If you read an article about retirement accounts (IRAs, 401(ks), etc.) in a respectable news outlet like the New York Times or the Wall Street Journal, it's often only a matter of time before someone says something blatantly wrong. I don't mean wrong as in maybe-probably-kinda wrong. I mean wrong as in mathematically-algebraically-demonstrably-provably wrong. I don't know what it is about the math of retirement accounts that trips people up. It's simple eighth grade algebra, but it's gotten a lot of people confused--even professionals managing hundreds of millions of dollars.
So when I was reading an article about IRAs in today's New York Times, I was expecting an error to pop up at some point. And sure enough, it did. And I'm going to use it as a jumping point to clarify how retirement accounts work.
Here's the offending paragraph:
So when I was reading an article about IRAs in today's New York Times, I was expecting an error to pop up at some point. And sure enough, it did. And I'm going to use it as a jumping point to clarify how retirement accounts work.
Here's the offending paragraph:
Michael E. Goodman, a certified public accountant and the president of Wealthstream Advisors, says he has a client who is a 45-year-old widow with children who looks each year at how much she can convert from a traditional retirement account to a Roth. Since she makes large charitable donations, she is often able to use the tax deduction to offset some of the tax bill from the Roth conversion.
“It’s much more powerful for my client at 45 than at 65,” he said, pointing out that it takes years for investment gains to surpass the tax losses. The exception is someone who is doing the conversion for heirs, who will have a longer time horizon. (emphasis mine)
The bolded part is wrong. It does not matter at all when the tax is paid. The only thing that matters is the tax rate. The time horizon left after the payment of the tax is irrelevant. That may sound a little counterintuitive. But the algebra behind it is ironclad. Let me explain.
The U.S. government allows us to save money in special accounts called Individual Retirement Accounts or IRAs. There are other special accounts called 401(k) and 403(b)s and 457 that work in much the same way. So understanding how IRAs work will help you understand these other accounts as well.
What's special about an IRA is that you don't have to pay capital gains tax on the growth of the money you put in that account. [Edit: More accurately, you don't have to pay tax on the growth of that money, whether it takes the form of capital gains, interest, or dividends.] That's a huge advantage. And that's why you are strongly encouraged to save your money in an IRA rather than in a regular ol' account.
But IRA accounts do not save you from the income tax. [Edit: More accurately, they do not save you from paying income tax on the original amount you place into the account. In other words, the original amount is taxable; the growth is tax free.] One way or the other, you have to pay your income tax in full. There are two types of IRA accounts, and the key difference between them is the timing of when you have to pay your income tax. With a Roth IRA, you pay the income tax when you put the money into the account. With a traditional IRA, you pay the income tax when you pull the money out of the account. Whichever you choose, there's no escaping the income tax.
So which is better? Paying your income tax at the beginning for the Roth or paying your income tax at the end for the Traditional account? Let's work it out. Suppose you want to put $100 in an IRA account today. You'll take the money out some time in the future--like thirty years from now. Over that time, your investment will grow by x percent.
Now suppose you go with the Roth IRA. Because it's a Roth account, you'll have to pay tax on that $100 today. If your income tax rate this year is T1 percent, after paying the tax, you'll have only $ 100*(1-T1) to put in your Roth IRA account. It grows by x percent in the account, so you'll end up with $ 100*(1-T1)*(1+x) in thirty years.
Now suppose you had gone with the Traditional IRA. Because it's a Traditional account, you don't have to pay tax on that $100 today. So the full $100 goes into the account. It grows x percent in thirty years, so you'll end up with $ 100*(1+x) in thirty years. But now you have to pay the income tax. Say your income tax rate when you're pulling out the money is T2 percent. After paying the tax, you'll have only $ 100*(1+x)*(1-T2) left.
Now, compare the two amounts. If your tax rate when you put the money in (T1) is the same as the tax rate when you take the money out (T2), then both Roth and Traditional accounts will net you exactly the same amount in thirty years. It comes down to the commuatitive property of multiplication: A x B = B x A. Whether the money is taxed first and then grows, or the money grows and then is taxed, if the growth rate and the tax rate are the same, you'll end up with the same amount of money at the end of it all. The timing of the tax does not matter. Only the tax rate does.
