Yup, I admit it… I fell into the trap, and until today I never realised!

17.5% to 15% is 2.5% difference… ah, easy sums I thought!

So, 2.5% of £10 is 25p, isn’t it?

Urm, yes… but no, actually!

Let me ask, how much does your £10 mobile top-up really cost?

£8.51 I’ve (re*)discovered…

Why?

It is all to do with this assumption we make about things costing 100%.

[It’s nice’n’simple, really 🙂 … we survive well enough in our 20% off sales and all that, because just to keep the maths simple, most folks stick with the convention of the customer-payment-amount being 100%.]

But these assumptions aren’t the whole picture.

Anything we buy actually costs 117.5%… That’s 100% for the shops and that’s 17.5% for the government. (Note: This is not 82.5% for the shops – the changing calculations would then mean the shops were *also* refunding us 0.35% as well… please don’t ask me to explain that percent, I’m just guessing 😛 )

So… now we have VAT changes coming in… *ahem* [EQUATION ALERT]

17.5% – old price of VAT

117.5% – old price of an item with VAT

15% – new price of VAT

115.0% – new price of an item with VAT

But when we go from 117.5% to 115%, it is most definitely not equivalent maths to 100% going down to 97.5%. This is where my earlier assumption went wrong – 25p would be the difference between 97.5% and 100%.

So, how do we calculate the difference between 115% and 117.5%?

Well, firstly you divide your £10 top-up cost by 1.175 to find the “100%” price without VAT: that would be £8.51. (That’s what the shops get.)

To check the logic: you work out 17.5% of £8.51. That’s £1.49. (That’s what the government gets.) Then you add £8.51 and £1.49 and get £10: that’s what you pay. All fine so far..

But when you work out VAT at 15%… 15% of £8.51 = 1.28 (Or 1.276 to be exact). This works out as you paying £8.51 to the shop, same as before, and £1.28 to the government. A total of £9.79.

Or 21p short of £10…

Ok, so my calculation gives 21p… but technically the real figure is somewhere almost in the middle of 21 and 22, but nearer the 21. That means that when we’re getting 22p back, we’re getting the over-generous side of the calculation!

Sorry, O2 for misjudging you. That’ll teach me to be cynical about society…! *ahem*

And maybe if I’d been paying more attention, I’d have heard lots of people mention the “22p” bit… I need more listening practice. Thankfully I am heading home soon, so I won’t have much choice but to practice, practice, practice… 😉

**Ps: scarily all the way through writing this post I’ve had this weird dejavu of sitting in my maths classroom at school hearing one of my teachers explain all this to me… clearly I never completely got it, ‘cos it still took me “figuring out time” to remember what was wrong!:-P*