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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.

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**Compound percentages A jacket is reduced by 20% in a sale.**

Two weeks later, the shop reduces the price by a further 10%. What is the total percentage discount? It is not 30%. To find a 20% decrease, multiply by 80% or 0.8. Teacher notes Emphasize that the second percentage change is found on a new amount and not on the original amount. To find a 10% decrease, multiply by 90% or 0.9. original price × 0.8 × 0.9 = original price × 0.72 72% of 100 is equivalent to a 28% discount altogether.

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**Compound percentages Jenna invests in some shares.**

After one week the value goes up by 10%. The following week they go down by 10%. Teacher notes To find a 10% increase, multiply by 110% or 1.1. To find a 10% decrease, multiply by 90% or 0.9. original amount × 1.1 × 0.9 = original amount × 0.99 Jenna has 99% of her original investment and has therefore made a 1% loss. Pupils may wish to discuss this problem by giving the original investment a value, $100 say. If this increases by 10% Jenna will have $110. When $110 is reduced by 10% Jenna will have $99. This is equivalent to a 1% loss overall. Photo credit: © Yuri Arcurs 2010, Shutterstock.com Has Jenna made a loss, a gain or is she back to her original investment? Show your working.

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**Compound percentages Teacher notes**

Use this slide to demonstrate the effect of following a percentage change with a second percentage change. Ask pupils to predict whether the final amount is going to be greater than or less than the original amount. Discuss methods to find the result of multiple percentage changes.

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Compound interest Jack puts $500 into a savings account with an annual compound interest rate of 5%. How much will he have in the account at the end of 4 years if he doesn’t add or withdraw any money? As a single calculation: $500 × 1.05 × 1.05 × 1.05 × 1.05 = $607.75 Teacher notes Explain that each year 5% of an ever larger amount is added to the account. Multiply by 105% or 1.05 for each year. Year 1: $500 × 1.05 = $525 Year 2: $525 × 1.05 = $551.25 Year 3: $ × 1.05 = $578.81 Year 4: $ × 1.05 = $607.75 (These amounts are written to the nearest cent.) As a single calculation: $500 × 1.05 × 1.05 × 1.05 × 1.05 = $607.75 Using index notation: $500 × = $607.75 It can be seen that the actual increase gets larger each time. In the first year $25 is added on. In the second year it’s $26.25, in the third year it’s $27.56 and in the fourth year it’s $28.94. This is an example of exponential growth. Ask pupils to verify that $500 × = $ using the xy key on their calculators. Photo credit: © prism , Shutterstock.com Using index notation: $500 × = $607.75

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**Compound interest Teacher notes**

Use this activity to demonstrate the effect of compound interest.

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Compound 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. Short term investment: year Medium term investment: 3 years Long term investment: years Bank account Shares Building Society $3500 3.4% annual interest $1000 7.9% annual interest $10000 1.2% annual interest Teacher notes Encourage pupils to work through the different combinations systematically. Pupils decide what constitutes the ‘best investment’ as it could be the most money gained or the biggest percentage increase. Discuss differences in risk. Money gained: 1 year - Building society, 3 years - Bank account, 10 years - Bank account Percentage increase: 1 year - Shares, 3 years - Shares, 10 years - Shares Bank account 1 year: – 3500 = = 3.4% increase Bank Account 3 years: – 3500 = = 10.55% increase Bank Account 10 years: – 3500 = = 39.7% increase Shares 1 year: – 1000 = = 7.9% increase Shares 3 years: – 1000 = = 25.62% increase Shares 10 years: – 1000 = = 113% increase Building Society 1 year: – = = 1.2% Building society 3 years: – = = 3.64% increase Building society 10 years: – = = 12.67% increase Photo credit: © youlian 2010, Shutterstock.com Where is the best place to invest for each time period?

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**Repeated percentage change**

Powers are used in solving problems involving repeated percentage increase and decrease. The population of a village increases by 2% each year. If the current population is 2345, what will it be in 5 years? Teacher notes To increase the population by 2%, multiply it by 1.02. 2345 × = 2589 (to the nearest whole) 2345 × = 2859 (to the nearest whole) Ask pupils to calculate each answer using the xy key on their calculators. Image credit: © Tenab 2010, Shutterstock.com What will the population be after 10 years?

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**Repeated percentage change**

The value of a new car depreciates at a rate of 15% a year. The car costs $ in 2005. How much will the car be worth in 2013? To decrease the value by 15%, multiply it by 0.85. Teacher notes Explain that a percentage depreciation is equivalent to a percentage decrease. Photo credit: © Maksim Toome 2010, Shutterstock.com There are 8 years between 2005 and 2013. $ × = $6540 (to the nearest dollar)

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**Repeated percentage change**

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Compound Interest Amount invested = £3000 Interest Rate = 4% Interest at end of Year 1= 4% of £3000 = 0.04 x £3000 = £120 Amount at end of Year 1= £3120.

Compound Interest Amount invested = £3000 Interest Rate = 4% Interest at end of Year 1= 4% of £3000 = 0.04 x £3000 = £120 Amount at end of Year 1= £3120.

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