I was asked whether it is better to contribute tax-deferred money to a Traditional IRA vs after-tax money to a Roth IRA.
The answer is remarkably simple (ignoring early withdrawal or other issues):
Do Traditional IRA if your tax rate is lower when you take the money out. Do Roth IRA if you expect your tax rate to be higher when you take the money out
I did a spread sheet, but the formulas are easy.
Suppose you put in pre-tax P dollars this year into a traditional IRA, or you put in aftertax P(1-Tin) dollars into a Roth IRA, where Tin is your current tax rate.
You let the money grow at rate r for N years and then you take it out when your tax rate is Tout.
The amount of money you have for either approach is
Traditional = P(1+r)^N (1-Tout)
Roth = P(1-Tin)(1+r)^N
The ratio is
Traditional/Roth = (1-Tout)/(1-Tin)
which is greater than 1 when Tout is less than Tin and less than 1 when Tin is less than Tout.
The result is independent of P and N and also would be true if the rate of earnings varied every year. Inflation is not an issue in this calculation.
For example, suppose your tax rate is now 25% and you expect it to be
20% when you start drawing from your IRA. ThenTraditional/Roth = (1-0.2)/(1-.025) = 0.8/0.75 = 1.06666
and you are 6.7 percent better off with the traditional IRA.
Nathan Liskov