ANCHORAGE, Alaska — Alaska Gov. Sarah Palin has until June 23 to reimburse the state for an estimated $10,000 in costs associated with trips taken by her children, under an agreement resolving an ethics complaint against her.

Palin was given 120 days to repay the state after the late February agreement filed by an Alaska Personnel Board special investigator. The complaint alleged Palin abused her power by charging the state when her children traveled with her.

The investigator, attorney Timothy Petumenos, has said Palin will repay the state for 10 trips.

State administrative director Linda Perez is responsible for tallying the exact figure, according to Palin spokeswoman Sharon Leighow.

"The governor is in full compliance with the resolution of the travel matter," Leighow said Friday in an e-mail. "The governor will provide the reimbursement on or before the due date in the amount determined by Linda Perez."

Anchorage resident Frank Gwartney, a Democrat, filed the complaint in late October. Palin was the Republican vice presidential candidate at the time and after the February settlement called the complaint "an obvious political weapon."

The board found no wrongdoing on Palin's part and Petumenos said in his report there is little guidance under state rules to determine ethical standards for travel by the governor's immediate family. But he interpreted the law to require that the state pay only if the first family serves an important state interest.

Palin is paying for the trips that were found to be of questionable state interest among 72 travel authorizations studied.

Questionable trips included daughter Bristol Palin accompanying her mother to New York for Newsweek's Third Annual Women and Leadership Conference in October 2007. Another was a February 2007 trip from Juneau to Anchorage for Palin's three daughters. The family then went to Big Lake, about 50 miles north of Anchorage, for the start of the Tesoro Iron Dog snowmobile race in which the governor's husband, Todd Palin, participated.

As part of the settlement, Petumenos asked the Alaska Department of Law to develop specific rules outlining when the state should pay for the travel of a governor's family.

That effort is under way, said Judy Bockmon, an assistant attorney general, with the goal to have a final draft by the end of the year.