Transcript Working with percentages Free-Standing Mathematics Activity © Nuffield Foundation 2012

Free-Standing Mathematics Activity
Working with percentages
© Nuffield Foundation 2012
© Nuffield Foundation 2012
A Compound interest
Amount invested = £3000 Interest rate = 4%
1 Step-by-step method
Interest at end of Year 1 = 4% of £3000
Think about
Is the answer
the same if you
divide by 100,
then multiply
by 4?
= 0.04 x £3000 = £120
Amount at end of Year 1 = £3120
Interest at end of Year 2 = 4% of £3120
= 0.04 x £3120 = £124.80
Amount at end of Year 2 = £3120 + £124.80
= £3244.80
and so on
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A Compound interest
Amount invested = £3000
Interest rate = 4%
2 Repeating calculations using a multiplier
Amount at end of Year 1 = 104% of £3000
= 1.04 x £3000 = £3120
Amount at end of Year 2
= 1.04 x £3120 = £3244.80
and so on
Try repeated calculations like this one on your calculator
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A Compound interest
£3000 invested at 4% interest
Repeated calculations
How much is in the account after 5 years?
End of year n
Amount £ A
0
3000.00
1
3120.00
2
3244.80
3
3374.59
4
3509.58
5
3649.96
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A Compound interest
Amount invested = £3000 Interest rate = 4%
3 Using indices
Amount at end of Year n = 1.04n x £3000
Amount at end of Year 2 = 1.042 x £3000 = £3244.80
Amount at end of Year 5 = 1.045 x £3000 = £3649.96
Try this A
An account gives 3% interest per annum. £5000 is invested.
How much will be in the account after 6 years? Use each method.
Think about
What are the advantages and disadvantages of each method?
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B Depreciation
A new car costs £16 000. Its value falls by 15% per year
What will it be worth when it is 5 years old?
In this case the multiplier is 0.85
Age of car (n years)
Value (£ A)
0
16 000
1
13 600
2
11 560
3
9826
4
8352
5
7099
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What will the car
be worth when it
is 20 years old?
Think about
What assumption
is being made?
Is it realistic?
B Falling sales
Try this B
A company’s sales of a product are falling by 6% per annum.
They sold 45 000 this year.
Estimate the annual sales 6 years from now.
In this case the multiplier is 0.94
Formula for annual sales n years from now = 0.94n x 45 000
Estimate of annual sales 6 years from now = 0.946 x 45 000
about 31 000
Check this by repeated calculations.
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C Combining percentage changes
A shareholder owns 2000 shares.
She expects to get 3% more shares
then plans to sell 25% of her shareholding.
How many shares will she have after these transactions?
Number after receiving 3% extra = 103% of 2000
= 1.03 x 2000 = 2060
Number after selling 25%
= 75% of 2060
= 0.75 x 2060 = 1545
What % is this of her original shareholding?
1545
 100 = 77.25% or 1.03 x 0.75 = 0.7725
2000
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C Combining percentage changes
Try this C
A shop marks up the goods it sells by 30%
In a sale it reduces its normal prices by 25%
What is the overall % profit or loss on goods sold in the sale?
Sale price = 75% of normal price
= 75% of 130% of cost price
= 0.75 x 1.3 x cost price
= 0.975 of cost price
The shop makes a 2.5% loss on goods it sells in the sale.
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D Reversing percentage changes
The price of a train fare increased by 2.5% recently.
It now costs £66.42
How much did it cost before the rise in price?
1.025 x previous price = £66.42
Previous price = £66.42  1.025
Previous price
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= £64.80
D Reversing percentage changes
Try this D
After a 12.5% discount, insurance costs £25.90
What was the cost before the discount?
0.875 x full price = £25.90
Full price = £25.90  0.875
Full price = £29.60
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Reflect on your work
• Which of the methods do you think is most efficient?
• How can a graphic calculator or spreadsheet help?
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