# depreciation charge

## Derivation of Formula for Sum of Years Digit Method (SYD)

The depreciation charge and the total depreciation at any time m using the sum-of-the-years-digit method is given by the following formulas:

**Depreciation Charge:**

$d_m = (FC - SV) \dfrac{n - m + 1}{SYD}$

**Total depreciation at any time m**

$D_m = (FC - SV) \dfrac{m(2n - m + 1)}{2 \times SYD}$

Where:

FC = first cost

SV = salvage value

n = economic life (in years)

m = any time before n (in years)

SYD = sum of years digit = 1 + 2 + ... + n = n(1 + n)/2