Tax-advantaged accounts: how they work

A tax-advantaged account is a container, not an investment. The same index fund, bond fund or cash deposit can sit inside one or outside it and it behaves identically either way: the same holdings, the same returns, the same risk. What changes is how the tax code treats what happens inside.

Every such account pulls at least one of three levers:

• A deduction on the way in. The contribution comes out of income before income tax is worked out, so the money arriving in the account is money you were never taxed on. Those are pre-tax dollars.
• A shelter on the growth. Interest, dividends and realised gains inside the account are not taxed in the year they happen, so nothing leaves the balance along the way.
• An exemption on the way out. A qualified withdrawal is not taxed at all.

In the United States the two big families pull different combinations. Traditional accounts, meaning a traditional 401(k) or a traditional IRA, pull the first two levers: contribute before income tax, shelter the growth, then pay ordinary income tax on withdrawals. Roth accounts pull the last two: no deduction now, shelter the growth, take qualified withdrawals untaxed. A health savings account is the unusual one that pulls all three at the federal level, for someone enrolled in a qualifying high-deductible health plan and spending the money on qualifying medical costs. A couple of states tax it anyway, which is the shape of this whole subject: a federal rule with local exceptions.

Education accounts such as a 529 sit in the middle, with no federal deduction but sheltered growth and untaxed qualified withdrawals, and many states add a deduction or credit of their own.

The arithmetic below travels. The account names do not. Other countries run the same two mechanisms under their own rules, including ISAs and pensions in the United Kingdom, the TFSA and RRSP in Canada, and superannuation in Australia. Some of them shelter less completely than the United States accounts described here, because the fund itself pays tax on its earnings, so the second lever is worth checking rather than assuming.

Most attention goes to the deduction, because it shows up on this year's tax return. The shelter on the growth is usually worth more, and it never appears on any return at all.

In an ordinary taxable account, part of the return is taxed as it arrives instead of being left to compound. Interest and non-qualified dividends are taxed in the year they are paid, and gains are taxed in the year they are realised. Whatever goes to tax stops compounding, and it stops compounding for every year that follows, which is what turns a small annual leak into a large gap over decades.

Put $4,680 of already-taxed money into a sheltered account returning an assumed 7 percent a year and after 30 years it holds $35,625.35. Put the same $4,680 into an account whose whole return is taxed each year at 22 percent, so it compounds at 5.46 percent instead of 7 percent, and it holds $23,061.04. Same investment, same gross return, same money in. The wrapper ends about 54 percent ahead, and not one cent of that came from a deduction. That 54 percent is the top of the range rather than a typical result, because it assumes every dollar of return is taxed in the year it arrives.

Two qualifications keep that honest. A taxable account holding a fund you never sell pays no tax on unrealised gains, so real taxable accounts sit between those two lines rather than on the lower one, and the more of the return that arrives as taxable income each year, the closer to the lower line they sit. And in the United States, long-term gains and qualified dividends are usually taxed on a lower schedule than ordinary income, which softens the drag for a buy-and-hold investor and leaves it at its worst for interest.

The compound interest calculator above will run both lines for you. Enter the full return, then enter the after-tax return, and the gap between the two totals is the most the wrapper can be worth on those assumptions.

Here is the result that surprises people. If your tax rate is the same when you contribute and when you withdraw, tax-deferred and tax-exempt accounts produce exactly the same amount. Not roughly the same. Exactly.

Take $6,000 of income, an illustrative 22 percent tax rate and an assumed 7 percent a year for 30 years. Both rates are stand-ins chosen to keep the arithmetic readable, not predictions, and bracket rates in particular are rewritten by legislation.

• Deferred. The whole $6,000 goes in, because no income tax was charged on it. It grows to $45,673.53. Income tax then takes 22 percent of the withdrawal, leaving $35,625.35 to spend.
• Exempt. Tax is charged first, so $4,680 goes in. It grows to $35,625.35, and nothing is taken out at the end.

Both routes multiply the same starting figure by the same two numbers, a growth factor of 7.612255 and a tax factor of 0.78, and multiplication does not care about the order. $6000 \times 7.612255 \times 0.78$ and $6000 \times 0.78 \times 7.612255$ are the same expression written twice.

That is also why the comparison people usually run is the wrong one. Putting $6,000 into a traditional account and $6,000 into a Roth account is not the same trade, because the first is pre-tax income and the second is post-tax income, so the Roth version costs more of your pay to fund. A fair comparison either starts from the same gross income, as above, or contributes $6,000 to each and invests the deferred account's tax saving as well. Skip that step and the deferred account looks better than it is, because part of the deduction has quietly been spent.

Which leaves exactly one question worth arguing about: is the rate the same at both ends?

Once the growth is sheltered either way, the whole difference comes down to two rates: the rate the deduction saves you now, and the rate the withdrawal costs you later.

