NEW YORK » AT&T is making it easier for customers to upgrade their cellphones more frequently, as long as they’re willing to pay more.

The country’s second-largest cellphone carrier says it’s introducing an option called AT&T Next on July 26. Instead of paying, for example, $200 up front to buy a smartphone, customers would pay monthly installments of $15 to $50 on top of their service plan, depending on the device.

The new plan is designed to satisfy customers who want the latest and greatest devices. The traditional two-year service contracts get in the way of annual upgrades. Last week, competitor T-Mobile US Inc. introduced Jump, which provides device insurance and more frequent upgrades for $10 a month.

Under the AT&T Next option, customers can trade in their phone after a year and get a new one, paying no upgrade or activation fees. As an alternative, they can stop paying the installments after 20 months and keep the device.

AT&T says a Samsung Galaxy S4 phone, for instance, would require monthly installments of $32, or $640 over 20 months. At that price, the installment plan makes for a far more expensive phone than one bought for the usual $200 up-front fee.

A customer who trades the S4 in after a year also loses money compared with someone who buys the phone for $200, then breaks the contract after 12 months, pays the early termination fee and sells the phone to finance a new one. With the installment plan, the customer pays $384 in a year. Without it, the customer pays $478 for the phone and for activation, termination and upgrade fees, but can make about $300 of that back by selling the old phone. AT&T Next does eliminate the hassle of ending a contract and finding a buyer.

T-Mobile introduced a more comprehensive change to its plans in March. In effect, it lowered the monthly service fees but introduced installment plans for its phones. The Jump plan announced last week is an extra $10 a month and allows people to upgrade up to twice a year. The customer must pay the $100 up-front fee for each new phone. There’s a deductible of up to $175 if the phone is lost, doesn’t work, has water damage or has a cracked screen. (AT&T Next does not have an insurance component.)

With Jump, customers break even when they replace at least every 16 months. At that point, a customer would have $160 left in installment payments, and Jump would have cost $160 in monthly fees. A person who upgrades the maximum of twice a year benefits with Jump over the regular installment plan, but would still pay $540 extra over the course of two years, compared with keeping the same device for two years. That’s $300 in up-front fees for three additional phones and $240 for the cost of Jump.