# Work with Compound Interest

In this worksheet students will learn how to calculate compound interest and apply the skill to various situations.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Discrete Growth and Decay

Difficulty level:

### QUESTION 1 of 10

Compound Interest is a percentage of money that is added to/ or taken away from an initial figure over a period of time.

Sometimes you love it

Sometimes you hate it.

For compound interest calculations, the interest earned in each period is added to the initial figure

So compound interest for any year is interest paid on the total sum of money invested and the interest earned the previous year.

Find the compound interest when £400 is invested for 3 years at an interest rate of 8%.

Interest for year 1 £400 x 0.08 = £32

Total for year 1 £400 + £32 = £432

Interest for year 2 £432 x 0.08 = £34.56

Total for year 2 £432 + £34.56 = £466.36

Interest for year 3 £466.36 x 0.08 = £37.31

Total for year 3 £466.36 + £37.31 =£503.67

Not a bad profit.  What are you going to spend it on?

Compound interest calculations are also used to find the depreciation of something.

You bought a speed boat that cost £18,000. Each year the price decreased in value by 5% at the beginning of each year.

Calculate the cost of the speed boat in 3 years time.

Year 1 £18,000 x 0.05 = 900

£18,000 - 900 = £17,100

Year 2 £17,100 x 0.05 = £855

£17,100 - £855 = £16,254

Year 3 £16,254 x 0.05 = £812.25

£16,254 - £812.25 = £15,441.75

Eagle eyes  -  Look out for an added extra throughout the activities.

Sam is invested some money to buy a new lap top.

He invested £500 in his bank with a compound interest rate of 3%.

How much money did he have

A student borrows £400 towards buying a bicycle.

Interest is added to the loan at 5% per annum (per year).

How much does the student owe after 4 years if no repayments are made?

£473.50

£490.21

£486.92

£486.20

Between 2012 and 2014 a bank paid an interest rate of 2% on savings.

Between 2014 and 2015 the bank paid an interest rate of 3% on savings.

If you invested £800 in 2012, how much money do you have in 2015?

Round your numbers to 2 decimal places as you work through.

You invest £575 for a period of 3 years with a compound interest rate of 5%.  How much do you have at the end of 3 Years?

£656.45

£665.64

£667.28

£655.55

Colin rents a house a £620 per month.  In the agreement it states that the rent will automatically increase by 4% each year.

What will Colin's rent be at the end of the 7 th year? Round your answer to 2 decimal places. Show your answer as £...

£816.28

£815.88

£815.96

£816.25

Match the answers to the questions

## Column B

Investment of £40 over 4 years -interest rate 3%
£1307.10
Investment of £250 over 3 years - interest rate ...
£146.98
Investment of £87 over 9 years interest rate 6%
£762.49
Investment of £642 over 5 years -interest rate 3...
£314.93
Investment of £66 over 7 years at 0.5%
£45.02
Investment of £1250 over 3 years - interest rate ...
£68.34

Your horse is getting old now and you want to sell it on.

You paid £7,000 for it 3 years ago.  The value of the horse has decreased by 3% each year.

What is the value of the horse now?

match up questions to the answers

## Column B

A car was bought for £5,000 , it depreciated 3% e...
£4293.67
A bicycle was bought for £250 , it depreciated 5%...
£845.96
An i-phone was bought for £450 , it depreciated 4...
£225.63
A computer was bought for £1200 , it depreciated ...
£269.13
A van was bought for £3,200, it depreciated 8% ea...
£398.13
an i-pad was bought for £325 , it depreciated 9% ...
£2292.46

How long would it take for an invested sum of £4500 to be worth at least £5000 with a compound interest rate of 4% per year?

2

4

3

5

James has invested his money unwisely.

Each year the value of his assets depreciates by 10%.

If James started with £5000, how many years will it take until his assets are valued at less than half their original worth?

• Question 1

Sam is invested some money to buy a new lap top.

He invested £500 in his bank with a compound interest rate of 3%.

How much money did he have

EDDIE SAYS
This is just a case of applying the skill. Year 1 £500 x 0.03 = £15 Total £500 + £15 = £515 Year 2 £515 x 0.03 =£15.45 Total £515 + £15.45 =£530.45 Year 3 £530.45 x 0.03 =£15.9135 Total £530.45 + £15.9135 = £546.36 (2 d.p) No wonder Sam is smiling, it looks like a nice laptop he has bought.
• Question 2

A student borrows £400 towards buying a bicycle.

Interest is added to the loan at 5% per annum (per year).

How much does the student owe after 4 years if no repayments are made?

£486.20
EDDIE SAYS
Here we go again £400 x 0.05 = £30 add it back in (£420) £420 x 0.05 = £21 add it back in(£441) £441 x 0.05 = £22.05 Add it back in (£463.05) £463.05 x 0.05 = £23.15 Add it back in (£486.20)
• Question 3

Between 2012 and 2014 a bank paid an interest rate of 2% on savings.

