Roth vs. Traditional IRA

The big difference between Roth and Traditional IRAs is when the taxes are paid. With a Roth IRA, you pay taxes before making the contribution (but not on withdrawal), and with a Traditional IRA, you do not pay taxes on the contribution but do pay taxes on withdrawal:

	Contribution	Withdrawn tax-free?
Roth IRA	Post-tax	Yes
Traditional IRA	Pre-tax	No

You may have heard the following advice before:

In effect, you’re trying to determine whether the tax rate you pay on your Roth IRA contributions today will be greater or smaller than the rate you’ll be paying on distributions from your Traditional IRA after you’ve retired (or have to start making them, at age 70½).

Source: rothira.com

In order to see why the key variable is your relative tax rate while working vs. in retirement, consider the following.

Suppose you invest money that grows at a rate \(r\)% per year for \(Y\) years. If you have $\(P\) to invest, then under a Roth IRA you will be able to withdraw at the end of the period:

\[ (P*t_c)(1+r)^Y \]

Under a Traditional IRA, you will be able to withdraw:

\[ t_f*\left(P(1+r)^Y\right) \]

Clearly, these two are equal if \(t_c = t_f\) (i.e., your current and future tax rates are equal).