Depreciation (OCR GCSE Maths) : Revision Note

Depreciation

What does depreciation mean?

  • Depreciation is where an item loses value over time

    • E.g. cars, mobile phones, etc

  • Depreciation is usually calculated as a percentage decrease at the end of each year

    • This works the same as compound interest, but with a percentage decrease

How do I calculate depreciation?

  • A similar method to compound interest can be used

  • Change the multiplier to one which represents a percentage decrease

    • e.g. a decrease of 15% would be a multiplier of 0.85

  • If a car worth £ 16 000 depreciates by 15% each year for 6 years

    • Its value will be 16 000 × 0.856, which is £ 6034.39

  • If you are asked to find the amount the value has depreciated by:

    • Find the difference between the starting value and the new value

Depreciation formula

  • An alternate method is to use the following formula to calculate the final balance

    • Final balance = P open parentheses 1 minus r over 100 close parentheses to the power of n space end exponent where

      • P is the original amount,

      • r is the % increase

      • and n is the number of years

    • Note that all of 1 minus r over 100 is the multiplier

      • e.g. 0.75 for a 25% depreciation

  • This formula is not given in the exam

Worked Example

Mercy buys a car for £20 000. Each year its value depreciates by 15%.

Find the value of the car after 3 full years.

Identify the multiplier

100% - 15% = 85%

m = 1 - 0.15 = 0.85

Raise to the power of number of years

0.853

Multiply by the starting value

£20 000 × 0.853

£12 282.50

Alternative method
Use the formula for the final amount   P open parentheses 1 minus r over 100 close parentheses to the power of n space end exponent
Substitute P = 20 000, r = 15 and n = 3 into the formula 

20 space 000 open parentheses 1 minus 15 over 100 close parentheses cubed

£12 282.50

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Jamie Wood

Author: Jamie Wood

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Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

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