BINGHAM — It took three rounds of voting this summer, but residents of School Administrative District 13 finally approved the 2012-13 budget Tuesday by a vote of 106-98.

Bingham voters rejected the $3,019,075 spending package 67-65, but residents of Moscow approved it 41-31, giving the “yeas” the day.

Residents in the two-town district sent the new budget, which is $98,000 less than previously proposed, to the polls at a budget meeting earlier this month.

Voters rejected the original $3.1 million budget in referendum voting in July. The proposed spending package failed by 40 votes — 153-113. Residents rejected the same spending package by four votes in a June 12 referendum.

It was the second time district voters approved the spending at a public budget meeting only to reject it at the polls.

Under the budget, Bingham will be assessed a total of $647,392. That figure includes the required local share and additional local spending, according to SAD 13 Superintendent Virginia Rebar.

Bingham First Selectman Steven Steward said town tax bills already have been sent out using the county tax, money raised at the annual town meeting and rates included in the previous $3.1 million school budget.

Steward said the tax rate in Bingham now is $19 for every $1,000 in property valuation and does not reflect the new schools budget. The owner of a home valued at $100,000 is paying $1,900 this year, up $90 over last year when the tax rate was $18.10.

In Moscow, residents will have to come up with $884,513 as their combined share of the school budget, according to Rebar. As in Bingham, the tax bills already have gone out, according to First Selectman Donald Beane.

The property tax rate in Moscow has increased from $16.90 per $1,000 in assessed value to $17.50. The owner of a home valued at $100,000 will see a $60 increase from the $1,690 paid this year.

Rebar has said that, despite failed votes this summer, she believes people in the district are supportive of education, but tough economic times have taken their toll.

“It’s just not a good time,” Rebar said in July. “It’s a struggle for many districts, and we’re one of them.”

She was unavailable for comment Tuesday night after the votes were counted