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CalcMax

IRA Calculator

Range: 0 – 10,000,000

Range: 0 – 100,000,000

Range: -20 – 30

Range: 1 – 60

Range: 0 – 100

Range: 0 – 100

Result

448,896.18

Final balance

Balance after tax
350,139.02
Tax saved while contributing
38,500.00
Total contributions
185,000.00
Investment earnings
263,896.18

An IRA calculator is usually asked one question and answers another. The question is what the account will hold; the answer that matters is how much of it is yours after the tax has been paid, and those two figures are one tax rate and several decades apart. This page models a traditional IRA — contributions go in before tax, nothing is taxed inside the account, and the withdrawal is taxed as ordinary income once it comes out — and it reports both ends of that: the balance your retirement savings grow to, and the after-tax balance the withdrawal leaves behind. It also reports the tax the deduction saved you while contributing, which is the figure people instinctively compare against the second one and are routinely surprised by. The account is tax-deferred, not tax-free: the tax deduction is computed on what you paid in, while the bill is computed on everything the account has become, so the deduction is almost always the smaller of the two. The one thing that reverses that is retiring into a lower tax bracket, and the second table on this page exists to show how much that is worth.

10,000 to start, 7,000 a year, 6%, taxed at 22% on the way in and out

YearsBalance at the endTotal you put inTax saved while contributingAfter tax when you withdraw
10113790.25800001540088756.4
15194185.1811500023100151464.44
20302625.915000030800236048.2
25448896.1818500038500350139.02
30646192.8622000046200504030.43
35912316.5225500053900711606.89
401271277.4729000061600991596.43

The two right-hand columns are the page in one line. The tax saved grows in a straight line, because it is a rate times contributions and nothing else; the tax on the way out grows with the balance, which is compounding. By forty years the deduction has saved 61,600 and the withdrawal costs nearly ten times that — at the same 22% rate on both ends.

The same 10,000, 7,000 a year and 6%, under different pairs of tax rates

Tax rate now (%)Tax rate when you withdraw (%)Balance at the endTax saved while contributingAfter tax when you withdraw
2212448896.1838500395028.64
2222448896.1838500350139.02
2224448896.1838500341161.1
2232448896.1838500305249.4
3212448896.1856000395028.64
3224448896.1856000341161.1
3232448896.1856000305249.4

Read down a column and the balance never moves: nothing about the accumulation depends on either rate, which is worth seeing plainly. What moves is the last column, and only ever by the gap between the two rates — the top block deducts at 22% and the bottom at 32%. The one row worth finding is the pair where the withdrawal rate is lower than the contribution rate: that is the case the traditional IRA is designed for, and on these figures it is worth about 45,000.

Formula

balance at the end = initial balance × (1 + i)^n + (annual contribution ÷ 12) × ((1 + i)^n − 1) ÷ i | after-tax balance = balance at the end × (1 − tax rate when you withdraw) | tax saved while contributing = annual contribution × years × tax rate now

Initial balance
What is already in the account on day one. It compounds for the whole term, so it is the only input whose contribution to the answer is entirely growth — nothing was ever deducted against it, and every dollar of it is taxed on the way out.
Annual contribution
The amount you put in over a year, as an absolute figure rather than a share of your pay. This is not how much lands in the account: for a traditional IRA the figure is pre-tax, which is the whole mechanism, so the account receives the full amount and the deduction is what makes it affordable. The statutory ceiling on this figure is not enforced here, for the reason in the limitations.
i
Return per period — the annual return divided by twelve, since contributions are spread evenly through the year and earn only for the periods remaining after each one. It is a nominal expected return rather than an APY, on the same reading as the goal page on this site and deliberately the opposite of the savings page, where a bank rate is assumed to already contain its compounding.
n
Number of periods — years times twelve, the same clock the contributions run on. Because both the initial balance and the contributions use it, extending the term raises the balance roughly geometrically while leaving everything the deduction depends on untouched.
Tax rate now
The rate at which the contribution is deducted, which is your marginal rate in the years you contribute. It sets the size of the deduction and nothing else — the balance is the same whatever you enter here, which is exactly why the second table has to hold the balance fixed while the rates move.
Tax rate when you withdraw
The rate applied to the whole balance as it comes out, including every dollar of growth that has never been taxed before. This is the number that decides how much of the account was ever yours, and it is the one nobody knows at the time they are contributing.

