1. Repeated Percentage Change
Objectives:
Calculate a repeated percentage increase or decrease
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2. Calculating a Percentage Increase Recap

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

4. Increase 27 by 7%
7%  0.07
= 1.07
27 x 1.07 =
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 =

5. Repeated Percentage Increase

6. 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 £
1st Year
1750 x 1.03 =
2nd Year
x 1.03 =
3rd Year
x 1.03 =
4th Year
x 1.03 =
5th Year
x 1.03 = to 2 dp.

7. 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

8. 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 =
2nd Year
x 1.03 =
3rd Year
x 1.03 =
4th Year
x 1.03 =
5th Year
x 1.03 = to 2 dp.

9. 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 =

10. 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 =

11. £2244.82 £769.71 Using the appropriate button, try these:
To what amount will £1250 have increased?
To what amount will £240 have increased? £
£769.71

12. 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? £
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 In 1950, £100 is invested in a bank on the understanding that it will not be withdrawn for 150 years and each year it will be increased by 3%.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 £
3.What will £10 invested at an annual fixed rate of 2% be worth in 1000 years time? £

13. Repeated Percentage Decrease

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

15. 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
 0.63
167 x 0.63 x 0.63 x 0.63 x 0.63 x 0.63 = …
We can do this, by…
167 x = to 2 dp

16. An example of a repeated percentage decrease
A forest contains 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
 0.93
x 0.93 10 =

17. Try this one…
There is population of 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
 0.86
10000
x 0.86 7
= 3479

18. 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?
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 , what had it fallen to by the end of the 7 years?
75993 rabbits