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Nat 5 Money www.mathsrevision.com Compound Interest Appreciation & Depreciation Working Backwards Exam Type Questions

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Nat 5 Sunday, 01 June 2014Sunday, 01 June 2014Sunday, 01 June 2014Sunday, 01 June 2014 Starter Questions Q1.Find the standard deviation for the data below Q2.Find the coordinates where the line and curve meet. www.mathsrevision.com

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Nat 5 Learning Intention Success Criteria 1.To know when to use compound formula. 1.We are learning how to use the compound formula for appropriate problems. 2.Solve problems involving compound formula. www.mathsrevision.com Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 3 Compound Interest

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Nat 5 www.mathsrevision.com Compound Interest Interest calculated on new value every year Real life Interest is not a fixed quantity year after year. One years interest becomes part of the next years amount. Each years 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. Initial value Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 4

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Nat 5 www.mathsrevision.com 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 = £457.06 + £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 Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 5 Compound Interest

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Nat 5 www.mathsrevision.com Easier Method Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 6 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. Compound Interest

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Nat 5 www.mathsrevision.com 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 Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 7 n = 3 ± = increase 1+0.07=1.07 I =400 Compound Interest

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Nat 5 Now try Ex 10.2 Ch2 (page 43) www.mathsrevision.com Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 8 Compound Interest

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Nat 5 Sunday, 01 June 2014Sunday, 01 June 2014Sunday, 01 June 2014Sunday, 01 June 2014 Starter Questions Q1.Solve the equations Q2.Find the coordinates where the line and curve meet. www.mathsrevision.com

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Nat 5 Learning Intention Success Criteria 1.To know the terms appreciation and depreciation. 1.We are learning about the terms appreciation and depreciation. 2.Show appropriate working when solving problems containing appreciation and depreciation. www.mathsrevision.com Appreciation & Depreciation Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 10

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Nat 5 www.mathsrevision.com Appreciation : Going up in value e.g. House value Depreciation : Going down in value e.g. car value Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 11 Appreciation & Depreciation

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Nat 5 Average house price in Ayr has appreciated by 79% over past 10 years. If you bought the house for £64995 ten years ago 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 Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 12 Quicker Method Easier % £ 100 64995 179

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Nat 5 Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 13 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 Appreciation & Depreciation

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Nat 5 www.mathsrevision.com Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 14 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 Appreciation & Depreciation

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Nat 5 Now try N5 TJ Ex 2.5 Ch2 (page 26) www.mathsrevision.com Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 18 Appreciation & Depreciation

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Nat 5 Sunday, 01 June 2014Sunday, 01 June 2014Sunday, 01 June 2014Sunday, 01 June 2014 Starter Questions Q1.Solve the equations Q2.Solve the coordinates where the line and curve meet. www.mathsrevision.com

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Nat 5 Learning Intention Success Criteria 1.To understand the process of work backwards. 1.We are learning how to work backwards to find the original/Initial value. 2.Solve problems using backwards process. www.mathsrevision.com Work Backwards Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 20

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Nat 5 www.mathsrevision.com After a 10% increase the price of a house is £88 000. What was the price before the increase. Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 21 Work Backwards Method % £ 110 88 000 100 Are we expecting more or less

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Nat 5 www.mathsrevision.com Example 2 The value of a car depreciated by 15%. It is now valued at £2550. What was its original price. Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 22 Work Backwards Method % £ 100 2550 85 Are we expecting more or less

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Nat 5 Now try N5 TJ Ex 2.6 Ch2 (page 27) www.mathsrevision.com Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014Sunday, June 01, 2014created by Mr. lafferty @ www.mathsrevision.com 25 Work Backwards

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