Percentages Percentage Multiplier October 2006 ©RSH
Introduction Percentages • Percentages are used all over the place Sale Now On 12% off Everything ! Pay rises by 4% October 2006 House Prices go up 12% a year ! VAT 17. 5 % Save with us and get 4. 5% a year! ©RSH Inflation up to 3. 5%
Introduction Percent – a reminder • 5% means 5 out of 100 or • To work out 5% of 60, do this 5% of 60 = = 0. 05 x 60 =3 October 2006 ©RSH
Notes Percentage Increase or Decrease • John’s wage is £ 15000 a year. He gets a 5% pay rise. What is his new wage ? Answer 5% of 15000 = New wage = 750 = 15000 + 750 = £ 15750 October 2006 ©RSH
Notes Percentage Increase or Decrease • My car cost £ 18500 last year. It dropped in value by 12%. What is it worth now ? Answer 12% of 18500 = New wage October 2006 = 2220 = 18500 - 2220 = £ 16280 ©RSH
Exercise Page 49 Ex 4 c October 2006 ©RSH
Notes Percentage Multipliers Example • Increase £ 60 by 5% Method 1 • 5% of £ 60 New value Percentage Multiplier New value = original + increase = 100% + 5% = 105% = 1. 05 = =3 = 60 + 3 = £ 63 Method 2 • New value is 105% of £ 60 = 1. 05 x 60 = £ 63 October 2006 ©RSH
Notes Percentage Multipliers Example • Increase £ 800 by 6% Percentage Multiplier New value = original + increase = 100% + 6% = 106% = 1. 06 Answer New value is 106% of £ 800 = 1. 06 x 800 = £ 848 October 2006 ©RSH
Notes Percentage Multipliers Example • Decrease £ 800 by 6% Percentage Multiplier New value = original - decrease = 100% - 6% = 94% = 0. 94 Answer New value is 94% of £ 800 = 0. 94 x 800 = £ 752 October 2006 ©RSH
Exercise Use the multiplier method a) b) c) d) Increase 200 by 4% Increase 150 by 12% Decrease 300 by 15% Decrease 1200 by 4% October 2006 ©RSH 1. 04 1. 12 0. 85 0. 96 x x 200 = 208 150 = 168 300 = 255 1200 = 1152
Notes Repeated % change • The multiplier is useful for working out repeated % change problems. Example • £ 1000 is put into a savings account paying 5% p. a. , what will be in the account after a) 1 year ? b) 2 years ? Answer The multiplier is 1. 05. a) After 1 year, 1. 05 x 1000 = £ 1050 b) b) After 2 years, 1. 05 x 1050 = £ 1102. 50 October 2006 ©RSH Check this 1. 05 2 x 1000
Notes Repeated % change Example • A car worth £ 15000 reduces in value by 15% each year. What will the car be worth in a) 1 year ? b) 2 years ? c) 3 years ? Answer The multiplier is 0. 85. a) After 1 year, 0. 85 x 15000 = £ 12750 b) After 2 years, 0. 85 x 12750 = £ 10837. 50 c) c) After 3 years, 0. 85 x 10837. 50 = £ 9211. 88 October 2006 ©RSH Check this 0. 85 3 x 15000
Notes Repeated % change To work out the value after a number of years (multiplier)years x original value Example In 2005, Sara earned £ 14000. She gets a 5% pay rise every year. What will she earn in 2010 ? Answer The multiplier is 1. 05. 1. After 5 years, she will earn 1. 055 x 14000 = £ 17867. 94 October 2006 ©RSH
Exercise 1) A computer operator is paid £ 12000 a year. Assuming her pay is increased by 6% each year, what will her salary be in 4 years time ? 1. 1. 064 x 12000 = £ 15149. 72 2) The price of a small flat was £ 78000 in 1995. At the end of each year, the price has increased by 8%. What was the flat worth in 2005 ? 1. 1. 0810 x 78000 = £ 168396 3) A new bike is valued at £ 8000. At the end of each year, its value is reduced by 15% of its value at the start of the year. What will it be worth after 4 years? 1. 0. 854 x 8000 = £ 4176. 05 October 2006 ©RSH
Notes Compound Interest • Banks and Building Societies pay interest on the amount in a saving account. • If you leave the interest in the account, you will get more interest next year. • This is called Compound Interest Example In 2006, Paul put £ 4000 in a saving account paying 4% compound interest every year. What will be in this account in 2016 ? Answer The multiplier is 1. 04. 1. After 10 years, Paul will have 1. 0410 x 4000 = £ 5920. 98 October 2006 ©RSH
Exercise 1) A bank pays interest of 14% on money in deposit accounts. Mrs. Wells puts £ 2000 in the bank. How much does she have after a) 1. 14 x 2000 = £ 2280 a) 1 year b) 3 years b) 1. 143 x 2000 = £ 2963. 09 2) £ 20000 is invested for ten years at 12% compound interest. What will the investment be worth then ? a) £ 62116. 96 October 2006 ©RSH
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