With the (extended) tax deadline just passing, I’ve been thinking a bit about taxes. I recently realized that I was thinking about tax-deferred contributions, such as contributions toward an IRA or 401(k), incorrectly. I’m reasonably “financially literate”, so if I’ve been making this mistake, I think there’s a decent chance that some of you may be as well.

I’ve been considering every dollar that I contribute towards a tax-deferred investment as saving me $1 * my current tax rate. Let’s say that, all in, I pay 35% in taxes. If I contribute$1 towards an IRA, I was thinking that I saved $0.35. I think that’s a bit too simplistic. When you invest in an IRA, you don’t pay income tax on that contribution. However, you do pay income tax on it when you withdraw the money. Let’s compare investing in an IRA vs. not by working through an example. ### Option 1: Invest$1 in an IRA

1. Contribute $1 towards an IRA today 2. Invest that$1 for the next 40 years.
3. Withdraw your money during retirement, paying income tax.

### Option 2: Invest $1, but not in an IRA 1. Pay income tax on$1.
2. Invest what you have left for the next 40 years.
3. Sell your investment, paying long-term capital gains tax.

Before being able to compute anything, we need to make some educated guesses about a few missing pieces of data:

Missing Data Educated Guess
What is your current tax rate? 35%
What is the average rate of return that you will get on your investment over the next 40 years? 4%
What will your tax rate be when you’re retired? 35%
What will the long-term capital gains tax be when you’re retired? 15%

Now we can crunch the numbers:

How much of your $1 are you left with after paying income 35% tax? $1 \cdot (1 - 0.35) = 0.65$ How much is your investment worth after 40 years of 4% returns? (Does this number look familiar?) $0.65 \cdot 1.04^{40} = \class{n}{3.12}$ When you sell your investment, how much capital gains tax do you owe? $\mathit{gains} = (3.12 - .65) = 2.47 \\ 2.47 \cdot 0.15 = 0.37$ How much are you left with? $3.12 - 0.37 = 2.75$ ### Recap So, how much do you save by investing in an IRA? 2.75 / 3.12 ~= 0.88, so about 12% in this case. Not anywhere close to the 35% that I had previously thought. Let’s understand why. Notice how in Option 2, our investment was worth$3.12 right before we sold it and had to pay capital gains tax, which is exactly the same as how much we were left with in Option 1. This makes sense because in both cases, we A) paid income tax and B) invested our money for 40 years at 4% per year. The only difference was that we did them in the opposite order (which doesn’t matter because multiplication is commutative, i.e. a * b = b * a).

The only difference in these two cases is that, in the second case, you need to pay long-term capital gains tax on your gains whereas in the first option you don’t.

So, is the takeaway point that an IRA only saves you capital gains tax and not income tax? Well, almost. As always, it’s a bit more complicated.

In our example above, we guessed that our tax rate when we’re retired would be the same as our current tax rate. That’s probably a overestimate. If you’re actually retired, then you have no ordinary income. You do have retirement savings (i.e. IRAs, 401(k)s), you may have pension income, and you may have rental or business income. Still, it seems fairly plausible that your total taxable income will be quite a bit less during retirement than it is when you’re working, which can put you in a lower tax bracket. This can change things a lot. If we guessed that our retired tax rate would be 20% (instead of 35%), then an IRA would save us about 28% (up from the 12%).

The savings rate is fairly sensitive to our inputs. Below is an interactive calculator for computing how much you save by investing in an IRA. Play around with the inputs to get a feel for how it changes the results!

Inputs:

Current Tax Rate: %
Retired Tax Rate: %
Average Return Rate on Investment
(/yr for 40 yrs):
%
Long-term Capital Gains Tax Rate: %

For the reasons stated above, I think assuming that you only save the long-term capital gains tax is too conservative, but assuming that you save your entire income tax is likely too generous. It’s probably somewhere in between - and the closer your retired income tax is to your current income tax, the closer your savings will be to capital gains.