2.2 Does the order of percentage change calculations matter?

Answer

Discount first, then VAT

Discount on dresser = 30% of £100 = 0.3 × £100 = £30

So price including discount = £100 – £30 = £70

Now add the VAT onto this discounted price.

VAT = 20% of £70 = 0.2 × £70 = £14.00

So the final price to pay = £70 + £14 = £84

VAT first, then discount

VAT on original price = 20% of £100 = 0.2 × £100 = £20

So price including VAT = £100 + £20 = £120

Discount on price = 30% of £120 = 0.3 × £120 = £36

So final price = £120 – £36 = £84

Both prices are the same!

It does not seem to matter whether the discount or the VAT is applied first. But can you be sure that this is always true from exploring one example? Doing more numerical examples would confirm it. However, these could just be lucky choices of numbers. What you need to do is analyse what you can tell about the maths being used by looking at these particular discount and VAT rates.

The original cost of the dresser is 100 per cent of the price – that is, the whole price. You know that the discount is 30 per cent, so the price after the discount will be 100% – 30% = 70% of the original cost. You can find the discounted price by multiplying the cost by 0.7, since 0.7 is 70% as a decimal.

To calculate the price including VAT, you need to find 20 per cent of the price and add this onto the price (100 per cent). To do this in one step, you can work out 100% + 20% of the price, which is the same as 120 per cent of the price (or 1.2 as a decimal).

So if the discount is applied first and then the VAT, it’s 120 per cent of 70 per cent of the original price and can be expressed as 1.2 × 0.7 × original price.

If the VAT is applied first and then the discount, it’s 70 per cent of 120 per cent of the original price, and can be expressed as 0.7 × 1.2 × original price.