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Author: dgulick Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 75807  
Subject: Re: Roth vs. Traditional Date: 7/21/2000 5:49 PM
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>> ..you'll owe maybe $644. If you're in the 15%, $345. I'd pay that in a second and consider it a downpayment on a million TAX FREE dollars.

I think thats over simplifying it. The tax you pay now no longer factors into the compounding part of the equation. People often compare a $2000 Tradition IRA to a $2000 Roth IRA contribution, but, as you pointed out, the Roth contribution will cost you more in taxes. To my figuring the tax upon withdrawal for the traditional IRA (that has compounded on the unpaid tax in the beginning) is exactly the same as the upfront tax for the Roth. Now I know equations make everyones head swim but these aren't too dificult.

Traditional IRA:
s=p*(1+i)^n*(1-r)
This states that value,s (what you get) equals principle times the quantity 1 plus interest (assummed returns, dividends, capital gains, etc.; most pick between 8 and 12%) raised to the power n (number of years invested) (so far this is simple compound interest, stick with me) times the quantity 1 minus the tax rate (to acount for taxes paid at retirement).

OK, lets compare to a Roth:
s=p*(1-r)*(1+i)^n
Here you've paid taxes up front so to compare apples to apples you're investing less. Then compound that amount. If you look closely these equations are identical.

The difference is that for the Roth your taxed at the current rate, for the Traditional IRA the tax rate is whatever it will be at retirement. Some believe taxes will go up. History has certainly shown us this. But you must also consider that you will have less income in retirement (typically you can live comfortably with 80% of your final income, and if you've paid off your mortgage, quite a bit less) so a traditional IRA is better.

Why then all the ballyhoo regarding the Roth? Because the Roth contribution is after tax and the limits for both IRA types are set at $2000, the Roth essentially allows a gross up contribution of ~$3000 depending on your current tax rate (this number comes from $2000/(1-r) assumming r is 33% (28% fed + 5% state)) (the p in the above equation). In essence, the Roth allows a larger annual contribution limit.

The other reason the Roth gets so much press is the limits for participation are set much higher, allowing more high income people to participate.

Doug
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