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October 2006 ©RSH Percentages Percentage Multiplier

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October 2006 ©RSH Percentages Percentages are used all over the place Percentages Percentages are used all over the place Introduction Sale Now On 12% off Everything ! Sale Now On 12% off Everything ! House Prices go up 12% a year ! VAT 17.5 % Pay rises by 4% Inflation up to 3.5% Save with us and get 4.5% a year!

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October 2006 ©RSH 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 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 Introduction

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October 2006 ©RSH Percentage Increase or Decrease Johns wage is £15000 a year. He gets a 5% pay rise. What is his new wage ? Answer 5% of 15000 = = 750 New wage= 15000 + 750 = £15750 Percentage Increase or Decrease Johns wage is £15000 a year. He gets a 5% pay rise. What is his new wage ? Answer 5% of 15000 = = 750 New wage= 15000 + 750 = £15750 Notes

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October 2006 ©RSH 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 = = 2220 New wage= 18500 - 2220 = £16280 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 = = 2220 New wage= 18500 - 2220 = £16280 Notes

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October 2006 ©RSH Exercise Page 49 Ex 4c

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October 2006 ©RSH Percentage Multipliers Example Increase £60 by 5% Percentage Multipliers Example Increase £60 by 5% Notes Method 1 5% of £60 = = 3 New value= 60 + 3 = £63 Method 1 5% of £60 = = 3 New value= 60 + 3 = £63 Method 2 New value is 105% of £60 105% of £60= 1.05 x 60 = £63 Method 2 New value is 105% of £60 105% of £60= 1.05 x 60 = £63 Percentage Multiplier New value = original + increase = 100% + 5% = 105% = 1.05 Percentage Multiplier New value = original + increase = 100% + 5% = 105% = 1.05

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October 2006 ©RSH Percentage Multipliers Example Increase £800 by 6% Percentage Multipliers Example Increase £800 by 6% Notes Answer New value is 106% of £800 106% of £800= 1.06 x 800 = £848 Answer New value is 106% of £800 106% of £800= 1.06 x 800 = £848 Percentage Multiplier New value = original + increase = 100% + 6% = 106% = 1.06 Percentage Multiplier New value = original + increase = 100% + 6% = 106% = 1.06

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October 2006 ©RSH Percentage Multipliers Example Decrease £800 by 6% Percentage Multipliers Example Decrease £800 by 6% Notes Answer New value is 94% of £800 94% of £800= 0.94 x 800 = £752 Answer New value is 94% of £800 94% of £800= 0.94 x 800 = £752 Percentage Multiplier New value = original - decrease = 100% - 6% = 94% = 0.94 Percentage Multiplier New value = original - decrease = 100% - 6% = 94% = 0.94

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October 2006 ©RSH Exercise Use the multiplier method a)1.04 x 200 = 208 b)1.12 x 150 = 168 c)0.85 x 300 = 255 d)0.96 x 1200 = 1152 a)Increase 200 by 4% b)Increase 150 by 12% c)Decrease 300 by 15% d)Decrease 1200 by 4%

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October 2006 ©RSH 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 ? 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 ? Notes Answer The multiplier is 1.05. a)After 1 year, 1.05 x 1000 = £1050 b)After 2 years, 1.05 x 1050 = £1102.50 Answer The multiplier is 1.05. a)After 1 year, 1.05 x 1000 = £1050 b)After 2 years, 1.05 x 1050 = £1102.50 Check this 1.05 2 x 1000 Check this 1.05 2 x 1000

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October 2006 ©RSH 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 ? 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 ? Notes 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)After 3 years, 0.85 x 10837.50 = £9211.88 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)After 3 years, 0.85 x 10837.50 = £9211.88 Check this 0.85 3 x 15000 Check this 0.85 3 x 15000

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October 2006 ©RSH Repeated % change To work out the value after a number of years (multiplier) years x original value Repeated % change To work out the value after a number of years (multiplier) years x original value Notes 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. After 5 years, she will earn 1.05 5 x 14000 = £17867.94 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. After 5 years, she will earn 1.05 5 x 14000 = £17867.94

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October 2006 ©RSH 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 ? 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 ? 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? Exercise 1.06 4 x 12000 = £15149.72 1.08 10 x 78000 = £168396 0.85 4 x 8000 = £4176.05

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October 2006 ©RSH 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 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 Notes 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. After 10 years, Paul will have 1.04 10 x 4000 = £5920.98 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. After 10 years, Paul will have 1.04 10 x 4000 = £5920.98

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October 2006 ©RSH 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 year b)3 years 2)£20000 is invested for ten years at 12% compound interest. What will the investment be worth then ? Exercise a)1.14 x 2000 = £2280 b)1.14 3 x 2000 = £2963.09 a)£62116.96

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