The rate going in is your marginal tax rate, because a deduction comes off the top slice of your income. The rate coming out is often not a single marginal rate at all. Under a progressive income tax, such as the federal income tax in the United States, withdrawals that make up most of your income in a later year refill the schedule from the bottom: some is covered by the standard deduction, some falls in the lowest bracket, and only the top of it meets a high rate. So the honest comparison is a top-slice rate now against something nearer an effective tax rate later.

The arithmetic answers sharply. Hold everything from the last example and change only the rate at withdrawal, from 22 percent to 12 percent. The deferred account now leaves $40,192.71 rather than $35,625.35, about 13 percent more, from an investment that did not change in any way. Reverse the two rates and the exempt account wins by the same mechanism, in the same proportion.

Stated plainly: contributing before tax comes out ahead when the rate at withdrawal is lower, contributing after tax comes out ahead when it is higher, and the two tie when the rates match. Everything else is detail.

Nobody knows their future rate. It depends on how much income arrives in the same year, on where you live, on what other retirement income lands alongside it, and on tax law that gets rewritten. That is why holding some of each is usually described as a hedge rather than a fudge. It splits the bet instead of settling it, and it leaves a second source to draw on in a year when pulling more from a deferred account would be expensive. Which mix suits a particular person turns on facts this page does not have, so what follows is the arithmetic behind the decision rather than the decision.

The order-does-not-matter result assumes one contribution, one rate at each end and no other rules. Real accounts add frictions, and almost all of them push one way rather than both.

• An employer match is extra pay, not a rate of return. Where a plan matches contributions, the match adds money once, at the moment of contribution. It is a large one-off addition rather than an annual return, and describing it as a percentage return invites the mistake of compounding it. It is not untaxed either: in the United States a match has usually landed on the pre-tax side and is taxed as ordinary income on the way out, although plans may now offer a Roth match instead. Vesting rules decide when it is genuinely the employee's.
• Contribution limits are written as nominal amounts, which favours the exempt account. Filling a nominal limit with post-tax money shelters more spendable value than filling the same nominal limit with pre-tax money, because the pre-tax version has a tax bill packed inside it.
• Eligibility is not symmetric either. In the United States the ability to contribute to a Roth IRA phases out above certain incomes, and the deduction for a traditional IRA phases out for someone already covered by a workplace plan. Those thresholds move with legislation and with inflation adjustments, so they are figures to look up at the time rather than to carry around.
• Deferred money has to come out eventually. In the United States, traditional balances face required withdrawals from a set age, because the tax was postponed rather than cancelled. That age has been moved by legislation more than once, so treat it as a rule to look up rather than one to memorise. Roth accounts largely escape this for the original owner, which is part of what the exempt side buys.
• Reaching the money early is expensive. Early withdrawals from retirement accounts generally trigger ordinary income tax plus an extra penalty, subject to a list of exceptions. The tax advantage is paid for partly in access. And qualified is a defined term rather than a description: for a Roth account it turns on reaching a set age and on the account having been open a minimum number of years, so a young account is not automatically untaxed on the way out.
• The deduction only counts if it is invested. Spend the tax saving from a pre-tax contribution and the deferred account was funded with less money than the exempt one, so it finishes behind.
• Deferred withdrawals are ordinary income. A gain that would have been taxed as a long-term capital gain in a taxable account comes out of a traditional account as ordinary income, which in the United States is usually the higher schedule. Sheltering can convert the character of a return as well as its timing.
• Retirement income feeds other calculations. A withdrawal can raise income-linked amounts elsewhere, so its true marginal cost is sometimes above its bracket rate.

None of these change the arithmetic. They change which account the arithmetic should be run on.

A deferred balance and an exempt balance are quoted in different currencies, and no statement mentions it.

$45,673.53 in a traditional account is a pre-tax figure, and what it can buy depends on a rate nobody has set yet. $35,625.35 in a Roth account is already spendable. Ranking two retirement statements by the number printed at the top therefore flatters the deferred one by roughly the tax rate that will eventually apply to it.

Two habits fix that, and both work with the calculator above:

• Grow first, then tax. Run the contribution and the full expected return through the compound interest calculator, then multiply the deferred result by one minus the rate you expect at withdrawal. That product is the figure to hold against an exempt balance.
• Or shrink the contribution instead. Enter the after-tax contribution, apply no tax at the end, and the result is already comparable. Both routes give the same answer, which is the point of the section above.

One further adjustment belongs here. Every figure on this page is in nominal money, and a withdrawal decades away buys whatever prices allow then rather than what they allow now. Running the same contribution at an inflation-adjusted return, which the real return calculator produces, restates the ending balance in today's spending power, and that is the version worth setting beside today's expenses. Tax and inflation are two separate deductions from the same headline return, and a plan that accounts for one and ignores the other is only half built.