Compound percentages

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Transcript of Compound percentages
© Boardworks Ltd 20111 of 11
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© Boardworks Ltd 20112 of 11
This icon indicates the slide contains activities created in Flash. These activities are not editable.
For more detailed instructions, see the Getting Started presentation.
This icon indicates teacher’s notes in the Notes field.
This is an excerpt from the “Compound Interest” presentation in Boardworks Maths for
Australia, which contains 129 presentations in total.
This is an excerpt from the “Compound Interest” presentation in Boardworks Maths for
Australia, which contains 129 presentations in total.
© Boardworks Ltd 20113 of 11
Compound percentages
To find a 10% decrease, multiply by 90% or 0.9.To find a 20% decrease, multiply by 80% or 0.8.
original price × 0.8 × 0.9 = original price × 0.72
A jacket is reduced by 20% in a sale.
Two weeks later, the shop reducesthe price by a further 10%.
What is the total percentage discount?
It is not 30%.
72% of 100 is equivalent to a 28% discount altogether.
© Boardworks Ltd 20114 of 11
Jenna invests in some shares.
Compound percentages
After one week the value goes up by 10%.
The following week they go down by 10%.
Has Jenna made a loss, a gain or is she back to her original investment? Show your working.
© Boardworks Ltd 20115 of 11
Compound percentages
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Jack puts $500 into a savings account with an annual compound interest rate of 5%.
Compound interest
As a single calculation:
$500 × 1.05 × 1.05 × 1.05 × 1.05 = $607.75
Using index notation:
$500 × 1.054 = $607.75
How much will he have in the account at the end of 4 years if he doesn’t add or withdraw any money?
© Boardworks Ltd 20117 of 11
Compound interest
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Compound interest
Where is the best place to invest for each time period?
Short term investment: 1 yearMedium term investment: 3 yearsLong term investment: 10 years
$35003.4% annualinterest
Bank account Shares$1000 7.9% annualinterest
Building Society$100001.2% annual interest
Rena is a financial advisor. She needs to work out where her client’s money would best be saved depending on how long they want to invest for.
© Boardworks Ltd 20119 of 11
If the current population is 2345,what will it be in 5 years?
Powers are used in solving problems involving repeated percentage increase and decrease.
Repeated percentage change
What will the population be after 10 years?
The population of a village increases by 2% each year.
© Boardworks Ltd 201110 of 11
Repeated percentage change
How much will the car be worth in 2013?
To decrease the value by 15%, multiply it by 0.85.
$24 000 × 0.858 = $6540 (to the nearest dollar)
The value of a new car depreciates at a rate of 15% a year.
There are 8 years between 2005 and 2013.
The car costs $24 000 in 2005.
© Boardworks Ltd 201111 of 11
Repeated percentage change