Depreciation & Appreciation (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

Depreciation & Appreciation

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

What does appreciation mean?

• Appreciation is the opposite of depreciation

• It is where an item gains value over time

  • E.g. Houses or antiques

• Appreciation is usually calculated as a percentage increase at the end of each year

  • This works the same as compound interest

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

How do I calculate appreciation?

• A similar method to compound interest can be used

• Use a multiplier which represents a percentage increase

  • e.g. an increase of 7% would be a multiplier of 1.07

• If an antique worth £ 2 000 appreciates by 7% each year for 5 years

  • Its value will be 2 000 × 1.07⁵, which is £ 2 805.10

• If you are asked to find the amount the value has appreciated 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 value

  • Final value = where

    • P is the original amount,

    • r is the % decrease

    • and n is the number of years

  • Note that all of  is the multiplier

    • e.g. 0.75 for a 25% depreciation using r = 25

• This formula is not given in the exam

Appreciation formula

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

  • Final value = where

    • P is the original amount,

    • r is the % increase

    • and n is the number of years

  • Note that all of  is the multiplier

    • e.g. 1.25 for a 25% appreciation using r = 25

• This formula is not given in the exam