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Hundreds of thousands of people are living without a paycheck amid the longest government shutdown in history. As a result, federal employees and contractors are digging into their retirement savings, filing for unemployment, picking up other jobs and unable to meet their rent or mortgage payments. Most people would be in the same bind if they missed even one pay period. Just 40 percent of Americans are able to cover an unexpected $1,000 expense, such as an emergency room visit or car repair, with their savings, according to a survey from personal finance website Bankrate. Instead, many would put the expense on their credit card or take a personal loan. (More than 1,000 people were interviewed in early January).

Even a small amount of savings can go a long way in an emergency, by reducing your chances of going into debt or racking up bank overdraft fees, said Annamaria Lusardi, an economics and accounting professor at the George Washington University School of Business. "It is like an umbrella to cover us up when the rain arrives unexpectedly," Lusardi said. "It is better to be prepared than get wet and perhaps sick."

Ways to grow an emergency savings account:

Automate your savings, so that a set amount of money is routed directly into your savings account each week or month, said Erin Lowry, author of Broke Millennial: Stop Scraping by and Get Your Financial Life Together. Try naming your bank account "Emergency savings," so you're reminded why that money is there and why you should keep contributing to it, she said. "Many banks will allow you to change the name of your savings account from a generic Bank Account 39341029 to something with actual meaning," Lowry said. You might also want to open your emergency savings account at a different bank than the one you normally use, she added.