By my calculations (which could be wrong or based on incomplete information) for last month...
Gross: €5,448
TAX
Single person standard rate band = €34K p.a. or €2,833.33 p.m. (check what it says on his statement of tax credits about his SRCOP - Standard Rate Cut Off Point)
Gross tax:
€2,833.33 @ 20% = €566.67
(€5,448 - €2,833.33) @ 41% = €2,614.67 @ 41% = €1,072.01
Total: €1,638.68
Net tax (gross tax minus tax credit)
€1,638.68 - €317.34 = €1,321.34
So I don't get the same figure as above but could be missing some info or there may be a payroll error.
PRSI
Monthly PRSI exemption (2% health levy only): €551 @ 2% = €11.02
Rest at 6% (2% health levy + 6% PRSI): €5,448 - €551 = €4,897 @ 6% = €293.82
Total: €304.84*
* If/when his cumulative annual earnings exceed the employee PRSI threshold of €48,800 then he will stop paying 4% PRSI on any earnings (assuming that he does not earn more than €100,100 in the year).