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41% of Americans would be able to cover a $1,000 emergency with savings

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Almost half of Americans can handle a $1,000 emergency, such as a medical bill or car repair, by dipping into savings.

Another 37% say they would use a credit card, take out a personal loan or ask family for financial help to handle unexpected expenses, according to a new poll from Bankrate of over 1,000 U.S. adults. Only about 3% of respondents say they don't know how they would handle a $1,000 emergency.

That's in line with other research. Last year, about 61% of American households said they would pay for an unexpected $400 expense with cash, savings or a credit card, the Federal Reserve found. About 12% said they would not be able to cover the expense at all.

But Americans' emergencies, on average, cost more than $1,000, Bankrate finds. The average unexpected expense for survey respondents was about $3,500. And these situations are not uncommon. Within the past year, 28% of people experienced a financial emergency.

Putting that type of expense on a credit card or taking out a loan may end up being a "high cost" solution, says Greg McBride, Bankrate.com's chief financial analyst. The average credit card APR is currently 17.30% and the average interest rate on a personal loan was 10.07% in September, according to loan marketplace Credible.

With those types of interest rates, it's more important than ever to build up emergency savings. "Whatever savings you can accumulate acts as a buffer from high-cost debt when unplanned expenses arise," McBride says.

But for many, debt is already a problem, which makes saving challenging. Americans over 18 owe about $29,800 on average, excluding home mortgages, according to Northwestern Mutual's 2019 Planning & Progress Study. About 15% of people believe they'll be in debt for the rest of their lives.

Emergencies play a role in racking up this debt. A third of Americans say they're still in debt from borrowing money to pay for a previous crisis, LendingTree finds. Of those who are still carrying debts from earlier emergencies, 33% owe $5,000 or more, while almost 20% owe over $10,000.

How to build a savings fund

To offset the next emergency, experts recommend putting aside three to six months of living expenses. While that may sound like a big number, you can start small and gradually build up a savings cushion to help you weather life's unexpected costs.

Make it as easy as possible on yourself. Set up a regular, automatic transfer from your checking account to a savings account, preferably a high-yield option that will pay you a good interest rate. This doesn't have to be a lot, maybe $5 a day or even $5 a week, says Farnoosh Torabi, personal finance author and host of the "So Money" podcast.

"The key is to have it leave your hands before you get a chance to spend it," Torabi says. "Over the course of six months, a year or even just a little bit of saving at a time... [it] will accumulate and it will motivate you to do more."

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Not only should you have robust emergency savings, you should live below your means. "You should not be living at capacity," says Tiffany Aliche, personal finance expert and founder of The Budgetnista.

To get your finances in good shape, Aliche recommends putting together a monthly budget so you can identify where you're spending money and where it may be possible to trim. That might mean packing your lunch more often or opting for a cheaper cable package — or it may require some bigger changes, such as finding an apartment with lower rent.

But once you have some room in your budget to funnel cash into savings, you'll not only be financially prepared to handle emergencies that come your way, you may find yourself stressing less about your finances in general.

CHECK OUT: Why January is a particularly great time to invest your money via Grow with Acorns+CNBC.

Disclosure: NBCUniversal and Comcast Ventures are investors in Acorns.