Repeated Percentage Proportional Change Reminder l How to

Repeated Percentage & Proportional Change

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

So…. l 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 End of Year 2 4 000 x 1· 05 4 200 x 1· 05 = 4 410 D N U O 4 000 x 1· 051 C P 4 000 x 1· 05 M O End of Year 3 E R E T = 4 200 IN 4 000 x 1· 05 4 410 x 1· 05 T S 4 000 x 1· 052 = 4 630· 50 4 000 x 1· 054 000 x 1· 053

Simple Interest? l l 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 End of Year 2 11 900 x 0· 85 = 10 115 14 000 x 0· 85 End of Year 3 14 000 x 0· 851 14 000 x 0· 852 10 115 x 0· 85 = 8 597· 75 14 000 x 0· 8514 000 x 0· 853

Proportionate Increase l l l 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