NASHVILLE (AP) — Tennesseans drawing unemployment benefits will soon lose a weekly $15-per-child allowance as part of a new law signed by Republican Gov. Bill Haslam.The Department of Labor and Workforce Development said Friday the change will help bolster the state unemployment trust fund, which could lead to a reduction in unemployment taxes paid by businesses.According to the department’s projections, ending the allowance for dependent children in the budget year beginning July 1 will save the state $40 million per year.Lawmakers created the child allowance in 2009 in order to qualify for a nearly $142 million federal stimulus grant. Since that money has been spent, the Republican-controlled Legislature earlier this year passed a bill to end the program.