Converting from a Traditional account to a Roth account in a particular year is basically a decision to pay the income tax in that year as opposed to paying it when the money is pulled out. The above algebra shows that the timing of the tax is irrelevant. The only thing that matters is the tax rate. So to maximize the money you will walk away with, you should pay your taxes in the years where your tax rate is the lowest. For most people, tax rates are likely to be lowest in retirement, because they're not earning much in retirement. So, for most people, a traditional IRA account makes sense.
(Now there are other reasons why you might still opt for the Roth account. If you've maxed out your Traditional IRA and want to shield more of your money, or you want to leave your IRA to your kids, it might make sense to switch to Roth. But that's another post for another day.)
The reason a lot of people, including professionals, often get this math wrong is that usually time horizons matter. But in this case, it simply doesn't.
FYI, one person in the personal finance field who I trust to be on top of these kinds of things is Kaye Thomas, founder of Fairmark.com. He's a real pro. And he has written a great primer on investing, That Thing Rich People Do, which I 'm always recommending to everyone.
The U.S. government allows us to save money in special accounts called Individual Retirement Accounts or IRAs. There are other special accounts called 401(k) and 403(b)s and 457 that work in much the same way. So understanding how IRAs work will help you understand these other accounts as well.
What's special about an IRA is that you don't have to pay capital gains tax on the growth of the money you put in that account. [Edit: More accurately, you don't have to pay tax on the growth of that money, whether it takes the form of capital gains, interest, or dividends.] That's a huge advantage. And that's why you are strongly encouraged to save your money in an IRA rather than in a regular ol' account.
But IRA accounts do not save you from the income tax. [Edit: More accurately, they do not save you from paying income tax on the original amount you place into the account. In other words, the original amount is taxable; the growth is tax free.] One way or the other, you have to pay your income tax in full. There are two types of IRA accounts, and the key difference between them is the timing of when you have to pay your income tax. With a Roth IRA, you pay the income tax when you put the money into the account. With a traditional IRA, you pay the income tax when you pull the money out of the account. Whichever you choose, there's no escaping the income tax.
So which is better? Paying your income tax at the beginning for the Roth or paying your income tax at the end for the Traditional account? Let's work it out. Suppose you want to put $100 in an IRA account today. You'll take the money out some time in the future--like thirty years from now. Over that time, your investment will grow by x percent.
Now suppose you go with the Roth IRA. Because it's a Roth account, you'll have to pay tax on that $100 today. If your income tax rate this year is T1 percent, after paying the tax, you'll have only $ 100*(1-T1) to put in your Roth IRA account. It grows by x percent in the account, so you'll end up with $ 100*(1-T1)*(1+x) in thirty years.
Now suppose you had gone with the Traditional IRA. Because it's a Traditional account, you don't have to pay tax on that $100 today. So the full $100 goes into the account. It grows x percent in thirty years, so you'll end up with $ 100*(1+x) in thirty years. But now you have to pay the income tax. Say your income tax rate when you're pulling out the money is T2 percent. After paying the tax, you'll have only $ 100*(1+x)*(1-T2) left.
Now, compare the two amounts. If your tax rate when you put the money in (T1) is the same as the tax rate when you take the money out (T2), then both Roth and Traditional accounts will net you exactly the same amount in thirty years. It comes down to the commuatitive property of multiplication: A x B = B x A. Whether the money is taxed first and then grows, or the money grows and then is taxed, if the growth rate and the tax rate are the same, you'll end up with the same amount of money at the end of it all. The timing of the tax does not matter. Only the tax rate does.
Converting from a Traditional account to a Roth account in a particular year is basically a decision to pay the income tax in that year as opposed to paying it when the money is pulled out. The above algebra shows that the timing of the tax is irrelevant. The only thing that matters is the tax rate. So to maximize the money you will walk away with, you should pay your taxes in the years where your tax rate is the lowest. For most people, tax rates are likely to be lowest in retirement, because they're not earning much in retirement. So, for most people, a traditional IRA account makes sense.
(Now there are other reasons why you might still opt for the Roth account. If you've maxed out your Traditional IRA and want to shield more of your money, or you want to leave your IRA to your kids, it might make sense to switch to Roth. But that's another post for another day.)
The reason a lot of people, including professionals, often get this math wrong is that usually time horizons matter. But in this case, it simply doesn't.
FYI, one person in the personal finance field who I trust to be on top of these kinds of things is Kaye Thomas, founder of Fairmark.com. He's a real pro. And he has written a great primer on investing, That Thing Rich People Do, which I 'm always recommending to everyone.
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