What is the GST component?

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Question from Jilly:

I need to find a quick and easy formula for finding the gst (10%) of the total amount in $ terms, eg: the total is $500 what is the gst component?
This might seem easy to you of course, thank goodness, but no one in my office can work out how to go backwards. We can all do the 'add' 10% but not when we have a total.

Hi Jilly,

Here in Canada the GST is 5%.

Suppose that the price before the GST is $B, the price after is $A and the tax rate is r. (In your example $A = $500 and r = 0.10.) If you know the before price and the tax rate then, as you said, you just add the tax

$A = $B + r × $B

$A = $B(1 + r)

To find $B you divide both sides by 1 + r to get

$B = $A/(1 + r)

Thus in your example with $A = $500 and r = 0.10

$B = $500(/1 + 0.10) = $500/1.10 = $454.55

I hope this helps,
Penny

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