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I'd like to be able to estimate the value of my portfolio over time given annual contributions and an expected return of a certain percentage. I found several simple online interest calculators, but each of these requires me to set the frequency at which the interest is compounded. This makes sense for savings accounts and loads, of course. But when one simply wants to estimate something like a diversified 403b or 401k, should yearly, monthly, daily, or continuous compounding be used?

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    Since your expected return is an estimate anyway, the compounding frequency is just a small perturbation on that estimate. Here, for example, it is shown that a rate of 24% compounded monthly is equivalent to a rate of 26.8% compounded yearly. The relative difference is even smaller for lower, more realistic returns.
    – nanoman
    Commented Jul 14, 2023 at 18:38

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But when one simply wants to estimate something like a diversified 403b or 401k, should yearly, monthly, daily, or continuous compounding be used?

If you are invested in individual stocks, or stock mutual funds or stock ETFs, there is no concept of compounding.

You can pick a company today, but a year later the price has gone down 50% because the CEO was fired, and the main product is dangerous. Even more confusing the share price can be dropping but they are still paying dividends.

It is also possible to pick an investment that rises in price but not in a pattern that matches any compounding curve of a bank account.

There is no way to look at the past performance and guarantee future performance.

You can make a guess and then divide it into the compounding chunks to be able to have numbers for your graphs, keeping in mind that the reality will never match the model.

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  • The closest thing to compounding is if you have set things up so dividends are automatically reinvested. (That's what compounding is, adding interest/dividends back into to the account so you now earn interest/dividends on those too.)
    – keshlam
    Commented Jul 14, 2023 at 17:43
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You would use the same frequency you are measuring your return. If you expect to earn 3% per quarter you would use quarterly compounding. If you expect to return 12% per year you'd use annual, etc.

If you used any other compounding frequency you'd have to convert the periodic return to your compounding frequency, which would just be the inverse of compounding. For example, if you wanted to compound a 12% annual return monthly, you'd use ((1 + 0.12)^-12) - 1 as the monthly rate of return, which would end up at the same annual return after compounding for 12 months.

Note, however, that the choice of compounding frequency usually doesn't make a material difference, unless you're talking about relatively high interest rates (e.g. 20% or more) or a long time frame (like 5+ years).

Even then, since your return is only an estimate, the choice of compounding frequency will keep you well within a reasonable "margin of error" for your estimates.

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