1. Produced by MEI on behalf of OCR © OCR 2013 Introduction to Quantitative Methods Percentage change

2. Produced by MEI on behalf of OCR © OCR 2013 At the sales You may have seen signs like the one below in shop windows. Special offers like this, lasting one or two days are quite common. A shop will not usually change all its price tags for a short sale. Special offer! 20% off today

3. Produced by MEI on behalf of OCR © OCR 2013 20% off £8 £14.99 £65 £48.99 £42.50 The price tags show the usual price. Can you work out the sale price without a calculator?

4. Produced by MEI on behalf of OCR © OCR 2013 Working out 20% How many ways can you think of for working out 20%? Did you use the same method for each of the reductions?

5. Produced by MEI on behalf of OCR © OCR 2013 Working out percentages in your head It can be useful to be able to work out percentages in your head – it is useful for one day sales but also handy when checking on numbers in the news. When working out percentages in your head, start from knowing that 100% is the whole amount.

6. Produced by MEI on behalf of OCR © OCR 2013 22 22 22  10 22 What other percentages can you work out in your head?

7. Produced by MEI on behalf of OCR © OCR 2013 A visual aid Some people like to imagine a bar to visualise 100%. 0% 100% 0£65 10% 20% £6.50£13 £65 reduced by 20% is £65 - £13 = £52

8. Produced by MEI on behalf of OCR © OCR 2013 At the till A decrease of 20% means that each £1 becomes £0.80. So to find the result of a 20% drop, you can multiply the original amount by 0.8. 65  0.8 = 52 0.8 is called a multiplier. Multipliers are useful for percentage change when using a calculator or spreadsheet.

9. Produced by MEI on behalf of OCR © OCR 2013 Using a spreadsheet It is possible to work out a large number of percentage change calculations very quickly on a spreadsheet. This is useful for an online shop having a one day sale – they can show reduced prices with little effort. It is also useful for small businesses calculating VAT.

10. Produced by MEI on behalf of OCR © OCR 2013 Displaying money with 2 dp Choose the cells by holding down the left mouse button. Then choose “format cells”

11. Produced by MEI on behalf of OCR © OCR 2013 Displaying money with 2 dp (pt2) Choosing Number with 2 decimal places will work. Alternatively, you can choose currency if this is an option on your spreadsheet.

12. Produced by MEI on behalf of OCR © OCR 2013 Working out sale prices Remember to start a formula with = To reduce by 20%, the multiplier is 0.8. Type the formula in once then copy down Because you have set 2 decimal places, the numbers will round to the nearest penny.

13. Produced by MEI on behalf of OCR © OCR 2013 Value Added Tax (VAT) A bill for simple car repairs is shown on the left. It includes VAT; this is a tax charged on many goods and services. Prices are sometimes quoted before VAT; some businesses can claim back VAT on things they buy for business use. The VAT rate for this bill was 20%.

14. Produced by MEI on behalf of OCR © OCR 2013 Percentage increase VAT increases prices by 20%. Inflation increases prices by a percentage. Interest on loans (or savings) increase money owed (or saved) by a percentage. When you worked out percentage profit, you were working out how many % the original investment had increased by. Percentage increase is also used in many other situations – not all to do with money.

15. Produced by MEI on behalf of OCR © OCR 2013 Working out VAT The garage bill was £58.99 before VAT. VAT at 20% is added on. This can be worked out mentally. £58.99 is nearly £59 – this will make working mentally easier. 0% 100% 0£59 10% 20%

16. Produced by MEI on behalf of OCR © OCR 2013 Multipliers for percentage increase When prices are increase by 20%, each £1 becomes £1.20. The multiplier for a 20% increase is 1.2. £58.99  1.2 = £70.788 which is £70.79 to the nearest penny. This is the total price including VAT.

17. Produced by MEI on behalf of OCR © OCR 2013 Down and up Imagine I buy some shares. The price goes down by 20% in the first week. The price goes up by 20% in the second week. Which of the following is true? A.The price is back to where it started. B.The final price is lower than the original price. C.The final price is higher than the original price. D.It depends

18. Produced by MEI on behalf of OCR © OCR 2013 Down and up Imagine the shares originally cost £100. 20% drop means they are now worth £80. 20% increase is 20% of £80. 10% is £8 so 20% is £16. The shares are worth £96 at the end. The final price is lower than the original price. What if the shares had not originally cost £100 – would the final price still be lower than the original?

19. Produced by MEI on behalf of OCR © OCR 2013 Percentage of what? The same percentage of a different amount gives a different result.

20. Produced by MEI on behalf of OCR © OCR 2013 Multipliers are handy for percentages A decrease of 20% means that each £1 becomes £0.80. So to find the result of a 20% drop, you can multiply the original amount by 0.8. An increase of 20% means that each £1 becomes £1.20. So to find the result of a 20% increase, you can multiply the original amount by 1.2.

21. Produced by MEI on behalf of OCR © OCR 2013 Change and change again A 20% drop followed by a 20% increase can be worked out by multiplying by 0.8 then multiplying the answer by 1.2. So for a 20% drop followed by a 20% increase; final amount = original x 0.8 x 1.2. Numbers can be multiplied in any order so final amount = original x 0.96