Hawaiian Electric Industries Inc. today reported a 5 percent increase in net income in the second quarter as gains at its bank subsidiary more than offset  lower earnings in its utility business.

The company earned $40.6 million, or 41 cents a share during the April-through-June period, up from $38.8 million, or 40 cents a share in the same quarter a year earlier.

The companies of Hawaiian Electric Co., which provide electricity service in Honolulu, Maui and Hawaii counties, earned $28.7 million in the second quarter, down from $29.4 million in the year-ago quarter.

HEI’s American Savings Bank subsidiary released its second-quarter financial results last week. The bank’s net income was up 12 percent to $15.9 million, compared with $14.2 million in the second quarter of 2012.

HEI shares closed up 36 cents at $26.81 on the New York Stock Exchange.