Appreciation and depreciation
Appreciation
Appreciation is the increase in value of an item. A common example of this is house prices. Each year, the value of a house increases, so we say that its value appreciates.
The rate of appreciation is often given as a percentage.
Example
A flat is bought for \(\pounds90,000\).
In each of the three years that follows, its value appreciates by \(8\%\).
How much is the flat worth after three years?
Year 1 appreciation: \(8\% of \pounds90,000 = \pounds7200\)
Flat Value = \(90,000 + 7,200 = \pounds97,200\)
Year 2 appreciation: \(8\%\,of\,\pounds97,200 = \pounds7776\) \(8\%\,of\,\pounds97,200 = \pounds7776\)
Flat Value = \(97,200 + 7,776 = \pounds104,976\)
Year 3 appreciation: \(8\%\,of\,\pounds104,976 = \pounds8398.08\)
Flat Value = \(104,976 + 8,398.08 = \pounds113,374.08\)
So after three years, the flat is worth \(\pounds113,374.08\).
Depreciation
Depreciation is the decrease in value of an item. A common example of this is car prices. Each year, the value of a car decreases, so we say that its value depreciates.
The rate of depreciation is often given as a percentage.
Example
A new car costs \(\pounds12,000\).
The car loses \(10\%\) of its value during the first year and \(15\%\) of its value during the second year.
How much is the car worth after two years?
Year 1 depreciation: \(10\% of \pounds12000 = \pounds1200\)
Car Value = \(12,000 - 1,200 = \pounds10,800\)
Year 2 depreciation: \(15\% of \pounds10800 = \pounds1620\)
Car Value = \(10,800 - 1,620 = \pounds9,180\)
So after 2 years, the car is worth \(\pounds9180\).
Percentage appreciation/depreciation
It is also possible to calculate how much an item has appreciated or depreciated simply by finding the difference in value as a percentage of the original value.
Example
A computer worth \(\pounds1500\) has depreciated in value to \(\pounds900\) in the past three years.
What is the percentage depreciation in the value of the computer?
Depreciation = \(1500 - 900 = \pounds600\)
Percentage depreciation = \(\frac{600}{1500}\times 100\)
\(= 40\%\)