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Should I be making my maximum allowable IRA contributions as early as possible in the year (for instance, Jan 1st 2023 for the 2023 contribution), or as late as possible in the year (for instance, April 15 2024 for the 2023 contribution).

I don't know if this answer is different for traditional or Roth IRAs. Depending on my income during the year, sometimes I contribute to traditional IRAs and sometimes I contribute to Roth.

Until I move the money to one of the IRAs, my money will be in taxable accounts invested in a portfolio of Vanguard index funds. My IRAs are also in Vanguard index funds, so the only difference is taxes.

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If you're concerned about being within an income phase out the best time is when you do your taxes. If you're not concerned about having an income limited contribution amount the best time is as soon as possible.

It's not an awful terrible headache to remove an overcontribution either, so you can always just make the full contribution ASAP and remove as needed. Vanguard will calculate the overcontribution and attributable gains for you, you just sign a paper and it comes back out.

Based on the Vanguard dollar cost averaging paper, once money is earmarked to be in the market the best place for it is in the market.

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Of course, the best time is the day the investments you are buying are lowest… but you don’t know that upfront…
Consider the reason you are investing in an IRA / Roth at all: you assume that in the long term, investments gain in value and are tax-advantaged, and the expected gain (and advantage) is larger the longer the investments run. From that follows directly that it is best to invest on Jan/2, as that gives you the longest possible run time. (and that’s what I do)

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Depending on my income during the year, sometimes I contribute to traditional IRAs and sometimes I contribute to Roth.

If you know on day X what type of contribution you will make for the year, you could make the investment that day.

If you are close to one of the annual income limits and if which side of the limit your income falls, determines the type of investment; then you may have to wait until the new year.

If you need to get your tax refund first, before making the contribution, then you might have to wait until that refund arrives.

You have know way of knowing what day will maximize the return for the year, but when the time frame is decades it might not make much of a difference.

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If you contribute early in the year, then your contribution limits will be calculated on pre-gain amounts. For example, suppose the contribution limit is $10k, and your investments are returning 4%. Then contributing at the beginning of the year means that your contribution will grow to $10.4k by the end of the year. You've effectively contributed $10.4k to your IRA. If you wait until the end of the year, you can contribute only $10k.

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