>>I see others have given the answer.
>>
>>I just wanted to point out that a government imposing a tax on another tax is one of the scummiest things it can do. But, your calculation example is correct: http://www.revenuquebec.ca/en/entreprise/taxes/tvq_tps/default.aspx
>
>Well, I am analyzing the replies to this thread and, so far, the closest one is from Andrew. But, it gives 500.03$ instead of 500.00$. I have been asking myself if this is possible. Because, of the problem of one tax over another. You pointed that out in your reply. I agree with that.

Re: the calculation, I'd just back out the values in the reverse order they were originally calculated.

If you start with total value $574.88 (actually $575.875), that is 1.095 * ( Price + FedTax ), so

( Price + FedTax ) = 574.88 / 1.095, = 525.00

Then, ( Price + FedTax ) = Price * 1.05, so

Price = ( Price + FedTax ) / 1.05, = 525.00 / 1.05, = 500.00

If you want to do it all in one step:

T = total dollar value including all taxes
P = provincial tax rate as a decimal e.g. 9.5% = 0.095
F = federal tax rate as a decimal e.g. 5% = 0.05
I = item price

Then I = ( T / ( 1 + P ) ) / ( 1 + F )