  # Calculate Compound Interest

In this worksheet, students will calculate compound interest, which assumes that the percentage increase or decrease is accumulating over time, including problems involving interest and depreciation. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Ratio, Proportion and Rates of Change

Difficulty level:   #### Worksheet Overview

Compound interest means a percentage of money that is added to or taken away from an initial figure over a period of time.  Sometimes you love it BUT sometimes you hate it!

For compound interest calculations, the interest earned in each period needs to be added to the starting amount.

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

Let's look at this in action now in an example. e.g. Find the compound interest when £400 is invested for 3 years at an interest rate of 8%.

Interest for year 1: £400 × 0.08 = £32

Total for year 1: £400 + £32 = £432

Interest for year 2: £432 × 0.08 = £34.56

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

Interest for year 3: £466.36 × 0.08 = £37.31

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

Not a bad profit there - what would you spend it on?

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

Depreciation occurs when items lose some of their value after being bought.

If you bought a car two years ago which you were now trying to sell, you would expect to receive less than you bought it for, right?

Let's review an example focused on depreciation now. e.g. Jim 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 value of the speed boat in 3 years' time.

Year 1: £18,000 × 0.05 = 900    -->    £18,000 - 900 = £17,100

Year 2: £17,100 × 0.05 = £855    -->    £17,100 - £855 = £16,245

Year 3: £16,245 × 0.05 = £812.25    -->    £16,245 - £812.25 = £15,432.75

It was not Jim's wisest decision to buy that boat, was it?

Keep your eyes peeled for a 'Eureka moment!' in this activity.

You will need to have a calculator handy at this point to learn about an alternative way of calculating compound interest. In this activity, we will calculate compound interest using the method above, which assumes that the percentage increase or decrease is accumulating over time. We will focus on problems involving interest and depreciation.

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