What makes a Roth IRA different from a savings account
A Roth IRA is an ordinary investment account wrapped in a tax exemption. You fund it with money you have already paid income tax on, it grows without generating any annual tax bill, and a qualified distribution comes out entirely untaxed under Internal Revenue Code §408A. There is no deduction going in and no tax coming out — the deal is that the government forgoes tax on everything the account earns in between.
That middle part is where the value sits. In a taxable brokerage account, every dividend, every bond coupon and every realised gain generates a tax bill in the year it occurs, and paying that bill removes capital that would otherwise have compounded. The loss is not the tax itself but the growth on the tax, and on the growth on the tax, repeated for every year of the horizon. Economists call it tax drag, and it is why a modest-sounding annual rate difference turns into a very large terminal difference.
The calculator quantifies the drag by running the same after-tax dollars, at the same gross return, through two comparison accounts. The first assumes all investment income is taxed each year at your marginal rate — the right model for bonds, for cash, for non-qualified dividends and for an actively traded fund. The second assumes you buy an index fund, never trade it, and pay long-term capital gains tax once when you sell at the end. Real taxable portfolios fall between those bounds, so read them as a range rather than a point estimate.
The word qualified is doing real work in "qualified distribution". Earnings come out tax free only if you are 59½ or older and the Roth has been open for at least five tax years. Your own contributions are different: they can be withdrawn at any age, at any time, free of tax and free of the additional tax, because you already paid tax on those dollars.
The two halves of the projection
The projection is the standard future-value expression, and it has two independent parts because your money arrives in two different shapes. The balance you already hold is a lump sum, so it grows by the compound factor (1 + r)^n. Your future contributions form an annuity — a stream of equal payments — and their combined future value is C · [((1 + r)^n − 1) / r], the factor that finance texts tabulate as FVIFA.
Understanding why that annuity factor takes that shape is worth a minute. A contribution made in the first year compounds for n − 1 years; the one made in the final year does not compound at all. Sum (1+r)^0 + (1+r)^1 + … + (1+r)^{n−1} — a geometric series — and it collapses to exactly ((1+r)^n − 1)/r. At r = 0 that expression is 0 ÷ 0, so the calculator substitutes the limiting value C·n, which is simply the total of your deposits.
Contributions are treated as arriving at the end of each year. That is the conservative convention: if you fund your IRA in January instead of the following April, each contribution earns roughly one extra year of return, and your real balance will run a few percent above this projection. If you want the optimistic bound, multiply the annuity term by (1 + r).
The comparison accounts reuse the same machinery. The yearly-taxed account grows at r(1 − t) rather than r, because the tax collector takes a fixed share of each year's return before it can compound. The buy-and-hold account grows at the full r and pays capital gains tax once on the terminal gain, so its formula is FV − t_cg(FV − basis).
Worked example: $7,000 a year for 30 years at 7%
Take a saver who opens a Roth IRA with nothing in it, contributes $7,000 at the end of every year for thirty years, and earns 7% a year. Their marginal rate on investment income is 22% and their long-term capital gains rate is 15%.
- Compound factor. 1.0730 = 7.612255.
- Annuity factor. (7.612255 − 1) ÷ 0.07 = 6.612255 ÷ 0.07 = 94.460786.
- Roth balance. 7,000 × 94.460786 = $661,225.50.
- Money in. 7,000 × 30 = $210,000.
- Tax-free earnings. 661,225.50 − 210,000 = $451,225.50. More than two thirds of the final balance is growth that never gets taxed.
- After-tax rate in the taxed comparison. 7% × (1 − 0.22) = 5.46%.
- Comparison annuity factor. 1.054630 = 4.927575, so (4.927575 − 1) ÷ 0.0546 = 71.9336.
- Yearly-taxed balance. 7,000 × 71.9336 = $503,535. The Roth advantage is 661,225 − 503,535 = $157,690, or about 31% more spendable money.
- Buy-and-hold balance. Same $661,225.50 of growth, minus 15% of the $451,225.50 gain: 661,225.50 − 67,683.83 = $593,541.67.
The two comparison figures bracket the answer. A taxable portfolio of individual index funds held for decades lands near the upper figure; one full of bond funds and actively managed strategies lands near the lower. The Roth beats both, and the margin widens with every year you extend the horizon.
Reading the result, and the traps in it
Look first at the split between contributions and earnings. Early in a Roth's life the balance is mostly your own money and the tax exemption is worth almost nothing; the exemption only becomes valuable once earnings dominate. In the thirty-year example above, earnings are 68% of the balance. Over ten years at the same rate they are barely 30%. That is the entire argument for opening a Roth early even with small contributions — you are buying tax-free treatment of growth that has not happened yet.
