Five things that people get wrong about retirement arithmetic.

There is something about retirement that leaves investors in an arithmetic fog. Maybe it’s the marginal tax rate or the compounding or the deferral that gets their numbers all jumbled up. Here are five things that people get wrong about IRAs and 401(k)s, usually because they are getting bad advice.

Bad advice #1: Your tax rate will be lower in retirement.

It probably won’t. Five factors will keep your bracket high in coming decades:

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—The federal government is spending money at a furious pace, and will eventually run out of rich people to soak.

—States are in sick shape and will be raising rates.

—The tax code tends to phase out tax deductions and exemptions, with the side effect of magnifying marginal rates for taxpayers in the phase-out range. This problem will get worse; Congress needs those phase-outs to pay for the goodies. The bracket creep will perhaps begin with the revival of the rate-boosting Pease and personal exemption rules in effect before 2018.

—Medicare premiums are set in a way that surtaxes retiree incomes.

—The cut-off points for the taxation of investment income and Social Security benefits are not adjusted for inflation. So over the years you could get pushed from a low-tax region into a high-tax one.

If you build your long-term planning around a cavalier assumption about lower rates, you’re making a mistake. Unless circumstances dictate otherwise (for example, you’re planning a move from California to Texas), make the neutral assumption that your marginal rate will stay put.

Bad advice #2: If you are temporarily in a lower bracket, you should take extra money from your IRA.

The following nonsense is being published by, believe it or not, a CPA firm: “If you’re a senior, withdraw money from your traditional IRAs sooner and faster than is necessary to comply with the required minimum distribution rules. That way, you pay taxes now at rates that may look low a few years later.”

No. If you’re temporarily in a low bracket, don’t make an extra withdrawal; instead, move some of that pretax IRA money into a Roth account.

Bad advice #3: IRAs turn capital gains into ordinary income.

No they don’t. But it’s easy to get tripped up here. Capital gains do pile up inside the account, and all withdrawals are taxed as ordinary income.

But what’s really going on? Say you’re in a 30% bracket (state and federal combined). Your IRA has a balance of $100,000 and you think this money is yours. It isn’t. The truth is that you have $70,000 in the account and you are also acting as custodian for $30,000 of government funds.

Suppose that capital gains, dividends and interest double the account. Apparent balance: $200,000. Reality: Your $70,000 has doubled in value to $140,000, and the tax collectors’ sum has doubled to $60,000.

Which is to say, your $70,000 has enjoyed $70,000 of investment gains, all untaxed. Your tax rate on the dividends was 0%, on the interest 0% and on the capital gains 0%.

My quarrel with the bad advice is not merely semantic. There are people who underfund their 401(k)s, figuring they can buy stocks outside the plan and pay favorable rates on the capital gains. When they do that they are paying tax they don’t have to pay.

Bad advice #4: The 3.8% investment surtax doesn’t apply to IRAs.

Another easy mistake to make. The Obamacare tax is levied on dividends, interest and capital gains earned outside retirement accounts. It ostensibly does not apply to either IRA withdrawals or conversions of IRA money to Roth money.

But look at the formula. The tax is on the lesser of investment income or the amount by which all income exceeds $250,000 (on a joint return). If you have $200,000 from salary and $30,000 from dividends, there’s no surtax; throw in a $50,000 Roth conversion and the dividends get taxed. In effect, $30,000 of the $50,000 conversion gets hit with the 3.8% tax.

Bad advice #5: It’s easy to be an IRA millionaire.

Typical mischief of this sort is a calculation, published a year ago, declaring that if you start at age 30 and put aside a mere $4,925 a year you will get to $1 million by the time you’re 67. Assumption: an 8% annual return.

That return expectation is preposterous.

What matters, of course, is not nominal returns (what you see in your brokerage statement) but real ones: growth in spending power. A reasonable expectation for the real return on stocks over the next several decades is more like 3%.

Yes, stocks have done way better than that over the past 40 years. Lucky you if you were just starting your career in 1981 and you’re retiring today. But today’s youngsters can’t expect a repeat.

Stocks have done well since 1981 because they went from trading at a very low multiple of earnings to trading at a very high multiple. Even if multiples remain at their lofty level, they are bad news for new investors. They dictate that a dollar put in today commands scarcely 3 cents of corporate earning power, and it’s that 3% return that determines how fast stock portfolios compound. For a fuller explanation, see Why High Stock Prices Are Bad For Future Retirees.

Let’s use a 3% return, and have you (or your employer) put in $19,500 a year, keeping the contribution up with rising prices. Then you get to $1 million of today’s purchasing power in 31 years. That $1 million would finance a $40,000-a-year retirement. Nice, but not a rose-strewn stroll to wealth.

Savers usually throw a few bonds into the mix, especially as they get older. The cautious stance lowers expected returns.

You don’t have to guess what the real return on safe Treasury bonds will be over the next 30 years; you can look it up. It’s -0.2%. With some of those things in your account you’ll earn less than 3% overall, and you’ll either have to put in more than $19,500 a year, or stick with your job for more than 31 years, to get to $1 million.

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