Use it to see what a contribution actually buys, rather than what it grows to. It is the right page for asking whether a deduction taken at today's rate is worth a withdrawal taxed at some future one, and the right page for seeing that a balance figure quoted without a withdrawal tax rate is not a number anyone can spend. It is not a page for deciding how much you are allowed to contribute — that is a rule about eligibility, and this page models none of it.

Worked examples

  1. The default case

    1. Periods: 25 × 12 = 300. Rate per period: 6% ÷ 12 = 0.5%.
    2. Growth factor: 1.005^300 = 4.46497.
    3. The 10,000 already in the account becomes 10,000 × 4.46497 = 44,649.70.
    4. Annuity factor: (4.46497 − 1) ÷ 0.005 = 692.994.
    5. The contributions are 7,000 ÷ 12 = 583.33 a month, worth 583.33 × 692.994 = 404,246.48 at the end.
    6. Balance: 44,649.70 + 404,246.48 = 448,896.18.
    7. You put in 10,000 + 7,000 × 25 = 185,000; growth is 448,896.18 − 185,000 = 263,896.18.
    8. Deduction at 22% on 175,000 of contributions: 7,000 × 25 × 0.22 = 38,500.
    9. Withdrawal at 22% of the whole balance: 448,896.18 × 0.78 = 350,139.02.

    The 38,500 saved is 11% of the 98,757.16 the withdrawal costs. Both come from a 22% rate, and they still differ by nearly nine to one, because one is 22% of what you paid in and the other is 22% of what the account became.

  2. Retiring into a lower tax rate

    1. Nothing in the accumulation changes: the balance is still 448,896.18 and the deduction still saves 38,500.
    2. The withdrawal is taxed at 12%: 448,896.18 × 0.88 = 395,028.64.
    3. Compared with the default case, 44,889.62 more survives — which is 448,896.18 × 10%, the difference between the two rates.

    This is the case the traditional IRA is actually for, and it is the only one in which the deduction looks like a good deal. The entire gain is the ten-point gap between the two rates — not the compounding, which is identical in both cases.

  3. Retiring into a higher tax rate

    1. Balance and deduction are unchanged again: 448,896.18 and 38,500.
    2. Withdrawal at 32%: 448,896.18 × 0.68 = 305,249.40.
    3. Versus the default case, 44,889.62 less survives — the same ten points, now working against you.

    The symmetry with the previous case is the whole lesson: the deduction is worth 38,500 whether or not you ever get a lower rate on the way out, and a ten-point move in either direction is worth 44,889.62. The deduction on its own does not make the account a good deal.

  4. Contributing nothing after the first year

    1. The annuity term drops out entirely, leaving only the initial balance: 10,000 × 4.46497 = 44,649.70.
    2. Growth is larger than the original deposit: 44,649.70 − 10,000 = 34,649.70.
    3. No contributions means nothing to deduct, so the tax saved is 0.
    4. Withdrawal at 22%: 44,649.70 × 0.78 = 34,826.77.

    A single deposit left alone for twenty-five years nearly quadruples, and every dollar of the 34,649.70 it gained will be taxed on the way out even though no part of it was ever deducted. That is deferral: the tax was not avoided, only postponed, and the postponed amount grew with the account.

  5. A zero return

    1. With no growth the balance is simply what went in: 10,000 + 7,000 × 25 = 185,000.
    2. Growth is 0, so the whole withdrawal is the money you contributed.
    3. The deduction still saves 7,000 × 25 × 0.22 = 38,500 — the deduction does not depend on the return at all.
    4. Withdrawal at 22%: 185,000 × 0.78 = 144,300.

    Here the account is taxed twice on the same dollars in the only sense that matters: 38,500 came off the way in and 40,700 goes out, on contributions that never earned anything. A deduction taken at one rate and repaid at the same rate is a loan, not a benefit — and with no growth, nothing else is going on.

