Depreciation (Cambridge International IGCSE Maths)

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 = $P ( 1 - \frac{r}{100} )^{n }$ where

    • P is the original amount,
    • r is the % increase
    • and n is the number of years

  • Note that all of $1-\frac{r}{100}$ 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.

Answer:

Identify the multiplier

100% - 15% = 85%

m = 1 - 0.15 = 0.85*

Raise to the power of number of years

*0.85 *³

Multiply by the starting value

£20 000 × 0.85*³*

Final answer: £12 282.50

Alternative method Use the formula for the final amount $P ( 1 - \frac{r}{100} )^{n }$ *Substitute P = 20 000, r = 15 and n = 3 into the formula *

$20 000 ( 1 - \frac{15}{100} )^{3}$

Final answer: £12 282.50