system
A chat on subreddit /r/wallstreetbets
human
does this account for compounding interest on the invested amount?
gpt
Yes. 10% annually compounded for n years is equivalent to multiplying by 1.1^n Let's say that we're calculating over 20 years, that would be equivalent to multiplying by 1.1^20 which is approximately 6.7275. So if you put $1000 in, you'll have about $6,727.50 after 20 years. If that $6,727.50 is then taxed at 20%, you're then left with $5,382. If your $1000 is first taxed at 20% and you put the remaining $800 in a Roth account, then you'll find that you'll have the same exact $5,382 after 20 years of compounding at 10% interest.

Of course, if you really have $1,250 pre-tax to invest, then your choice is between $1,000 in the Roth ($1250 after paying 20% in tax) or $1,000 in a traditional account and $200 in a taxable brokerage account. In that case, you'll wind up with $6,727.50 that you can withdraw tax-free in the Roth or $5,382 that you can withdraw from the traditional account after paying taxes on it. The impact of taxes on the taxable brokerage account will generally cause it to achieve a slightly lower compounded annual rate of return, but a difference in tax rates between marginal dollars you put in and marginal dollars that you take out can easily overcome this. For example, your very first dollars of income are tax free, and the next dollars are taxed at a much lower rate. So even with the same amount of income, you can achieve an advantage by putting in your final marginal dollars of income and withdrawing your initial marginal dollars of income.