Limitations

The statutory annual contribution limit is not enforced. Real traditional IRA contributions are capped each year (with a catch-up amount above a certain age, and a phase-out when you are covered by a workplace plan), and amounts over the limit are not deductible — the IRS page in the references has the current figures. This page takes whatever you type, because the limit is a rule about eligibility rather than about what a contribution turns into, and the arithmetic is identical on either side of it. Contributions are spread evenly through the year rather than made in one lump. Real IRA contributions are often made in a single deposit near the filing deadline and can be back-dated to the previous tax year, so this page slightly understates the balance; the effect is days-to-months of growth on one year's contribution, far smaller than the decades the page is actually about. One rate now and one rate at withdrawal is a simplification of a lifetime of brackets. A progressive schedule, a move between states, and a retirement income that changes as accounts are drawn down all mean the effective rate varies year by year, whereas this page applies a single flat rate to the whole balance. State and local income tax is not modelled, and in places where the deduction does not exist or the withdrawal is taxed differently, the after-tax figure will be wrong in a direction this page cannot tell you. The additional tax on distributions taken early is not modelled. A distribution before age 59½ generally carries an extra tax on top of the ordinary income tax, subject to a list of exceptions that Publication 590-B sets out — this page computes an ordinary withdrawal only. Required minimum distributions are not modelled either. A traditional IRA must begin distributing at a set age whether or not you need the money, so the deferral modelled here has an end date the page does not show; the RMD page on this site covers that part.

Frequently asked questions

Is the money in an IRA tax-free?
No, and the distinction is the whole page. A traditional IRA is tax-deferred: the contribution is deducted when it goes in, nothing is taxed while it is invested, and the entire balance — contributions plus every dollar of growth — is taxed as ordinary income when it comes out. Nothing was forgiven; the bill was moved, and by the time it arrives the balance is several times what was contributed, so the tax is levied on several times as much.
Why is the tax I saved smaller than the tax I pay?
Because the two are percentages of different things. The deduction is a percentage of what you paid in, while the withdrawal tax is a percentage of what the account became. At a steady 22% on the default case, the deduction is 38,500 and the tax is 98,757 — a ratio of about one to two and a half, purely from the fact that the balance is two and a half times the contributions. Same rate, different base. That is the entire meaning of the word deferral, and it is what makes the comparing of the two figures misleading unless you notice the bases.
Does this page enforce the annual contribution limit?
No. Real traditional IRA contributions are capped each year, with a catch-up amount for older savers and a phase-out of the deduction when you are covered by a workplace plan, and the IRS page linked in the references has the current numbers. This page takes any figure you enter, because whether you are allowed to contribute is a different question from what a contribution becomes — and on the second question the limit changes nothing. If you are checking what you are allowed to put in, that is a tax question, not a compounding one.
What if I take the money out early?
This page computes an ordinary withdrawal and does not model the extra tax that generally applies to a distribution taken before age 59½, which comes on top of the ordinary income tax and is subject to a list of exceptions. Publication 590-B has both the rule and the exceptions. The effect is one-directional — it makes an early withdrawal worse than the figure shown here — so treat the after-tax balance as a best case if the money is coming out early.
Should the tax rates be marginal or average?
Both figures are single flat rates applied to a whole amount, which is a simplification of a progressive schedule. Strictly, the deduction is worth your marginal rate in the year you contribute, while a withdrawal large enough to fill several brackets is taxed at a blend. Entering your marginal rate for the first and a blended estimate for the second is the closest you can get here; entering your average rate for the first understates what the deduction is worth.
Why is the contribution an amount rather than a percentage of my salary?
Because an IRA contribution has no proportional relationship to pay. The 401(k) page on this site takes a percentage, since that is how a workplace plan is normally expressed; an IRA is expressed as a figure, and its shape is a statutory ceiling rather than a share of earnings. The two pages are otherwise the same cash flow — set the employer match on the 401(k) page to zero and take away the salary percentage, and you have this one.
How is this different from the 401(k) calculator?
The employer match, and the shape of the contribution — that page takes a percentage of salary and adds a match, this one takes a figure and adds nothing. The tax treatment is the same for both, which is why the balance here and the balance there agree exactly once the match is zero. What differs is the ceiling: a 401(k) has a much higher statutory limit than an IRA, so the practical question of how much can go in is answered differently even though the arithmetic of what it becomes is not.

References

Related calculators

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