# Math’s take on the Roth IRA v. traditional IRA question

Last week I got an email asking me which is better, a Roth IRA or a traditional IRA. I’ve answered this question before, but it had been awhile so I decided to revisit the question. As I was writing the column, I discovered a new take on the question I hadn’t ever thought of before. Yes, I had a new idea. It doesn’t happen terribly often so pay attention. It’s pretty complex, but if you can stick with it you might be as excited as I was when I wrote it.

First, let’s lay out some definitions to get everyone up to speed. An IRA is an Individual Retirement Account, most often used by those who do not have an employer sponsored retirement plan (typically a 401(k) or a 403(b)). A traditional IRA is taxed like a 401(k) in that all contributions are made pre-tax, and at the time of withdraw the funds are subject to income tax. Contributions to a Roth IRA are subject to income tax at the time of contribution, and withdrawals are done tax-free.

Now that we are on the same page, which IRA type is best? This is where it gets tricky. Often the two are compared as though the choices are similar but it’s really more of an apples and oranges situation.

Give me a minute to get really technical, I promise there is a pay off.

When you contribute \$5,500 to a Roth IRA, you have to earn more than \$5,500 to complete the deposit. Why? Because you have to pay taxes on the income. Your traditional IRA contribution of \$5,500 costs you \$5,500 now, but your \$5,500 Roth IRA contribution costs you \$7,000ish, depending on your tax rate. If you really want to compare apples to apples, you need to invest the tax savings, too. In other words, the \$1,500 you didn’t pay in taxes because you contributed to a Roth IRA needs to be tucked away in an investment as well. We need to determine what’s the better use of \$7,000, not \$5,500. If you invest the tax savings, created by contributing to a traditional IRA, then the traditional IRA ends up beating out the Roth in our previous example. As noted, you’d owe taxes of \$72,734 on the traditional, but you’d have an additional \$84,349 from investing your tax savings. Therefore, the traditional IRA may be worth \$11,615 more than the Roth IRA. Yet, if the average rate of return increases, the math starts to shift back toward the Roth. (courtesy of the Indy Star)

But it doesn’t stop there. There are other factors to consider. For example, you must begin withdrawing from your traditional IRA at the age of 70 1/2. For a Roth IRA, there are no withdrawal regulations, the funds can continue to grow tax-free as long as you want.