Depreciation refers to when the value of something goes down over time.
The value of a car is usually decreases in value with time. Therefore its value is said to depreciateDepreciation is a term used to indicate a value is decreasing. .
Example
Jack and Trisha bought a new car for £8500 in 2009. In the first year, its value depreciated by 20%, in the second year by 15% and in the third by 10%.
Calculate the value of the car at the end of each year.
Answer
Value at the end of Year 1:
Percentage has gone down by 20%, therefore 100% - 20% = 80%
\(80\% \,of\,8500\)
\(= 0.8 \times 8500\)
\(= \pounds6800\) (Another way of doing this calculation is to find 20% and then subtract)
Value at the end of Year 2:
Percentage has gone down by 15%, therefore 100% - 15% = 85%
\(85\% \,of\,6800\)
\(= 0.85 \times 6800\)
\(= \pounds5780\)
Value at the end of Year 3:
Percentage has gone down by 10%, therefore 100% - 10% = 90%
\(90\% \,of\,5780\)
\(= 0.9 \times 5780\)
\(= \pounds5202\)
Now try the example questions below.
Question
Jean bought an antique ring for £200. Its value appreciates by 10% each year.
Calculate the value of the ring after 10 years.
\({(1.1)^{10}} \times 200\)
\(= \pounds518.75\)
Question
Ahmed bought a car for £6000. It depreciated at 17% per year for the next 3 years. How much was it worth after 3 years.
Depreciation makes the value lower.
The multiplier is 1 - (17% of 1). This is 1 – 0.17 which is 0.83.
