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Lesson Objective By the end of the lesson you should be able to work out repeated percentage increases or decreases.
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Repeated Percentage changes We see repeated percentage change problems all the time. The most common example will be in your bank account. example 1 – I invest £1000 in a bank account with an interest rate of 5%. How much will I have after a)1 year? b)4 years? c)10 years?
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Repeated Percentage changes example 1 – I invest £1000 in a bank account with an interest rate of 5%. How much will I have after a)1 year b) 4 years Is this a percentage increase or decrease problem? What is the multiplier for a 5% increase? a) after 1 year there is: £1000 x 1.05 = £1050
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Repeated Percentage changes example 1 – I invest £1000 in a bank account with an interest rate of 5%. How much will I have after a)1 year b) 4 years b) 1 year = £1000 x 1.05 = £1050 2 years = £1050 x 1.05 = £1102.5 3 years = £1102.5 x 1.05 = £1157.625 4 years = £1157.625 x 1.05 = £1215.5063 Is there any way we could have done this quicker?
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Repeated Percentage changes b) You may have noticed that each time we multiplied by 1.05. We did this 4 times so we could have just done this on the calculator. £1000 x 1.05 x 1.05 x 1.05 x 1.05 = £1215.5062 Is there a way of doing this without typing in 1.05 so many times? £1000 x 1.05 4 = £1215.5062 c) Using this same method how could we find out the money after 10 years? £1000 x 1.05 10 = £1628.89 to 2dp This type of interest is called COMPOUND INTEREST This type of interest is called COMPOUND INTEREST
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Repeated Percentage changes Here is an example of a repeated percentage decrease. example 2 – A car loses 20% of its value every year. How much will a £6000 car be worth after a)1 year? b) 3 years? c) 8 years? The multiplier for this is 0.8. Why? a)£6000 x 0.8 = £4800 b)£6000 x 0.8 3 = £3072 c)£6000 x 0.8 8 = £1006.63 to 2 dp Notice – the power is the same as the number of years! Notice – the power is the same as the number of years!
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Now it’s your turn. Calculate the new values after the repeated changes. Round each number to the nearest whole number (pound) then find the 4 digit answer in the grid. e.g. Question 1 1000 invested at 7% for 3 years 1000 x 1.07 3 = 1225.043 =1225 to nearest pound Tip – it is better to circle your answers like this rather than drawing lines through them as you may need to use the numbers more than once.
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e.g. Question 9 3000 depreciating at 15% for 4 years 3000 x 0.85 4 =1566.0188 =1566 to nearest pound
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Answers Question 1 1225
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Answers Question 2 2319
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Answers Question 3 1825
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Answers Question 4 1694
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Answers Question 5 2074
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Answers Question 6 8319
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Answers Question 7 5624
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Answers Question 8 1579
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Answers Question 9 1566
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Answers Question 10 1475
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Answers Question 11 3242
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Answers Question 12 1968
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Answers Question 13 2067
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Answers Question 14 3479
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Answers Question 15 2454
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Answers Question 16 8941
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