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\%