Question: Do 401K plans pay dividends quarterly? Also, do they pay them even if the funds have been performing poorly this quarter? This is the first quarter I've contributed to my company's plan.

Answer: 401K plans do not pay dividends.  The funds you invest in inside the 401K plan may or may not.  Usually, mutual funds pay dividends only once a year.  Dividends are also usually paid out every year regardless of how well the fund does (the NAV of the fund), but the amount may vary every year.
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