Repeated Percentage Change Objectives: Calculate a repeated percentage increase or decrease Terms and Conditions: To the best of the producer's knowledge, the presentation’s academic content is accurate but errors and omissions may be present and Brain-Cells: E.Resources Ltd cannot be held responsible for these or any lack of success experienced by individuals or groups or other parties using this material. The presentation is intended as a support material for GCSE maths and is not a comprehensive pedagogy of all the requirements of the syllabus. The copyright proprietor has licensed the presentation for the purchaser’s personal use as an educational resource and forbids copying or reproduction in part or whole or distribution to other parties or the publication of the material on the internet or other media or the use in any school or college that has not purchased the presentation without the written permission of Brain-Cells: E.Resouces Ltd.

Calculating a Percentage Increase Recap

Here is an example of how to increase 153 by 17%. Change the percentage into a decimal Increase 153 by 17% 17%  0.17 1 + 0.17  1.17 153 x 1.17 = 179.01 Add the decimal onto 1 Multiply by this number The number after the increase

Increase 27 by 7% 7%  0.07 1 + 0.07 = 1.07 27 x 1.07 = 28.89 Using the example as a guide, increase these by the given percentage Sometimes, we want increase a number by a percentage several times. Here is an example… 1. 53 by 19% 2. 12 by 3% 3. 14 by 27% 4. 7.2 by 8% 5. 8.7 by 19% = 63.07 = 12.36 = 17.78 = 7.776 = 10.353

Repeated Percentage Increase

We multiply by 1.03 five times like this… If £1750 is invested, what will it have increased to in 5 years time? We multiply by 1.03 five times like this… It will increase to £2028.73 1st Year 1750 x 1.03 = 1802.5 2nd Year 1802.5 x 1.03 = 1856.575 3rd Year 1856.575 x 1.03 = 1912.2725 4th Year 1912.2725 x 1.03 = 1969.640418 5th Year 1969.640418 x 1.03 = 2028.73 to 2 dp.

If £250 is invested, what will it have increased to after 5 years? £304.16 If £50 is invested, what will it have increased to after 10 years? £81.44

If we look at this problem again… If £1750 is invested, what will it have increased to in 5 years time? If we look at this problem again… 1st Year 1750 x 1.03 = 1802.5 2nd Year 1802.5 x 1.03 = 1856.575 3rd Year 1856.575 x 1.03 = 1912.2725 4th Year 1912.2725 x 1.03 = 1969.640418 5th Year 1969.640418 x 1.03 = 2028.73 to 2 dp.

If £1750 is invested, what will it have increased to in 5 years time? We multiply by 1.03 five times like this… 1st Year 2nd Year 3rd Year 4th Year 5th Year 1750 x 1.03 x 1.03 x 1.03 x 1.03 x 1.03 Multiplying by 1.03 five times is 1.035 1750 x 1.035 = 2028.73

There will be a button to do this on your calculator If £1750 is invested, what will it have increased to in 5 years time? There will be a button to do this on your calculator Probably… x ^ 5 = 1750 x xy 5 = or… 1750 x 1.035 = 2028.73

£2244.82 £769.71 Using the appropriate button, try these: To what amount will £1250 have increased? To what amount will £240 have increased? £2244.82 £769.71

Like winning 20 million on the lottery every week for 4 years Try these: 1. A business aims to increase its taking by 17% each year. If its takings are £3134 now, what will be the aimed for takings in 7 years time? £9405.89 2. In 1950, £100 is invested in a bank on the understanding that it will not be withdrawn for 150 years and each year it will be increased by 3%. What will it have increased to in this 150 year period? Like winning 20 million on the lottery every week for 4 years £8425.27 3.What will £10 invested at an annual fixed rate of 2% be worth in 1000 years time? £3 982 646 517

Repeated Percentage Decrease

To find a percentage decrease, we… Change the percentage into a decimal Decrease 167 by 37% 37%  0.37 1 - 0.37  0.63 167 x 0.63 = 105.21 Subtract the decimal from 1 Multiply by this number The number after the decrease

We need to multiply by 0.63 five times What number do we get if we decrease 167 by 37% five times? We need to multiply by 0.63 five times 37%  0.37 1 - 0.37  0.63 167 x 0.63 x 0.63 x 0.63 x 0.63 x 0.63 = 16.573… We can do this, by… 167 x 0.635 = 16.57 to 2 dp

An example of a repeated percentage decrease A forest contains 1000000 trees. If 7% of the trees in are cut down each year, how many trees will the forest contain after 10 years if no new trees are planted? 7%  0.07 1 - 0.07  0.93 1000000 x 0.93 10 = 483982

Try this one… There is population of 10000 fish in a lake, but it was discovered that this population is decreasing by 14% year. If this decrease continues, what will be the fish population in 7 years time? 14%  0.14 1 - 0.14  0.86 10000 x 0.86 7 = 3479

Try these: 1. Because of faulty equipment, a firm loses 2000 hours a year of production. It is hoped that new equipment will reduce this time by 7% each year. What will be the number of hours lost in 5 years time? 1391.38 hours 2. A disease called myxomatosis killed 53% of the rabbits in Britain each year during a 7 year period in the 1950s. If the rabbit population at the start of this period was 15000000, what had it fallen to by the end of the 7 years? 75993 rabbits