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1.13 Going down, going up

This activity involves working out increases and decreases together.

Activity 7 Going down, going up

You have set your eyes on a new dresser for your room, which is on sale at 30 per cent off. Have you ever asked yourself if it makes a difference if the discount is applied first, and then VAT (currently 20 per cent), or if it is done in the opposite order: VAT applied first, and then the discount?

Comment

Try a numerical example first to get a feel for the problem. For example, what happens if the price of the dresser was £100 (before the discount and VAT have been applied)?

Answer

If the item costs £100, reducing the price first gives pound times 100 minus pound times 30 equals pound times 70.

VAT is 20 per cent of £70, which is £14.00. So the final bill is pound 70 postfix plus pound 14 equals pound 84.

Now, let's try it the other way. Adding the VAT first gives 1.2 multiplication pound times 100 equals pound times 120. (The cost of the dresser represents 100 per cent and the VAT is 20 per cent, to calculate to cost plus VAT we need to work out 100 per cent + 20 per cent = 120 per cent of the cost, or 1.2 of the cost. This a quicker way of working out 20 per cent and then adding it separately to the cost).

The discount is 30 per cent of £120, which is 0.3 multiplication pound times 120 equals pound times 36. So the total bill is pound 120 postfix minus pound 36 equals pound 84.

It does not seem to matter whether the discount or the VAT is applied first. But can you be sure? Doing more numerical examples would confirm it. However, these could just be lucky choices. Let’s analyse what we can tell using these particular discount/VAT rates.

If the discount is 30 per cent, the price after the discount will be 100 percent negative 30 percent equals 70 percent of the original cost. You can find the discounted base price by multiplying the cost by 0.7.

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

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

Since it does not matter in which order the multiplication operations are carried out, as multiplication is commutative, the answer will be the same using either method. This will work with any type of discount and VAT.