The recent years of very low interest rates that pleased ­borrowers also produced lots of pain for savers. But now, savers are finally seeing yields perk up on some savings and money-market accounts…certificates of deposit (CDs)…and rewards checking accounts. That’s a result, in part, of the Federal Reserve’s ongoing increases in its benchmark interest rates as the economy gains traction.

Our expert Ken Tumin has sifted through thousands of savings, checking and CD ­offerings to pinpoint the best ones for different situations and the best strategies for maximizing both yields and convenience…

Money-Market and Savings Accounts

Traditional brick-and-mortar banks continue to provide minuscule annual percentage yields (APYs) in the 0.01%-to-0.06% range on savings and money-market accounts, and they aren’t likely to become more generous until short-term interest rates move up another percentage point or more. In contrast, some online-only banks now are offering APYs as high as 2% on savings accounts (that’s $200 on a $10,000 deposit) and 1.75% on money-market accounts. Money-market accounts typically give you more flexibility than savings accounts, allowing you to write checks and use debit cards and ATMs, although you may have to pay ATM fees.

Shrewd strategy: For no-fee ATMs…branch services…and convenience, keep a checking account at a nearby brick-and-mortar bank with many ­locations, and meet its requirements to avoid monthly fees. But put the rest of the savings that you want to be quickly accessible into higher-yielding online money-market and savings accounts. It’s pretty easy to initiate electronic transfers between online and brick-and-mortar banks, although it takes a few days for the money to shift. Keep in mind that federal law limits savings and money-market accounts to six withdrawals per statement cycle (typically one month). If you exceed that limit, you are likely to be charged a fee or even risk having your account closed.

Here are five of the most attractive savings and money-market accounts, all of which are online, starting with the best recent yields (ATM cards and check writing are offered only where ­indicated)…

Popular ­Direct Exclusive Savings: 2% APY on deposits of any size. This rate is available only to new customers and requires a $5,000 minimum to open an account. PopularDirect.com

Salem Five Direct eOne Savings: 1.85% APY on ­deposits up to $1 million…0.05% on the portion of the balance above $1 million. The rate is available only to customers opening new savings accounts. The bank offers ATM cards but does not reimburse ATM fees. SalemFiveDirect.com

DollarSavingsDirect Savings: 1.8% APY on deposits of any amount. ­DollarSavingsDirect.com

Bank7 High Rate Online Money Market: 1.8% APY on deposits between $5,000 and $999,999.99. There is a $5,000 minimum deposit to open an account. The bank offers ATM cards but does not reimburse ATM fees. Bank7.com

All America Bank Mega Money-Market Checking: 1.75% APY on deposits up to $50,000…0.5% on the portion of the balance above $50,000. The account offers free check writing and an ATM card. It does not reimburse ATM fees. ­AllAmericaBank.com

Checking Accounts

If you are willing to forgo a large network of brick-and-mortar bank branches altogether, consider high-yield rewards checking accounts, the best of which are available at some credit unions and small banks with online access. Some of these, which offer extensive networks of linked ATMs around the country, are offering very high annual yields now—yields that average 1.92% (the highest in five years) and as high as 4.33%.

Typically, the accounts, including the three below, require that you meet monthly minimum requirements such as making 10 to 15 debit card transactions…paying at least one bill online…signing up for paperless statements…and/or having at least one recurring ­direct deposit. Otherwise, for the months in which you don’t meet requirements, you earn a default interest rate that is typically extremely low—possibly as low as 0.01%.

Rewards checking accounts available online with high recent yields…

Consumers Credit Union (CCU) Free Rewards Checking: If you meet the minimum requirements and charge at least $1,000 monthly on a CCU Visa credit card, rewards checking pays a 4.59% APY on balances up to $20,000…0.2% on balances above $20,000…and up to $25,000…and 0.1% on balances over $25,000. In months when you don’t meet the requirements, a 0.01% APY applies. CCU has nine branches in Illinois and, in addition to online banking, access to more than 30,000 ATMs and 1,800 branches in shared networks nationwide. All ATM fees charged by CCU and other banks are reimbursed if you meet the monthly requirements. CCU membership is open to anyone who pays a onetime membership fee of $5 to join the Consumers Cooperative ­Association. ­MyConsumers.org

First Advantage Bank Maximum Earnings: If you meet the minimum requirements, rewards checking pays a 4.5% APY on balances up to $10,000…then a range of 4.5% to 2.01% on balances from $10,000.01 up to $50,000…and 2.01% to 0.51% on balances above $50,000. First Advantage offers online banking, eight brick-and-mortar ­branches in Tennessee and access to a network of tens of thousands of ATMs nationwide. All ATM fees are reimbursed if requirements are met. In months when you don’t meet the requirements, you earn 0.05% APY on all account ­balances and ATM fees are not reimbursed. FirstAdvantageBanking.com

One American Bank Kasasa Cash: This checking account pays a 3.5% APY on balances up to $10,000 in months when you meet the minimum requirements…and above that amount, 0.25%. Although the bank has only three branches, all in South Dakota, ­account holders can bank online and have access to a network of 25,000 no-fee ATMs. The bank reimburses fees from ATMs outside the network up to $25 per month. OneAmericanBank.com

CDs

CD yields offered by online banks have risen much more quickly than those from traditional banks—but only for short-term CDs of up to two years. Long-term CD rates, across the board, aren’t paying enough to make it worth locking up your money. Strategy: For now, avoid CDs longer than two years.

Recent highest-yielding, nationally available, short-term CDs, both of which are online-only…

Live Oak Bank CDs: Two-year term, 2.55% APY, $2,500 minimum, $250,000 maximum, early-termination fee of 180 days of interest. Live Oak also offers a 2.40% APY on 18-month CDs…2.15% APY on 12-month CDs…and 1.95% APY on six-month CDs, all with early-termination penalties of 90 days of interest. LiveOakBank.com

CIT 11-month No-Penalty CD: 1.85% APY, $1,000 minimum. This CD can be cashed in with no penalty starting seven days after your money has been received. BankOnCIT.com

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