance company a lump sum — say, $100,000 — and the insurance company agrees to pay you a monthly amount for life. According to ImmediateAnnuities.com, the average 65-year-old male would get $598 a month for life from a $100,000 deposit.

Financial planners typically advise that you take about 4% a year from your savings if you want your money to live longer than you do. At that rate, you'd pull $333 a month from a $100,000 account. So an immediate annuity would give you a larger payout than a conservative withdrawal strategy.

Naturally, there's a catch. In the simplest form of annuity, your heirs get nothing if you get hit by the 5:19 Cannonball a year after signing the contract. The insurance company gets the unpaid balance.

Pocketing those unpaid balances is one way insurers can offer a higher payout than the 4% rule. Your insurer doesn't know when you will die. But in a given pool of 100,000 annuitants, the insurer knows that half will die before they reach median life expectancy, and half after. Money from those who die early go to those who live longer than expected.

Insurance companies offer many different payout options, but those options generally lower your payout. For example, suppose our 65-year-old man had a 65-year-old wife, and they wanted payouts to last as long as they both live. In this case, the payout would shrink to $501 a month, nearly $100 less, in large part because women tend to live longer than men.

Now let's say our 65-year-old annuitant wanted payments to continue for his spouse, and the remaining cash — if any — to go to their beneficiaries. The payout would then fall to $484 a month.

Finally, let's say that Mr. Annuitant wanted his payments to rise with inflation, a reasonable request. Inflation erodes the value of a fixed payment. If he had a $500 monthly payout and inflation was 3% a year, his payment's buying power would fall to $207 in 30 years.

But an inflation rider isn't cheap. Consider an inflation-adjusted annuity through Vanguard (and issued by American General Life Cos.) for a 65-year-old man, with no payments to beneficiaries. Starting payout for a $100,000 contract: $433 a month.

As we saw earlier, a $100,000 payment without an inflation adjustment would pay $598 a month. If inflation were 3% a year, it would take about 12 years to get above $598 a month. It would take much longer to get the same amount of money from the inflation-adjusted annuity as you do from the one with no inflation-adjusted one.