Lesson Objective By the end of the lesson you should be able to work out repeated percentage...
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Transcript of Lesson Objective By the end of the lesson you should be able to work out repeated percentage...
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.