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Complaints about student loans are up almost 40 percent nationwide over the past year, a federal agency said this week. But gripes about local servicer Discover Financial Services are down slightly despite education lending being a bigger part of the Riverwoods-based company’s balance sheet.

The Consumer Financial Protection Bureau said in its annual report Tuesday that it handled about 5,300 complaints about private student loan providers in the year ended Sept. 30, up 38 percent from the preceding year.

Student loans are a relatively small but growing piece of business for Discover, which is best known for its credit cards. It had $4.3 billion in private student loans on its books at the end of June, up from $4 billion at the end of the year.

The bureau, which has an online portal that enables consumers to submit complaints about student loans and other financial products, said beefs about Discover student loans dropped to 165 over the one-year period, from 174 the prior year.

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But Discover’s track record of fewer complaints is scoring it few points with the bureau.

The company revealed in an SEC filing that it is under investigation by the agency over its student loan servicing practices.

Discover noted, for example, that issuers of private student loans are under pressure to expand the availability of loan modifications for borrowers.

Concerns also have been raised about the liability of student borrowers in the event of a co-signer’s death or bankruptcy. Consumer advocates also have asked Congress to pass legislation that would make it easier to discharge private student loan debt in bankruptcy; currently student loans are rarely dischargeable in bankruptcy court.

Concerns also have been expressed about everything from how service members’ debt is treated to how federal student loan interest rates are determined, which could also affect the private student loan market.

Additional federal action “may increase the complexity and expense of servicing student loans,” Discover warned investors.

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