Check your bank account. It may have jumped today if you have children ages 17 or younger—thanks to the Internal Revenue Service, of all things.

But before going on a splurge, find out if the extra dollars are truly extra for you. If they aren’t, you could be in for a bad surprise at tax time next year.

The IRS has now made the first of six monthly payments in 2021 to more than 35 million families with nearly 60 million children. These payments can be large: An eligible family with three young children could receive up to $900 per month for the rest of the year. The first round of payments comes to about $15 billion, according to a Biden administration official.

The payments spring in part from Congress’s March expansion of the child tax credit to as much as $3,600 per child for this year, up from $2,000 normally, in a bid to reduce child poverty. The expansion is just for this year and is expected to cost about $100 billion. Unlike a tax deduction, a credit is a dollar-for-dollar reduction of taxes.

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Later today, join the Journal’s deputy Washington bureau chief, Jeanne Cummings, in conversation with tax reporter Richard Rubin and White House reporter Catherine Lucey as they discuss who’s eligible, the potential benefits of the new payments and President Biden’s speech on the expanded tax credit. Click here to learn more about the event.

In a historic move, Congress also told the IRS to use existing records to send families monthly prepayments of part of their total 2021 child credits this year so they don’t have to wait to claim them on tax returns. Most payments will be by electronic deposit.

Amanda Ray, a 34-year-old widow whose husband died when their daughter was six months old, says the child-credit expansion has already changed her life. Ms. Ray wanted to leave a dangerous area of Chicago for a suburb with safer schools for her daughter, now age 5, but was having trouble finding an apartment after she lost her food-service job during the pandemic. She says she was able to move to Villa Park, Ill., in June, after her now-landlord learned she would receive prepayments.

“The pandemic made everything uncertain, but he and I knew I could pay the rent because of the child credit,” says Ms. Ray, who expects to be rehired soon. Meanwhile, her daughter will attend a town-sponsored camp with swimming lessons and kindergarten prep.

For many families, however, the prepayments could bring unwelcome surprises next spring. The IRS is making the payments based on income shown on 2020 or sometimes 2019 returns. So families whose income has risen or who have had other changes could have to pay back some or all of the prepayments on their 2021 tax returns.

Even filers who are eligible for the prepayments could see far smaller refunds or larger tax bills next year, because they are getting half their child credits up front. For this reason, Phyllis Jo Kubey, an enrolled agent practicing in New York City, has advised most of her clients to opt out of the prepayments.

“The child credits are large and they’re a dollar-for-dollar tax offset, so taxpayers who get half this year could come up short and owe the IRS at tax time—which most people dread,” says Ms. Kubey.

About 1 million filers have already opted out of the prepayments, according to an administration official. Here’s what to know about this new and complex benefit.

How much is this year’s child tax credit, and how much is the IRS sending now?

Just for 2021, the maximum child tax credit is $3,600 for each child under age 6 and $3,000 for each child ages six through 17 as of Dec. 31, 2021.

Without the expansion, the credit would be $2,000 per child for children age 16 and under.

Also just for 2021, the IRS is sending half of each family’s total estimated credits in six monthly installments beginning July 15. So an eligible family with three children ages six, 10 and 14 will get up to $9,000 of child tax credits for 2021, and $4,500 of that should come in six monthly payments this year.

The IRS has sent letters notifying recipients of their prepayments, and its website has many more details. The prepayments are based on the latest tax return processed—usually 2020, but sometimes 2019. So if a family’s 2021 income is different, the prepayments could be too high or low.

Parents who don’t receive monthly payments can claim the full child credits they qualify for on 2021 tax returns.

Does the 2021 child credit have income limits?

Yes, and they can be confusing. The part of the credit that’s just for 2021—either $1,600 or $1,000 per child—begins to phase out at $75,000 of adjusted gross income for most single filers and $150,000 for most married couples. Above these limits, the taxpayer loses $50 of total credits for every $1,000 of additional income, so the cap varies according to income, number of children and filing status.

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For example, say a couple filing jointly has $200,000 of income and three children ages six, 10, and 14. The phaseout would cost them $2,500 of their $3,000 in child credits that apply only for 2021, according to an IRS spokesman.

But this couple would still get the permanent credit of $2,000 for each child, because its phaseout begins at $400,000 for most married couples ($200,000 for most single filers). As a result, this family’s total child tax credits for 2021 would come to $6,500 and they should get monthly payments of about $540 for the rest of this year.

In a change from prior years, filers don’t need to have earned income to claim child credits in 2021.

Are there other eligibility requirements?

Yes. Among other things, the child must have a Social Security number.

If a family gets prepayments they aren’t eligible for, do they have to give the money back?

In many cases, yes—either through a lower refund or else a higher balance due to the IRS.

Taxpayers getting prepayments this year will settle up with the IRS on 2021 tax returns. Filers who aren’t eligible for some or all of their prepayments—say because their income rose, or because an ex-spouse is claiming the child this year—could owe the IRS for them unless their income is below $40,000 for single filers and $60,000 for couples filing jointly.

I’m eligible for my child-credit prepayments. How will that affect my 2021 taxes?

It could affect them a lot, either by lowering your refund or raising your tax bill, because you’ve already received a large chunk of your child tax credits.

Here’s a simplified example. Say a married couple with two children over age 5 and $220,000 of income got a $500 refund for 2020. Their 2021 income is similar, so that’s too high for this year’s extra child credit. But they’ll still get permanent credits totaling $4,000—and receive half of that in prepayments this year of about $333 a month.

Next year, when they do their 2021 tax return, the $2,000 of prepayments won’t be available to lower their tax bill. So instead of getting a $500 refund, they could owe the IRS $1,500.

How will taxpayers know if they’re getting payments only for the permanent child credit, not the expansion? A tip-off is that the monthly payments are likely to be about $167 for one child, $333 for two, $500 for three, and so on.

How do I stop monthly prepayments, or change them? What if I need to change my address or bank account information?

You can go to the IRS’s child-tax-credit update portal and follow the instructions. Those who don’t have an account with the IRS or other government agency will need to create one and in some cases provide a photo ID.

For taxpayers opting out of prepayments, detailed information is available in Topic J of the IRS’s FAQs on the child tax credit, and it includes deadlines to un-enroll. Note: Each spouse of a married couple must opt out separately.

Taxpayers who don’t want to use the IRS’s portal to opt out could also adjust by raising their paycheck withholding or quarterly estimated taxes.

Can the IRS apply my child credit prepayments to unpaid tax debts or child support?

No, according to an IRS spokesman. But the agency can apply 2021 tax refunds to such debts or child support.

Write to Laura Saunders at laura.saunders@wsj.com