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Simple Interest / Compound Calculating Percentages www.mathsrevision.com Int 2 Compound Interest Appreciation / Depreciation Inflation / Working back created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 20151

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Starter www.mathsrevision.com Int 2 created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 2

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www.mathsrevision.com Int 2 Calculating Percentages Just Calculating Percentages Simple Interest Compound Interest Appreciation More Depreciation Less Inflation Rising Prices Working backwards created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 3

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Learning Intention Success Criteria 1.To know the meaning of the term simple interest. 1.To understand the term simple interest and compound interest. 2.To know the meaning of the term compound interest. www.mathsrevision.com Int 2 Calculating Percentages 3.Know the difference between simple and compound interest. created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 20154

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Calculating Percentages Just working out percentages www.mathsrevision.com Int 2 Simple Interest I have £400 in the Bank. At the end of each year I receive 7% of £400 in interest. How much interest do I receive after 3 years. How much do I now have? created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 5

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Now try Exercise 1 Ch2 (page 8) Odd Numbers www.mathsrevision.com Int 2 Calculating Percentages created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 6

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www.mathsrevision.com Int 2 Calculating Percentages Compound Interest Interest calculated on new value every year Real life Interest is not a fixed quantity year after year. One year’s interest becomes part of the next year’s amount. Each year’s interest is calculated on the amount at the start of the year. Example Daniel has £400 in the bank. He leaves it in the bank for 3 years. The interest is 7% each year. Calculate the simply interest and then the compound interest after 3 years. Principal value created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 7

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www.mathsrevision.com Int 2 Calculating Percentages Compound Interest Daniel has £400 in the bank. He leaves it in the bank for 3 years. The interest is 7% each year. Calculate the compound interest and the amount he has in the bank after 3 years. Y1 : Interest = 7% of £400 = £28 Amount = £400 + £28 = £428 Y 2 : Interest = 7% of £428 = £29.96 Amount = £428 + £29.96 = £457.96 Y 3 : Interest = 7% of £457.96 = £32.06 Amount = £457.96 + £32.06 = £490.02 Compound is £490.02 - £400 = £90.02Simple Interest is only £84 Interest = 7% of £400 = £28 3 x 28 = £84 Simple Interest Interest calculated on new value every year created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 8

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Now try Exercise 2 Ch2 (page 8 & 9) www.mathsrevision.com Int 2 Calculating Percentages created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 9

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Starter www.mathsrevision.com Int 2 created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 201510

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Learning Intention Success Criteria 1.To calculate compound interest using calculator.. 1.To understand how to use the calculator to calculate compound interest easier. 2.Show appropriate working when solving problems. www.mathsrevision.com Int 2 Calculating Percentages created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 201511

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www.mathsrevision.com Int 2 Calculating Percentages Using a calculator to do Using a calculator to do Compound Formula created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 12 n = period of time Days, months years ± = increase or decrease I = initial value V = Value IMPORTANT Can only use this when percentage is fixed This is called the multiplier.

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www.mathsrevision.com Int 2 Calculating Percentages Using a calculator Using a calculator to do Compound questions Calculate the money in the bank after 3 years if the compound interest rate is 7% and the initial value is £400. V= 400 x (1.07) 3 = £490.02 created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 13 n = 3 ± = increase 1+0.07=1.07 I =400

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www.mathsrevision.com Int 2 Calculating Percentages Using calculator Using calculator to calculate Compound questions In a jar bacteria grows 4% every hour. Initially there were 200 bacteria in the jar. How many bacteria are in the jar 4 hours later. V= 200 x (1.04) 4 = 234 created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 14 n = 4 ± = increase 1+0.04=1.04 I =200

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www.mathsrevision.com Int 2 Calculating Percentages Using calculator Using calculator to calculate Compound questions A car reduces in price by 14% each year. Initially it cost £12 500. much is it worth 5 years later. V= 12 500 x (0.86) 5 = £5880.34 created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 15 n = 5 ± = increase 1-0.14=0.86 I =12 500

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Now try worksheet www.mathsrevision.com Int 2 Calculating Percentages created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 16

