Certainly! Let's delve into the concept of compound depreciation.
When we say that the rate of compound depreciation is 10% per annum, it means that the value of an asset decreases by 10% each year, and this decrease is applied to the current value of the asset at the beginning of each year. This reduction in value accumulates over time, meaning the depreciation in subsequent years is calculated on the already depreciated value from the previous year.
Let's break down the steps with an example:
1. Initial Value of the Asset:
Suppose the initial value of the asset is [tex]$1000.
2. First Year Depreciation:
In the first year, the asset depreciates by 10%. So, you calculate the value of the asset after one year by reducing 10% from the initial value.
\[
\text{Value after first year} = \text{Initial Value} \times (1 - \frac{\text{Depreciation Rate}}{100})
\]
\[
\text{Value after first year} = 1000 \times (1 - \frac{10}{100}) = 1000 \times 0.9 = 900
\]
3. Second Year Depreciation:
In the second year, the asset again depreciates by 10%, but this time it is 10% of the value of the asset at the beginning of the second year, which is $[/tex]900.
[tex]\[
\text{Value after second year} = \text{Value after first year} \times (1 - \frac{\text{Depreciation Rate}}{100})
\][/tex]
[tex]\[
\text{Value after second year} = 900 \times (1 - \frac{10}{100}) = 900 \times 0.9 = 810
\][/tex]
To summarize our results:
- Initial value of the asset: [tex]$1000
- Value of the asset after one year: $[/tex]900.00
- Value of the asset after two years: [tex]$810.00
Thus, with a compound depreciation rate of 10% per annum, the asset's value decreases to $[/tex]900 after the first year and further to $810 after the second year.
