Repeated Percentage & Proportional Change

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

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

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 4 000 x 1·05 = 4 200 COMPOUND INTEREST 4 000 x 1·05 4 000 x 1·051 End of Year 2 4 200 x 1·05 = 4 410 4 000 x 1·052 4 000 x 1·05 x 1·05 End of Year 3 4 410 x 1·05 = 4 630·50 4 000 x 1·05 x 1·05 x 1·05 4 000 x 1·053

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

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 14 000 x 0·85 = 11 900 14 000 x 0·85 14 000 x 0·851 End of Year 2 11 900 x 0·85 = 10 115 14 000 x 0·852 14 000 x 0·85 x 0·85 End of Year 3 10 115 x 0·85 = 8 597·75 14 000 x 0·85 x 0·85 x 0·85 14 000 x 0·853

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