Appreciation and depreciation
Appreciation is when the value of an item increases and depreciation is when an item decreases in value. There are many examples of appreciation and depreciation in real life. For example, a brand new car is worth less money as soon as it’s taken off the forecourt of the garage selling it. The car depreciates in value.
The rate at which an item appreciates or depreciates is usually given as a percentage. This is given as an annual rate which means it will be applied at the end of each year.
Example
£200 is invested by a company into another company and the money appreciates at 4% each year.
1. How much is in the account after three years?
2. How much has it appreciated by?
Solution
1. The amount in the account is £224.9728. However, when we are dealing with money we round to two decimal places. So our answer is £224.97.
2. We subtract the initial amount from the final amount to calculate the amount it has appreciated by:
£224.97 – £200 = £24.97
Appreciation and depreciation using the formula - Higher
Appreciation
There is another way of calculating the above using a formula.
The formula is \({V}~=~{l}(1~+~i){^n}\) where:
- V is the final value of the money
- l is the initial value of the money
- i is the interest as a decimal
- n is the number of years
1. \({V}~=~{l}(1~+~i){^n}\)
\({V}~=~{200}(1~+~0.04){^3}~=~£224.97\) to two decimal places.
You can then work out part 2 as above.
Depreciation
When we are calculating depreciation you subtract from the initial amount instead of add each year.
The formula changes slightly for depreciation but you subtract inside the bracket instead of add.
\({V}~=~{l}(1~-~i){^n}\)
Question
A company has £15,000 worth of assets but this is set to devalue by 8% annually for two years. By how much have the assets depreciated?
