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I'm relatively new to investing, and although I have a general understanding of how traditional and Roth IRA's work, I do have one question. Has anyone done a mathematical comparison of the difference between taxation upon withdrawal (traditional IRA) and taxation before contribution (Roth IRA)? I would imagine that would have some effect on the capital gains over time, but I can't figure out exactly what the difference would be. Is anyone aware of a resource that shows the differences with early and late taxation?
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Has anyone done a mathematical comparison of the difference between taxation upon withdrawal (traditional IRA) and taxation before contribution (Roth IRA)?

Lots of folks have.

Basically, this is an arbitrage decision. Is your tax rate when the IRA money is withdrawn going to be more or less than your current tax rate? If the current rate is higher, defer the taxation and go with the traditional. If the future tax rate is higher, pay the taxes now and go with the Roth.

This assumes that any tax savings related to a traditional IRA are also saved and invested. If that doesn't happen, you get a significant bias toward the Roth.

The big problem is that proper application of this formula requires knowledge of the future. My staff swami just quit, so I can't help with predicting the future. The best we can do is make educated guesses. And your educated guess may be different from my educated guess.

--Peter
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Lets assume you are 30, contribute 4K a year, and retire at 65. Lets also assume your effective tax rate today is 20%, and when you retire it drops to 15%, and you can earn 11% on the money.

With the IRA you will end up with 796,084 and the ROTH 636,867 (because you only put in 3.2K per year due to taxes.)

Now let us assume that you will withdraw every cent of the money. With the IRA, you will end up with 676,671.

The ROTH you will still have the 636,867.

In this simulation you are better with the IRA. The higher your current tax rate, the better you are off with the IRA. 20% may be too low, because that money is taxed at the highest rate rather than the average rate. If you bumb the rate up to 25%, the ROTH comes out at 597,063.

I guess you have to do that kind of math to figure it out. Heck it surprised me.

In order for the choices to be equal, you have to have a retirement tax rate of 20% and 25% respectively.

Wow, thanks for asking that question.
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In addition to having to make assumptions about unknowable future events, there are several other problems with trying to do a mathematical model of which is best there are several other problems with mathematical models.

1) The consequences of making an incorrect choice is not symmetrical. By this I mean that if you choose the Roth and end up having low income in retirement, the lack of money could have severe consequences. If you choose the Traditional IRA, and end up very wealthy in retirement, then the higher taxes could cause you to have to take a shorter cruise for your vacation.

2) In all likelihood, there isn't a correct choice and the real answer is to have a mixture of both.

3) The right type of account when you are 65, may not be the right choice when you are 95 and have drawn down most of you retirement savings. Assuming that you have a paid off house when you retire, once you start slowing down in your 70's then, other than medical expenses, you really won't need that much income live on while you health is reasonably good.

4) If you end up with excess money in a traditional IRA, you can roll it into a Roth when you are retired and have years where you are in a low tax bracket. You can't do the opposite if you end up with too much in a Roth.

My approach has been to focus on the Tradition IRA and 401k early in my savings because I could save more because of the tax deduction. I considered this my core savings to cover my basic needs in retirement.

Greg
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I'm relatively new to investing, and although I have a general understanding of how traditional and Roth IRA's work, I do have one question. Has anyone done a mathematical comparison of the difference between taxation upon withdrawal (traditional IRA) and taxation before contribution (Roth IRA)? I would imagine that would have some effect on the capital gains over time, but I can't figure out exactly what the difference would be. Is anyone aware of a resource that shows the differences with early and late taxation?
--------------------

http://www.fairmark.com/rothira/decision.htm

Regards,
Bill
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The problem with the TIRA/ROTH comparisons is they assume that you always will take out the money in equal amounts for paycheck-like stream of income. Unfortunately, that's not the way it always goes. You may need a large lump sum to pay off your house, pay the entry fee into a retirement community, etc. Or if you're really flush, perhaps even to pay college tuition for a grandchild.

The point is, if you need to pull \$100k or more out of tax-deferred retirement funds all at once you will be in a high tax bracket no matter what. Pull \$100k out of a Roth and there should be no tax issues.

For that reason, I fund my Roth fully every year and fund my 401k to the extent I'm able. Most of the money from a previous job's 403b has been rolled into an IRA. I've never had a TIRA except for the rollover.

Guby
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Oops! Forgot to check back for replies. Thanks everyone for the insight! That helped a lot, and I think I understand a little better now.