Calculate the finance charge and new balance using the previous balance method. previous balance = $179.32 annual rate = 16% finance charge = $ new purchases = $117.42 payments/credits = $85.00 new balance = $

Annual Rate = 16% = 16/100 = 0.16
Monthly Rate = (annual rate)/12
Monthly Rate = (0.16)/12
Monthly Rate = 0.01333 ... this is approximate

Finance Charge = (Monthly Rate)*(Previous Balance)
Finance Charge = (0.01333)*(179.32)
Finance Charge = 2.3903356
Finance Charge = 2.39

The purchases and payments do not factor in the finance charge since they are made during this current billing cycle. The previous balance method only looks at the balance at the end of the previous cycle. 

Once the finance charge is calculated, we add on the new purchases and the finance charge to the old balance. We also subtract off the payments/credits. Doing all this calculates the new balance for this billing cycle. 

New Balance = (Old balance) + (Purchases) + (Finance Charge) - (Payment)
New Balance = 179.32 + 117.42 + 2.39 - 85
New Balance = 214.13

In summary, 
Finance Charge = $2.39
New Balance = $214.13

This does not make sense