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

© Nuffield Foundation 2012


Free-Standing Mathematics Activity

Working with percentages


Amount invested = £3000 Interest rate = 4%

Interest at end of Year 1

= 4% of £3000

= 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

1 Step-by-step method

Think aboutIs the answer the same if you divide by 100, then multiply by 4?

A Compound interest



Amount at end of Year 1 = 104% of £3000

= 1.04 x £3000 = £3120

and so on

2 Repeating calculations using a multiplier

Amount at end of Year 2 = 1.04 x £3120 = £3244.80

Try repeated calculations like this one on your calculator

A Compound interest


£3000 invested at 4% interest

End of year n Amount £ A

0 3000.001

2

3

4

5

3120.00

3244.80

3374.59

3509.58

3649.96

How much is in the account after 5 years? Repeated calculations

A Compound interest



3 Using indices

Amount at end of Year n = 1.04n x £3000

Amount at end of Year 2

Amount at end of Year 5

= 1.042 x £3000

= 1.045 x £3000

= £3244.80

= £3649.96

Think aboutWhat are the advantages and disadvantages of each method?

Try this AAn account gives 3% interest per annum. £5000 is invested. How much will be in the account after 6 years? Use each method.

A Compound interest


A new car costs £16 000.

Age of car (n years) Value (£ A)

0 16 0001

2

3

4

5

13 600

11 560

9826

8352

7099

What will it be worth when it is 5 years old?

What will the car be worth when it is 20 years old?

In this case the multiplier is 0.85

Think aboutWhat assumption is being made?

Is it realistic?

B DepreciationIts value falls by 15% per year


Formula for annual sales n years from now

Try this BA company’s sales of a product are falling by 6% per annum.

Estimate the annual sales 6 years from now.

They sold 45 000 this year.

= 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.

In this case the multiplier is 0.94

B Falling sales


C Combining percentage changes

Number after receiving 3% extra = 103% of 2000 = 1.03 x 2000

A shareholder owns 2000 shares.

How many shares will she have after these transactions?

She expects to get 3% more shares then plans to sell 25% of her shareholding.

= 2060

Number after selling 25% = 75% of 2060 = 0.75 x 2060 = 1545

What % is this of her original shareholding?

= 77.25% or 1.03 x 0.75 = 0.7725 1545 2000

100


Sale price = 75% of normal price

= 75% of 130% of cost price

Try this C

A shop marks up the goods it sells by 30%

What is the overall % profit or loss on goods sold in the sale? In a sale it reduces its normal prices by 25%

The shop makes a 2.5% loss on goods it sells in the sale.

= 0.975 of cost price

= 0.75 x 1.3 x cost price

C Combining percentage changes


D Reversing percentage changes

1.025 x previous price = £66.42

Previous price

The price of a train fare increased by 2.5% recently.

How much did it cost before the rise in price?

It now costs £66.42

Previous price = £64.80

= £66.42 1.025


0.875 x full price = £25.90

Full price

Try this D

After a 12.5% discount, insurance costs £25.90

Full price = £29.60

= £25.90 0.875

What was the cost before the discount?

D Reversing percentage changes


Reflect on your work

•Which of the methods do you think is most efficient?

• How can a graphic calculator or spreadsheet help?

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

Documents

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