1. Repeated Percentage & Proportional Change

2. Reminder How to calculate a PERCENTAGE change Decrease £17·60 by 15% 85% of 17·60 = £14·96 Left with 85% of 17·60 = 17·60 x 0·85 MULTIPLIER of 0·85

3. So…. We can use this procedure for repeated changes such as: (i) Interest of money in bank account (ii) Depreciation of a motor car

4. COMPOUND INTEREST e.g. Interest on Bank Account £4 000 earns 5% interest each year. How much is it worth after 3 years? End of Year 1 End of Year 2 End of Year 3 4 000 x 1·05= 4 200 4 200 x 1·05= 4 410 4 410 x 1·05= 4 630·50 4 000 x 1·05 4 000 x 1·05 x 1·05 4 000 x 1·05 x 1·05 x 1·05 4 000 x 1·05 2 4 000 x 1·05 3 4 000 x 1·05 1

5. Simple Interest? If an account only receives SIMPLE INTEREST, the £200 earned in the first year would be the same for every year In our example, that means 4 000 + 3 x 200 = £4 600

6. e.g. Value of a car David buys a new Ford for £14 000. It loses value at the rate of 15% each year. How much is it worth after 3 years? End of Year 1 End of Year 2 End of Year 3 14 000 x 0·85= 11 900 11 900 x 0·85= 10 115 10 115 x 0·85= 8 597·75 14 000 x 0·85 14 000 x 0·85 x 0·85 14 000 x 0·85 x 0·85 x 0·85 14 000 x 0 · 85 2 14 000 x 0 · 85 3 14 000 x 0 · 85 1

7. Proportionate Increase Andrew said he would increase his donation to charity by 6% each year. He starts with £120. How much did he give after 5 years? After 1 year: £120 x (1·06) = £127·20 After 5 years: £120 x (1·06) 5 = £160·59 to nearest penny