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Starter www.mathsrevision.com Int 2 created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 201517

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Learning Intention Success Criteria 1.To know the terms appreciation and depreciation. 1.To understand the terms appreciation and depreciation. 2.Show appropriate working when solving problems containing appreciation and depreciation. www.mathsrevision.com Int 2 Calculating Percentages created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 201518

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www.mathsrevision.com Int 2 Calculating Percentages Appreciation / Depreciation Appreciation : Going up in value e.g. House value Depreciation : Going down in value e.g. car value created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 19

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Average house price in Ayr has appreciated by 79% over past 10 years. If you bought the house for £64995 in 1994 how much would the house be worth now ? Appreciation = 79% x £ 64995 = 0.79 x £64995 = £ 51346.05 New value = Old Value + Appreciation = £64995 + £51346.05 = £ 116341.05 Just working out percentages created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 20 Quicker Method Easier 1.79 x 64995 = £116341.05

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A Mini Cooper cost £14 625 in 2002 At the end 2003 it depreciated by 23% At the end 2004 it will depreciate by a further 16% What will the mini cooper worth at end 2004? End 2003 Depreciation = 23% x £14625 = 0.23 x £14625 = £3363.75 New value= Old value - Depreciation = £14625 - £3363.75 = £11261.25 www.mathsrevision.com Int 2 Calculating Percentages created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 21

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www.mathsrevision.com Int 2 Calculating Percentages End 2003 Depreciation = 23% x £14625 = 0.23 x £14625 = £3363.75 New value= Old value - Depreciation New value= Old value - Depreciation = £14625 - £3363.75 = £11261.25 End 2004 Depreciation = 16% x £11261.25 = 0.16 x £11261.25 = £1801.80 New Value = £11261.25 - £1801.80 = £9459.45 = £9459.45 created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 22

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Now try MIA Ex 4 Ch2 (page 12) Odd Numbers www.mathsrevision.com Int 2 Calculating Percentages created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 23

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Starter www.mathsrevision.com Int 2 6cm 5cm created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 201524

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Learning Intention Success Criteria 1.Know the term inflation. 1.Understand term inflation and work out associated real-life problems. 2.Work out real-life problems involving inflation. www.mathsrevision.com Int 2 Calculating Percentages created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 201525

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www.mathsrevision.com Int 2 Calculating Percentages Inflation Inflation is normally given in percentage form and is normally in the range 0 – 10% Example 1 In 2004 a worker received a wage of £300 per week. If inflation is 2% in 2004, what should be his wage be in 2005. 2004 inflation = 2% 2% of £300 = £6 His wage should be £300 + £6 = £306 created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 26 Measure of how much prices rise each year.

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www.mathsrevision.com Int 2 Calculating Percentages Inflation Measure of how much prices rise each year. Inflation is normally given in percentage form and is normally in the range 0 – 10% Example 2 In 2002 a CD cost £8. The cost increases in line with inflation. What is the price in 2003 if inflation is 1.5%. 2002 inflation = 1.5% 1.5% of £8 = £0.12 Price is £8 + £0.12 = £8.12 created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 27

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Now try MIA Ex 6 Ch2 (page 15) www.mathsrevision.com Int 2 Calculating Percentages created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 28

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www.mathsrevision.com Int 2 Calculating Percentages Example 1 After a 10% increase the price of a house is £88 000. What was the price before the increase. Reversing the change Price before is 100% :£800 x 100 = £80 000 1 % : 100 % + 10 % = £88 000Deduce from question : 110 % = £88 000We have : created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 29

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www.mathsrevision.com Int 2 Calculating Percentages Example 2 The value of a car depreciated by 15%. It is now valued at £2550. What was it’s original price. Reversing the change Price before is 100% :£30 x 100 = £3 000 1 % : 100 % - 15 % = £2 550Deduce from question : 85 % = £2 550We have : created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 30

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Now try MIA Ex 7 Ch2 (page 17) www.mathsrevision.com Int 2 Calculating Percentages created by Mr. lafferty @ www.mathsrevision.com Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015Monday, April 13, 2015 31

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