Roth IRAs

I heard a commentator on NPR's "Smart Money" claim that Roth IRAs are always better than regular IRAs. The argument goes something like this: although you have to pay the interest up front, your money grows tax-free, so you don't have to pay the government tax on your earnings.

This is a common argument, but it's completely wrong. Let P be your investment, T be your tax rate, R be your return, and N be your years of investment. With a Roth IRA, you pay tax upon investment into your IRA, so your amount after N years is (TP)(R^N). With a regular IRA, you pay tax when you withdraw, so your amount is T(P * R^N). They're the same!

Except the argument is more subtle. With Roth IRAs you typically can shelter more income. But with regular IRAs, you may benefit if your tax rate is lower in retirement. This article explains the difference and provides some helpful calculators.