1. Repeated Percentage & Proportional Change

2. 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

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. 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

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
x 200 = £4 600

6. e.g. Value of a car
David buys a new Ford for £
It loses value at the rate of 15% each year.
How much is it worth after 3 years?
End of Year 1
x 0·85 =
x 0·85
x 0·851
End of Year 2
x 0·85 =
x 0·852
x 0·85 x 0·85
End of Year 3
x 0·85
= 8 597·75
x 0·85 x 0·85 x 0·85
x 0·853

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