Between 2014 and 2015 the bank paid an interest rate of 3% on savings.

If you invested £800 in 2012, how much money do you have in 2015?

Round your numbers to 2 decimal places as you work through.

£833.01
EDDIE SAYS
This is where you need to be careful when calculating with your money. You don' t want to miss out do you. Beginning of 2012 800 x 0.02 = £16 Beginning of 2013 816 x 0.02 = £16.32 Beginning of 2014 £832.32 x 0.03 = £24.97 (interest rate went up at the beginning of the year) Beginning of 2015 £857.29 x 0.03 = £25.72 Add it back in to find the total for the end of 2015. £857.29 + £25.72 = £883.01
• Question 4

You invest £575 for a period of 3 years with a compound interest rate of 5%.  How much do you have at the end of 3 Years?

£665.64
EDDIE SAYS
Now you must be getting pretty expert at this by now. So here is the eagle eye moment I talked about in the introduction. You have to know how to calculate compound interest in this way to know what is actually happening. And you may be asked to do this without a calculator. However there is a quicker way to do this with a calculator. You know you want to invest the money at 5% over 3 years. so in your calculator 575 x 1.05 (power of button) 3 = £665.64 Power of buttons vary on different calculators so make sure you use your own calculator all the time as you will be familiar with the buttons. Be honest if you had known the short cut first you wouldn't have done it the long way round would you.
• Question 5

Colin rents a house a £620 per month.  In the agreement it states that the rent will automatically increase by 4% each year.

What will Colin's rent be at the end of the 7 th year? Round your answer to 2 decimal places. Show your answer as £...

£815.88
EDDIE SAYS
Easy when you know how. £620 x 1.05 (power of 7) = £815.88 (2.d.p) I bet you love these eagle eye moments.
• Question 6

Match the answers to the questions

## Column B

Investment of £40 over 4 years ...
£45.02
Investment of £250 over 3 years ...
£314.93
Investment of £87 over 9 years ...
£146.98
Investment of £642 over 5 years ...
£762.49
Investment of £66 over 7 years a...
£68.34
Investment of £1250 over 3 years...
£1307.10
EDDIE SAYS
This is pretty cool stuff isn't it. £40 x 1.03(power of 4) = £45.02 £250 x 1.08(power of 3)=£314.93 £87 x 1.06(power of 9) =£146.98 £642 x 1.035(power of 5) = £762.49 £66 x 1.005(power of 7) = £68.34 £1250 x 1.015(power of 3) = £1307.10
• Question 7

Your horse is getting old now and you want to sell it on.

You paid £7,000 for it 3 years ago.  The value of the horse has decreased by 3% each year.

What is the value of the horse now?

£6388.71
EDDIE SAYS
Two ways of doing this the longer way e.g £7000 x 0.03 = £210 £7000 - 210 = £6790 £6790 x 0.03 = £203.70 £ 6790 - £203.70 =£6586.30 £6586.30 X 0.03 = £197.59 £6586.30 - £197.59 = £6388.41 Or we could adopt the quick way As the percentage is decreasing we take 3% away from 100% which give us 97% £7000 x 0.97(to the power of 3)
• Question 8

match up questions to the answers

## Column B

A car was bought for £5,000 , it...
£4293.67
A bicycle was bought for £250 , ...
£225.63
An i-phone was bought for £450 ,...
£398.13
A computer was bought for £1200 ...
£845.96
A van was bought for £3,200, it ...
£2292.46
an i-pad was bought for £325 , i...
£269.13
EDDIE SAYS
Easy peasy when you know how the calculator can work for you. It is important you know the long way round to help understand with any explanations you may have to give. However, us mathematicians love a short cut ..oh we do. 5000 x 0.97(power of 5) 250 x 0.95 (power of 2) 450 x 0.96(power of 3) 1200 x 0.89 (power of 3) 3200 X 0.92(power of 4) 325 x 0.91 (power of 2)
• Question 9

How long would it take for an invested sum of £4500 to be worth at least £5000 with a compound interest rate of 4% per year?

3
EDDIE SAYS
take 4500 x 0.04 = £180. We know that he will earn £180 in year 1. Add it back in to the £4500. Start year 2 with £4680 x 0.04 = £1872 Add it back in. Start year 3 with £4867.2 x 0.04 = £194.69. Add it back in. Yes. £5061.89 after 3 years or you could just do 4500 x 1.04 (and play around with the powers) 4500 x 1.04(to the power of 3).
• Question 10

James has invested his money unwisely.

Each year the value of his assets depreciates by 10%.

If James started with £5000, how many years will it take until his assets are valued at less than half their original worth?

7
EDDIE SAYS
You are an expert by now. £5000 x 0.90 (we are taking off 10 because it is a depreciation) Now play around with the powers until you get an answer below £2500. 5000 x0.90(power of 7)
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