I've read many articles in the past about the differences between Roth IRAs and Traditional IRAs and no matter how I read it, it always seems like the author leaves some detail out that makes the Traditional option sound better, but when considered the Roth is actually better. I think my confusion boils down to a single misunderstanding of a general rule in the Roth setup.
referencing this stackoverflow post: Why is a Roth 401(k) good if there is a long time before retirement?
The top answer goes into a big discussion of why fidelity has a misleading post on their site about the benefits of a Roth over a traditional account.
Here, he says this statement:
The Roth side, they assume the $5000 goes in at a zero tax rate. This is nonsense, as Elaine can't deposit $5000, she has to pay tax first, no? She'd deposit $3600, and would have the identical $27,404 at withdrawal time."
The next solution down says something similar:
You invest 10k into a Roth. After paying the taxes, your initial investment is $7500. After 50 years, you have $880,431 - the same you have with the traditional.
This is what I have been seeing anywhere, and it literally doesn't make sense. These numbers are talking about a 401k, but the concept is similar. So, lets assume that you're maxing your contribution at $5,550. So, for a traditional you would invest $5,500 and pay taxes later on the earnings and contribution. From what these people are saying, it is impossible for you to put $5,500 in if it were a Roth though, because the money has to be taxed.
From my understanding of taxes, they are paid completely separate of the actual account in which I choose to invest my money in. So, when the end of the year comes, and its time to pay my taxes, this $5,500 would be considered taxable and be calculated in my tax return. I would pay taxes on that money normally, as if I had put it in a Roth account or done nothing with it. The taxes does not have to come from this $5,500 I invested, it can come from the other money I made the rest of the year as part of my salary. So, in a maxed out traditional and Roth account, the limit is still 5.5k, not 5.5k for the traditional and then 5.5k - taxes on the Roth, since I can choose to use other money I have made to pay those taxes if need be.
If the statements above are wrong, then do not continue to read any further, as the rest of the post just goes to back my logic. If my reasoning so far is correct, then you may continue to see if everything else I am saying is making sense.
Now that we're in agreement, let me run through a few scenarios:
Let's assume that you are 25 years old, married, and making $90,000 jointly. This puts you dead in the center of the 25% tax bracket (today's tax bracket), and you are going to invest $5,500 a year. So when you contribute to the account, you pay 25% of 5,500 for 1,375. Lets assume that you withdraw in 40 years and made 6% interest each year on average (long term CAGR of the market has shown to be at least this, so its reasonable to say). 5,500e^0.06(40) = 60,627. Of this amount, 1,375 / 60, 627 = 2.27% tax rate on total balance.
Now, for that same person, a traditional would have been $0 up front. We will do the same scenario where it grew to 60,627. Say you manage to live a very simplistic life and only need 40,000 a year to survive. So with today's tax brackets, that would give you an actual tax rate of 12.67% for a total of $7,687 in taxes. Obviously the numbers don't quite add up, since the next year your remaining balance is less, so the tax rate is less, but over numerous years of investment this trend would continue since you would be able to lean on profits from additional years. Which leads to the long term example:
So, from a 40 year calculation standpoint, assuming the same amount was invested each year and the interest rate was flat across all 40 years. My Traditional would grow to 946k, and upon depleting it all at 40k a year, I would have paid 120k in taxes, leaving me with 826k. For the Roth IRA, I paid $55,000 in taxes and made the same 946k, leaving me with a profit of 891k. This number is greater than the previous example, and one might even argue that because they have already paid the taxes, it is nice to know that you will have 946k starting at retirement, not 826k after taxes.
Now, on the extreme example, lets say you make 180k a year, which is the max you can make to still contribute to the plan. Now, without boring you with all the math, the Traditional would remain the same 12.68%, while the Roth only increases to 2.54% from the 2.27%. Still almost a factor of 6 times as large!
From my calculations, this trend would continue to repeat itself until roughly 10-12 years out from retirement for salaries under 90k and 12-14 years for salaries up to the maximum 180k limit for investing into the Roth. This calculation also assumes that upon retirement, your money is placed in some investment where it stops growing interest (money market?).
Interestingly, the spread only increases when the CAGR increases. This is not intuitive at first, but think about it this way. If you push off paying taxes for your traditional plan, and then it does very well, there is a larger sum of money, which means there is no more money to tax. With more money to tax, the difference in tax paid is even higher than the initially analyzed factor of 6. I could never imagine investing into an account that literally relies on less growth for your amount of taxes to change. Also, if you were to use a more detailed example that included the compounding interest after retirement (maybe from bonds?), then I believe the case for a Roth account would be even more extreme, although I haven't run the numbers yet. Intuitively at this point, if increasing the growth causes more taxes on the traditional, but not the roth, then the roth will benefit even more over a longer period.
Also, some people may mention the argument of getting a tax deduction with the traditional and possible reinvestment of that money. I did run the numbers here and in this case, the traditional does come out on top (1,033,000 vs 946,000). However, this case requires that literally every single year you take the tax break money and invest it into the market to grow. What happens when your taxes are off one year and, even with the tax break here, you end up owing money or break even? Now it's going to be hard to balance that money out to ensure that you meet this case.
Also, one detail that is overlooked with a traditional IRA is that there is a maximum salary where a deduction can be made. If you make more than 99k a year, than the deduction decreases until eventually nothing around 120k. This further limits who benefits from the traditional.
So in conclusion, a traditional is only the better option if you make less than 99k a year and religiously reinvest the tax returns from the deductions, even if your tax return is bad that year. Otherwise, a Roth seems to be superior.
I can show my excel spreadsheet if anyone is interested, and any feedback would be greatly appreciated. Thanks.
EDIT: A link to my personal git with my excel spreadsheet
Changing the annual investment and CAGR changes the rest of the calculated numbers, and depending on whether or not the taxes per year of the traditional are greater than, less than, or roughly equal to, I shade the value red to show higher, green lower, and yellow equal. This is compared to the 28% tax bracket that the 120k and up salary holds, since I imagine myself being within that bracket most of my working career.