Second, remember that the balance is in future dollars. A $661,000 projection thirty years out, at 2.5% inflation, is worth 661,000 ÷ 1.02530 = about $315,000 in today's purchasing power. If you would rather see the whole projection in today's money, enter a real return — roughly your nominal expectation minus expected inflation — and read every output as inflation-adjusted.
Third, the Roth advantage figure is sensitive to the comparison tax rate in a way that is easy to over-read. It answers a narrow question: what would the same dollars have become in an account that pays tax annually at that rate? It does not answer whether Roth or pre-tax contributions are better for you, because that comparison turns on your tax rate now versus in retirement, not on the drag. Use the traditional versus Roth comparison calculator for that decision.
Finally, treat any single-number projection with suspicion. Markets deliver sequences, not averages. Run the calculation at 5% and at 9% as well as your central case; the band you get is a more honest picture of what a thirty-year projection can tell you than any single figure.
What a maxed $7,000 annual contribution becomes
| Years contributing | At 5% | At 6% | At 7% | At 8% |
|---|---|---|---|---|
| 10 years ($70,000 in) | $88,045 | $92,266 | $96,715 | $101,406 |
| 20 years ($140,000 in) | $231,462 | $257,499 | $286,968 | $320,334 |
| 30 years ($210,000 in) | $465,072 | $553,407 | $661,225 | $792,982 |
| 40 years ($280,000 in) | $845,598 | $1,083,334 | $1,397,446 | $1,813,396 |
Every figure is tax-free at withdrawal if the distribution is qualified. Doubling the horizon from 20 to 40 years at 7% multiplies the balance by nearly five, while total contributions only double — that gap is compounding.
Two rules that decide whether earnings come out tax free
A Roth IRA distribution is qualified only when both conditions are met: you are at least 59½ (or the distribution is due to death, disability, or a first-time home purchase up to the $10,000 lifetime cap), and at least five tax years have passed since your first contribution to any Roth IRA. The five-year clock starts on 1 January of the tax year for which your first contribution was made, so a contribution made in April 2026 for tax year 2025 starts the clock on 1 January 2025. Miss either condition and the earnings portion is taxable as ordinary income and may attract the 10% additional tax under IRC §72(t); your own contributions still come out untouched, because Roth IRA distributions are ordered contributions first, then conversions, then earnings. Conversions carry their own separate five-year clock.
What this projection does not model
- Eligibility. Direct Roth contributions require earned income and phase out above a modified adjusted gross income threshold the IRS resets each year. Above the threshold, savers commonly use a conversion instead — with its own tax consequences and its own five-year clock.
- The contribution limit rising over time. The IRA limit is indexed in $500 steps, so a long projection at a fixed $7,000 understates what you will actually be allowed to contribute in later years.
- Sequence-of-returns risk. A constant return is a reasonable model for the accumulation phase and a poor one once you begin withdrawing, when the order of good and bad years matters as much as the average.
- Fees. Enter a return already net of fund expense ratios and any advisory fee. A 1% advisory fee on a 7% gross return is a 6% net return, which over 30 years costs roughly a sixth of the terminal balance in this table.
- State tax. The comparison account is modelled with a single federal-style rate. If your state taxes investment income, the real drag on a taxable account is larger and the Roth advantage understated.
- Required minimum distributions. A Roth IRA has none during the original owner's lifetime, which is one of its structural advantages over pre-tax accounts and over the balances projected by the 401(k) growth calculator.
Where the Roth IRA sits in a savings plan
The conventional priority order puts the employer match first, because nothing else returns 50 cents on the dollar instantly, and puts the Roth IRA next, ahead of unmatched 401(k) deferrals. The reason is not tax treatment but cost and control: an IRA at a low-cost provider gives you the entire investable universe, while a 401(k) gives you the menu your plan sponsor selected and charges plan-level fees on top of fund expenses.
Against a pre-tax 401(k) or traditional IRA, the Roth wins when your tax rate in retirement is higher than it is today and loses when it is lower — the mathematics is symmetric, and the break-even is precisely the point where the two rates match. Young savers, people in a temporarily low-income year, and anyone expecting a large pension or substantial required minimum distributions later usually come out ahead in the Roth. That comparison is worked out in full in the traditional versus Roth IRA calculator.
Against a taxable brokerage account, the Roth wins unconditionally on tax and loses on flexibility. Money in a taxable account is available at any time without conditions; Roth earnings are locked behind age and the five-year rule, and pulling them early costs both income tax and the 10% additional tax priced by the early withdrawal penalty calculator. Keep your emergency fund outside the Roth, or at least confine early access to the contribution layer.
If you are weighing an IRA contribution against a different use of the same money — paying down a loan, buying property, funding a business — the general time-value tools apply. The net present value calculator puts competing cash-flow streams on one basis, and the internal rate of return calculator tells you the annualised return the alternative must beat to be worth choosing.