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Interest rates on savings accounts have been close to zero for a while. But if you’ve been building an emergency cash fund or got money as part of a graduation gift this spring, you need to put those dollars somewhere.

What’s your best option?

You’ll likely be disappointed if you head to the branch of a major bank. At these institutions, savings accounts tend to pay a meager 0.01 percent to 0.15 percent in annual interest.

Low interest rates were one of the top reasons that customers switched banks during the past year, according to the latest banking satisfaction study by J.D. Power.

For a better deal, try the following:

• Shop around. A national bank is not the only place to park your cash.

“You’ve got to shop around for the highest yields,” said Greg McBride, chief financial analyst at Bankrate.com, which keeps tabs on banking trends.

You can start your search with sites such as bankrate.com, bestcashcow.com, nerdwallet.com and gobankingrates.com, which compile the latest offers from banks and credit unions.

Credit unions are not-for-profit organizations and, as a result, may pay slightly higher interest rates than banks do.

According to a quarterly report by SNL Financial, which tracks the financial services industry, the average rate for a traditional savings account was 0.13 percent nationally at credit unions and banks as of the end of March.

But on other savings products, credit unions had the edge.

For example, on money market accounts, which tend to have higher minimum balance requirements than traditional savings accounts, credit unions paid 0.16 percent; banks only 0.12 percent.

You have to qualify to join a credit union, which may be based on where you work, whether someone in your family is a member or where you live, among other things. For details, go to mycreditunion.gov.

• Bank online. If you’re willing to bank online, you may find even better deals.

Today, online savings accounts pay as much as 0.95 percent in annual interest. What’s more, some of the accounts have low- or no-minimum balance requirements. Many do not charge monthly fees. (You can find these offers using the websites mentioned earlier.)

For even bigger payouts, consider a rewards checking account. Annual rates go as high as 2.5 percent to 3 percent, up to a certain balance (usually $25,000 or less).

But there’s a catch: To get the big yields, you have to meet specific terms, such as making 10 or more debit card transactions each month and receiving statements electronically.

Fail to meet the terms, and the interest rate drops to a fraction of a point.

Said McBride: “You have to be a savvy saver.”

Some community banks and credit unions participate in a nationwide program for rewards checking called Kasasa. To find them, go to kasasa.com.

• Go with Uncle Sam. Finally, you may earn a better rate if you can commit your cash, say, for a year or more. In that case, consider a Series I saving bond offered by the U.S. Treasury. The bond’s yield is made up of two parts: a fixed rate that remains unchanged for the life of the bond, and a variable rate that is adjusted twice a year with inflation.

For bonds bought through Oct. 31, the combined rate is 1.94 percent. If interest rates eventually start to rise, the I-bond’s yield could also go higher. (Likewise, if rates fall further, the yield could drop.)

You can buy the bonds in any amount from $25 to $10,000 per year. You can cash in the bonds after one year, but if you redeem before five years, you lose the last three months of interest. To purchase, go to treasurydirect.gov.