IRAs: Round 3. This time, with pictures.
For this post, I’m going to assume you understand what an IRA is and how a Traditional IRA differs from a Roth IRA, otherwise this will get too long. If that doesn’t describe you, take a look at my previous two posts: How much does an ira really save? and Isn’t a Roth (vs. Traditional) IRA usually a bad idea?.
We’ll save the explanations for later. To start, play around with these knobs and get a feel for how it affects the value of $1 and the value of a “maximumum pretax roth contribution” (more on that later) after being invested for 40 years in one of three methods: not using and IRA
, using a Roth IRA
, and using a Traditional IRA
.
(/yr for 40 yrs):
What are we looking at?
The first graph shows what 1 pretax dollar will become in 40 years if it’s invested using each of the three methods in question (not using an IRA
, using a Roth IRA
, and using a Traditional IRA
) as you vary your retirement tax rate.
The second graph shows what an investment of the maximum pretax Roth IRA contribution would become in 40 years, invested using the same methods, also as you vary your retirement tax rate. The second graph is not just a multiplied version of the first.
Here’s why. Let’s say the maximum pretax roth contribution is ~$8,500. You can’t invest $8,500 in a Traditional IRA. You can only invest a maximum of $5,500 pretax dollars in a Traditional IRA. So the additional ~$3,000 pretax dollars has to be invested “normally”, i.e. without the assistance of an IRA. Which means it’s taxed twice (income tax and capital gains).
So what is the maximum pretax Roth IRA contribution? Well it depends on your current tax rate. If you can contribute $5,500 to a Roth IRA using posttax dollars, and your tax rate is 50%, then you’re effectively contributing $11,000 pretax dollars. If your tax rate is 10%, then you’re only contributing ~6,100 dollars. Notice how the labels of the second graph change as you slide around the current tax rate input.
Understanding the differences
Now that we understand what we’re looking at, let’s highlight a few things:

The investment methods
not using an IRA
andusing a Roth IRA
do not depend on the retirement tax rate at all. That makes sense since the only way in which you end up paying income tax in retirement (on your investment) is if you use a Traditional IRA. Consequently,using a Traditional IRA
becomes a worse value as your expected retirement income tax increases. 
In the first graph,
using a Roth IRA
=using a Traditional IRA
when your current tax rate = your expected retirement tax rate. This also makes sense since, for a fixed pretax contribution, the only difference between the two is whether you pay income tax now or later. However, that is not true in the second graph. Here’s why. 
using a Roth IRA
=not using an IRA
if you take your expected average return rate to 0% or if you take longterm capital gains tax to 0%. In bothusing a Roth IRA
andnot using an IRA
case, you pay income tax upfront. The difference is that, in a Roth IRA you don’t have to pay capital gains tax, whereas you do if you’re not using an IRA. If you expect to make 0% on your investment, then you expect to have no gains, and therefore they become the same thing. Likewise, if there is no capital gains tax, they’re also the same thing. 
And finally to round things off, if current tax rate = your expected retirement tax rate AND long term cap gains tax = 0% (or expected average return rate = 0%), all these methods are equivalent.

Oh, and one more thing: compound interest is crazy. This isn’t really about IRAs at all, but notice how if you take your average return rate from 4% to 8%^{1}, your $1 goes from tripling to being multiplied by about 14x!
Information overload!? Just tell me what to do!
Here’s what I think you should do (with all the normal caveats about how I’m not a tax professional):

Contribute the maximum amount in an IRA (probably a Traditional IRA, but more on that later). Which means you should focus on the second graph.

Invest your IRA in something diversified  something like SPY. Adjust the expected average return rate slider (above) to something realistic given your choice. For SPY, it’s probably something between 3% and 8% (although that’s a huge range).

Adjust the current tax rate slider (above) to the correct value for you.

Keep the longterm cap gains slider at 15%.

Estimate your retirement tax rate. As I described in an earlier post, I think it’s highly likely that your retirement tax rate will be considerably less than your current tax rate.

Look at the second graph, specifically the point on the xaxis that you estimated for your retirement tax rate, and pick whichever type of IRA has a higher value! Q.E.D.
If I do all that, here’s what I come up with:
 Expected average rate of return: 5%
 Current tax rate: 35%
 Expected retirement tax rate: 25%
 Value of $8462 pretax contribution in Roth IRA = ~$39,000
 Value of $8462 pretax contribution in Traditional IRA = ~$41,000
Traditional IRA it is!

That was assuming current tax = 35% and longterm cap gains tax = 15%. ↩