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

2. Produced by MEI on behalf of OCR © OCR 2013 Average percentage change A new car costs £25 000 After 3 years it is worth £10 500 What is the average percentage depreciation each year? £25 000 Can you get a rough idea of what the average depreciation is each year?

3. Produced by MEI on behalf of OCR © OCR 2013 A rough idea Using the growing money spreadsheet with negative percentage growth shows that the average is about 25% depreciation a year.

4. Produced by MEI on behalf of OCR © OCR 2013 Getting a more accurate answer Suppose the multiplier for each year’s depreciation is x

5. Produced by MEI on behalf of OCR © OCR 2013 Getting a more accurate answer cntnd

6. Produced by MEI on behalf of OCR © OCR 2013 Some points to note It is useful to have a rough idea of the answer from using a spreadsheet to check the answer. For the overall multiplier, remember that original x multiplier = final value Check the final answer A reduction of 25.1% each year for 3 years from an initial value of £25 000 would be 25000 x 0.749 3 = 10504.74 this agrees with the final value of 10500 once rounding is taken into account.

7. Produced by MEI on behalf of OCR © OCR 2013 Another example The RPI basket of goods increased in price from £100 to £250 in 26 years. What is the average annual percentage increase? Suppose the multiplier for each year’s increase is x. For 26 years, the multiplier is x 26. £100£250 x x 26

8. Produced by MEI on behalf of OCR © OCR 2013 continued £100£250 x x 26 X 2.5

9. Produced by MEI on behalf of OCR © OCR 2013 Powers and roots