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Traditional gets taxed upon withdrawal, which means that both your contributions as well as the growth of your investments gets taxed, with ROTH only the contributions get taxed, the growth is yours to keep in full in retirement.
In short, roth accounts pay less in taxes in the long run which lets you keep more of the money in them.
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I know the basics, I wanted a better explanation of why you think that. I don't think it works the way you think it is. I'm going to give you 3 basic scenarios that show the difference.
#1 Tax rates are equal during contribution and during retirement, lets say 25%
You have $5,000 to contribute
If you put it in a Traditional IRA/TSP you have $5k that grows at the market avg 8% for 40 years $108,622.61, upon withdrawal it's taxed at 25% leaving you with: $81,466.96
If you put it in a Roth IRA/TSP you are taxed up-front so you only put in $3750, that grows at the market avg of 8% for 40 years and you end up with: $81,466.96
#2 Tax rate during career is higher than retirement, lets keep career at 25% and retirement at 15%
If you put it in a Traditional IRA/TSP you have $5k that grows at the market avg 8% for 40 years $108,622.61, upon withdrawal it's taxed at 15% leaving you with: $92,329.22
If you put it in a Roth IRA/TSP you are taxed up-front so you only put in $3750, that grows at the market avg of 8% for 40 years and you end up with: $81,466.96
#3 Tax rate during retirement is higher, lets keep retirement at 25% and career at 15%
If you put it in a Traditional IRA/TSP you have $5k that grows at the market avg 8% for 40 years $108,622.61, upon withdrawal it's taxed at 25% leaving you with: $81,466.96
If you put it in a Roth IRA/TSP you are taxed up-front so you only put in $3750, that grows at the market avg of 8% for 40 years and you end up with: $92,329.22
As you can see, if we don't factor in other tax/income implications other than the basic tax rate, the 2 are completely equal. Your contribution is taxed up-front, or your withdrawals are taxed on the back end, it doesn't matter much which way it's done. The reason they are equal is because even though your withdrawals are tax-exempt on the back end with the Roth options the overall account balance you have to "grow" is reduced by taxes on the front end, which sets it back.
So, what are the advantages then? A few that I know of are outlined below...
As you can see from my examples the prime advantage is that if you can reliably predict your tax rates during retirement and compare them to your rates now you can work the angle that is best for you. Of course it's impossible to reliably predict what the tax rates will be in 40 years so either option is a crapshoot if you currently fall in the middle of the road on the tax bracket. If you're really high on the bracket now then you're reasonably assured that your rates will LIKELY be lower in retirement, if you're reasonably low on the bracket and you're maxing contributions then you can be reasonably sure your rates will be higher in retirement.
The above examples and explanation completely neglect the fact that the tax brackets are a scaled system, your withdrawals on a traditional IRA won't automatically all be taxed at the rate at which you fall, it's the scaled tax bracket, whereas your contributions on the front almost always fall in with the highest bracket you're in (because that is where they reduce the tax burden if you choose traditional over Roth). This offers an immediate advantages to traditional if you will be in the same tax bracket during retirement. A more detailed description of the tax implications would need to be done to show the real benefit.
Also worth mentioning is if you can qualify for other tax exemptions etc now by reducing your income it may be more advantageous to go traditional so your contributions reduce your net income. IE, last year I worked in Afghanistan and made some extra dough, our combined household income would have disqualified us from the child tax credit but I maxed my traditional contributions to reduce my income enough that we still earned most of the child tax credit...
There are other advantages as well, I'll add them as I think of them...