Queue up the Stones…. “Time is on my side, yes it is.” But, is it?

If we freeze all other variables, that is, we’ll assume that your marginal rate is the same on the deposit and on the withdrawal. And for easy math, we’ll assume the 25% rate. If we start with $1000 in our traditional IRA, and it grows ten fold. Note – this is about 10%/yr over 25 years. Not too crazy, and just for this example, not a prediction. So, after a time we have $10,000 and after the 25% tax there’s $7,500 left.

If instead, we pay the tax upfront and use a Roth IRA, the $1000 is $750 after tax, and after growing ten fold, it’s $7,500. Hmm. When I show this to people, their gut reaction is to say, “that’s highly significant.” I can’t help but agree. You see, time doesn’t change the result. This is actually simple to any 6th grade math student, and is known as the Commutative Law of Multiplication. This law says that A x B = B x A and in our example, any starting sum of money results in the same amount if we say T x G (that is, tax, here, 25% or multiply by .75, and growth, here, 1000% or 10x) is the same as G x T.

This was a quick one. Or was it? On Friday, we’ll look at this question a bit more to understand why the commutative law sometimes breaks.

Disclaimer – I made this question up. It was my reaction to reading others’ articles that spoke of time being an important factor. I could comment and explain why it’s nonsense, at their sites, or simply summarize my thought here. By the way, I’m still taking questions from readers. You can ask anonymously if you wish, as the more detailed the question, the better I can analyze your situation.

{ 4 comments… read them below or add one }

Aloha Joe,

Very interesting analysis. In this case, the regular IRA might do better simply because of the higher initial contribution of $1000 vs the $750 of the Roth IRA, and the compounding effect over the years.

However, color me blind, but I love the Roth and the zero tax rate consequences of growth and distributions. The 25% tax rate is current, but who knows where it will be in 25 years? We might have another Ronald Reagan in office with a heavy hand toward raising taxes across the board. Our own individual State tax rates also come into play, and I can see Hawaii income taxes increasing rather than decreasing.

Given the choice, I’d forego $250 worth of doodads and dining out and boost my Roth IRA contributions to $1000 in order to sit prettier in 25 years.

Aunty

Aloha again, Aunty!

The question comes back – will the couple in this example have $90,000 per year in income? Remember, the exemptions and standard deduction keep adjusting for inflation. All else the same, will the $90K couple see their marginal rate rise? As Yogi Berra once said (or at least it was attributed to him) “It’s tough to make predictions, especially about the future.”

Interesting question, good analysis. Let me make the waters a bit murky if I might. A key variable (that is really tough to quantify) is the time value of money. This ‘what is the value of the future tax savings at withdrawal’ vs. ‘the immediate tax savings available from a deductible traditional IRA’? Taking this a step further the question gets more interesting if you look at a 401(k) participant with the option of making a Roth contribution with all or some of their tax deferral amount. Here you might also get into the realm of folks in higher tax brackets as well which further complicates things. Don’t get me wrong I like the Roth it provides a great option for some. The future is tough to predict but I think many folks in my industry are assuming a huge tax increase that may or may not come to fruition. This can easily morph into a multi variable, multi scenario analysis very quickly.

Roger, thanks for the visit, and comment. I think there are too many variables to cover all at once. At any given moment we do know one’s current rate and propensity to save. There are 1%ers out there who somehow burn through every dime (at a marginal 35%) and some in the 15% bracket who are frugally saving their way to retire at a higher rate. As I discussed with Aunty, I think it’s important to understand the number you’d need to save pre tax to actually fill the lower brackets at retirement. In today’s dollars, it’s $90K per year or over $2M as a pretax nest egg to just retire in the 15% bracket. Along the way to that $2M, there are probably going to be times when some funds can get converted at 10 or 15%, or in high income years, maybe one couldn’t take an IRA deduction, so few would ever save 100% pre-tax.

I do agree with you – the high income high saver will be best served with a mix, some of it forced on them.