The formulas to calculate depreciation using the Declining Balance Method (Matheson Formula) are:

1. Depreciation Rate (\(K\)):

\[ K = 1 - \left(\frac{Cn}{Co}\right)^{\frac{1}{n}} \]

2. Annual Depreciation (\(d_m\)):

\[ d_m = K \cdot C_{m-1} \]

3. Book Value at the End of \(m\) Years (\(C_m\)):

\[ C_m = Co \cdot (1 - K)^m \]

4. Salvage Value (\(C_n\)):

\[ C_n = Co \cdot (1 - K)^n \]

Where:

• \(d\) is the annual depreciation.
• \(Co\) is the original cost.
• \(n\) is the useful life in years.
• \(Cn\) is the salvage value or the scrap value.
• \(m\) is the age of the property at any time less than \(n\).
• \(Cm\) is the book value at the end of \(m\) years.