Math Is Fun Forum

AJ_1

Member

Registered: 2009-06-03

Posts: 1

VAT (Sales Tax) calculation and error

Hi All,

I am looking into an interesting question/problem that has arisen from an application I am working on.

The application takes a collection of costs, and then calculates the VAT (sales tax for you Americans ) for the cost, before finally giving a total cost including VAT.

If we say VAT is calculated at 17.5% of the price of the cost of the goods, then the customer will be charged:

The total cost of goods (including VAT) is rounded to 2 decimal places, so it is in a correct pricing format (£xx.xx).

My question is this... If there are multiple costs for a single person, is it more accurate to calculate the VAT costs individually, and then sum the total of the costs (inc VAT), OR to sum the costs then calculate the VAT on top of that?

I have created an excel spreadsheet containing ~800 individual costs.  If I calculate the VAT (and round to 2 decimal places) then take a total, the cost that the customer will be charged is larger than if I calculate the sum of the costs (exc VAT) and THEN calculate the VAT on the total sum.  In my example, the difference between the two final costs was £1.11.

Many thanks in advance for any advice you can give,

AJ

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: VAT (Sales Tax) calculation and error

It's more accurate to sum the prices and then put VAT on the total, because that way you're only rounding once and so the result can't be further than 1p from the 'true' price.

For an extreme example, consider what would happen if your 800 items were all pennies.
They cost 1p, so the price of each one with VAT would be 1.175p ≈ 1p.
The total cost is then £8, and VAT has no effect at all.

By contrast, adding them up first to get £8 and then adding VAT gives £9.40, which is much more sensible.

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Why did the vector cross the road?
It wanted to be normal.