Depreciation Aqa Foundation

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Exam code:8300

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 <img alt=”P open parentheses 1 minus r over 100 close parentheses to the power of n space end exponent” data-mathml='<math ><semantics><mrow><mi >P</mi><msup><mfenced ><mrow><mn>1</mn><mo>-</mo><mfrac><mi>r</mi><mn>100</mn></mfrac></mrow></mfenced><mrow ><mi>n</mi><mo> </mo></mrow></msup></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ data-type=”commentary” height=”47″ role=”math” 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Maths Gcse Aqa Foundation