Lesson Objective

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

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?

Repeated Percentage changesexample 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 yearsIs 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

Repeated Percentage changesexample 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 yearsb) 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?

Repeated Percentage changesb) 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 1.054 = £1215.5062

c) Using this same method how could we find out the money after 10 years?

£1000 x 1.0510 = £1628.89 to 2dp

This type of interestis called COMPOUND

INTEREST

This type of interestis called COMPOUND

INTEREST

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 0.83 = £3072

c)£6000 x 0.88 = £1006.63 to 2 dp

Notice – the power isthe same as thenumber of years!

Notice – the power isthe same as thenumber of years!

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 1.073 = 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.

e.g. Question 9

3000 depreciating at 15% for 4 years

3000 x 0.854=1566.0188

=1566 to nearest pound

Answers

Question 1

1225

Answers

Question 2

2319

Answers

Question 3

1825

Answers

Question 4

1694

Answers

Question 5

2074

Answers

Question 6

8319

Answers

Question 7

5624

Answers

Question 8

1579

Answers

Question 9

1566

Answers

Question 10

1475

Answers

Question 11

3242

Answers

Question 12

1968

Answers

Question 13

2067

Answers

Question 14

3479

Answers

Question 15

2454

Answers

Question 16

8941