A machine depreciated by \( 10 \% \) each in the First two Years and by \( 40 \% \) in the third year. Find out the average rate of depreciod

To find the average rate of depreciation over the three years, we first need to determine the total depreciation. Assuming the initial value of the machine is \( V \), after the first year, the value will be \( V \times (1 - 0.10) = 0.9V \). After the second year, it will depreciate another \( 10\% \), leading to \( 0.9V \times (1 - 0.10) = 0.81V \). In the third year, the machine depreciates by \( 40\% \) from its value at the end of the second year, giving a value of \( 0.81V \times (1 - 0.40) = 0.486V \). Now, total depreciation in terms of initial value \( V \) is \( V - 0.486V = 0.514V \). To find the average rate of depreciation, we can divide the total depreciation by the number of years, resulting in: \[ \text{Average Rate of Depreciation} = \frac{0.514V}{3V} \times 100 = 17.13\% \] So, the average rate of depreciation over the three years is approximately \( 17.13\% \). This depreciation may seem steep, but it’s a common concern in businesses that rely on machinery. Regular assessments and understanding the rate of depreciation help in planning for reinvestment or tax! If you're keen to learn more about depreciation, consider delving into topics like the different methods of depreciation such as straight-line and declining balance. It's fascinating how different approaches can impact financial statements! Plus, there are a ton of online resources and books that explore these concepts in depth, providing great practical examples along the way.