1. Lesson Objective By the end of the lesson you should be able to work out repeated percentage increases or decreases.

2. 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?

3. 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

4. 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?

5. 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

6. 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!

7. 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.

8. e.g. Question 9 3000 depreciating at 15% for 4 years 3000 x 0.85 4 =1566.0188 =1566 to nearest pound

9. Answers Question 1 1225

10. Answers Question 2 2319

11. Answers Question 3 1825

12. Answers Question 4 1694

13. Answers Question 5 2074

14. Answers Question 6 8319

15. Answers Question 7 5624

16. Answers Question 8 1579

17. Answers Question 9 1566

18. Answers Question 10 1475

19. Answers Question 11 3242

20. Answers Question 12 1968

21. Answers Question 13 2067

22. Answers Question 14 3479

23. Answers Question 15 2454

24. Answers Question 16 8941